Composite materials are crucial for advancing sustainable engineering practices as they offer high strength-to-weight ratios, making them ideal for applications in aerospace, automotive and civil engineering. Meeting global sustainability goals demands a shift towards efficient materials, resulting in composites becoming increasingly significant. Besides difficulties in producing highly complex composites there are also challenges in computational methods to accurately predict the behavior of structures made from composite materials within a reasonable computational time frame. In most civil engineering practices, the Finite Element Analysis (FEA) is a useful method to derive stress-strain paths. However, these methods often rely on homogenized material assumptions which fail to capture complex microstructural stresses in high-performance composites. A more suitable method to predict the behavior of these materials under complex loading conditions is available using multi-scale modeling techniques. This approach is essential but computationally expensive, especially when high accuracy at the microscale is needed. Surrogate models based on a machine learning framework have been investigated in prior research. These models typically make predictions on homogenized average stress at macroscale rather than the maximum stress at microscale, which identifies as the research gap. The maximum microscopic stress has been recently used as a failure indicator. The main objective of this research is to design a surrogate model, based on the physically recurrent neural network (PRNN) designed in previous research, that can accurately predict the local maximum stress at the microscale in heterogeneous composite materials. Additionally, this research explores how knowledge from existing models that predict average stresses can be leveraged to enhance new models that predict local quantities at the microscale through transfer learning and multi-task learning techniques. Among the three developed models, two models using an encoder-decoder architecture performed poorly because the decoder averages the results instead of being able to find the limits. The decoder was removed in the third model and this yielded promising results. This model maintains high fidelity in stress predictions with lower computational costs because the number of trainable parameters in this model is limited. Transfer learning yielded faster convergence but did overall not improve significantly in terms of error. The decrease in computational time is very limited when transfer learning is applied over direct training as the models used in this thesis are small and do not need extensive datasets or epochs to converge. The multi-task approach achieved very promising results as it enables accurate predictions for average and maximum stresses in a single model. Cross validation showed strong model robustness and flexibility across unseen loading scenarios. Finally, a triple-task model showed that the PRNN is able to act as a modular framework as also the minimum microscopic stress can be accurately predicted without increasing the model and or training set size. The developed surrogate model shows that the architecture of the PRNN developed in previous research can be effectively modified to make predictions on other tasks. It provides a viable tool for simulating composite materials behavior at microscale.

With the progressively more widespread exploitation of post-buckled skin-stiffened structures in the aerospace industry, aimed at making them more weight efficient, assessing the failure of such structures is of utmost importance. Additionally with the trend of moving towards fastener free connections, one of the potential failure modes of skin-stiffened structures is the skin-stiffener separation that leads to a sudden and drastic reduction in the load carrying capacity of the structure. Hence, it is imperative that structures are designed against such failure modes, being crucial to have predictive models for the initiation and propagation of delaminations at the connection interface.

Given this motivation, the present thesis investigates the development of a novel multi-domain semi-analytical cohesive zone approach to predict the initiation and propagation of damage along a two-dimensional interface. In the multi-domain method the main structure being analyzed is decomposed into multiple smaller domains for computational advantage, with each domain having its own set of continuous approximation functions based on the Ritz method. A penalty formulation governs the inter-connection of domains. To extend the multi-domain framework to model damage, the interface connection is modelled as a cohesive zone with the traction-separation law governing its response. The area connection from the multi-domain method is modified to include a damage-dependent penalty stiffness term, whose degradation is controlled by the traction-separation law of the cohesive zone model. Lastly, the energy dissipated to create a crack is included in the formulation. Since the framework is based on the Ritz approach, the appropriate choice of continuous approximations to model damage is investigated, presenting their limitations and the proposed methods to overcome them.

Finally, the results obtained from the multi-domain framework were verified against finite elements for a multitude of cases, which in turn had been validated by experimental data. The results were subsequently followed by discussions and the caveats of the developed framework. Results indicate that the developed multi-domain semi-analytical cohesive zone method predicts the results within 4.3% of finite element results, while taking 75% less time on average.

Finally, having somewhat successfully modelled the initiation and propagation of damage along a two-dimensional interface, this thesis establishes a robust basis for future research involving the use mixed-mode behaviours with multi-linear cohesive laws, whose formulations can just be slotted into the current framework. All of this forms a solid foundation to efficiently model damage initiation in larger structures and, more concretely, skin-stiffener separation.

Membrane structures are material efficient structures made with a lightweight flexible membrane. Usually the membrane is made out of a woven textile. Because of the size restrictions of the woven patches of fabric, the membrane will contain multiple seams. This will not be the case when the membrane is a knitted fabric. Membrane structures are suitable for making lightweight formworks for concrete structures with complex geometries. Knitted fabrics can be made using a CNC knitting machine which uses weft-knitting. This machine uses two needle beds with needles which can catch the yarn and perform different knitting operations like a plain stitch, a float stitch, a tuck stitch, a transfer stitch and an interlock stitch. Different configurations of these knitting operations create different knitting patterns. The mechanical properties of the knitted textiles that are considered during this research are the Poisson’s ratio and Young’s modulus. Since knitted fabrics show orthotropic behaviour, the fabrics have to be tested in both directions (wale and course direction). The properties can be determined when fabrics are tested in a uniaxial tensile test, a wide jaw test or a biaxial tensile test. Digital image correlation can be used to measure the strain of the fabric in lateral direction. This research addresses the effect of different knitting patterns on the Poisson’s ratio and Young’s modulus of weft-knitted fabrics. To achieve this objective, homogeneous fabrics of multiple knitting patterns have been tested. The knitting patterns that are considered in this thesis are interlock, eightlock, hexagon, tuck, interlock_1float and interlock_2float. Afterwards, non-homogeneous textiles have been fabricated in which two knitting patterns have been combined. This is done with interlock as a primary pattern and tuck or eightlock as a secondary knitting pattern. The secondary knitting pattern is applied as a circle in the centre of the fabric. The results of the tensile tests show large differences in mechanical properties for the fabrics with different knitting patterns. In wale direction the Poisson’s ratios for the interlock, tuck, interlock_1float and interlock_2float pattern are between 0.5 and 0.65, while the ratios for the eightlock and hexagon patterns are larger; between 0.8 and 0.9. In course direction, the ratios are smaller than in wale direction. For the interlock, tuck and interlock_1float show a Poisson ratio between 0.45 and 0.5 while the ratio for the eightlock pattern is around 0.6. In wale direction, the Young’s modulus for the interlock, tuck and interlock_1float are between 0 and 2.5 MPa, while the Young’s modulus for the eightlock and interlock_2float pattern are between 8 and 12 MPa. The hexagon pattern is even more stiff, with a Young’s modulus around 30 MPa. In course direction, the Young’s moduli are way lower (between 0 and 0.5 MPa for all fabrics). In this direction, the stress-strain curves of the fabrics do not reach the elastic region because of rotation of the clamps in the test setup. For the non-homogeneous interlock_tuck fabrics, the Poisson’s ratio in wale direction is larger than the homogeneous interlock and tuck fabrics. This is caused by the interaction between the different knitting patterns. This effect is not visible in course direction. For the non-homogeneous interlock_eightlock fabrics, this is the other way around. The interaction between the knitting patterns plays a role in course direction, but is not visible to the same extent in wale direction. The Young’s modulus of the secondary knitting pattern is larger for both the interlock_tuck and interlock_eightlock fabrics. Therefore the Young’s modulus increases when the diameter of the circle containing the secondary knitting pattern increases.

Many steel bridges in the Netherlands, built in the 1950s and 1960s, are nearing the end of their service life, with steel bridge decks suffering from fatigue damage due to high traffic loads. Replacing these decks with Glass Fibre Reinforced Polymer (GFRP) Web-Core Sandwich Panel (WCSP) decks is a potential solution due to their superior strength-to-weight ratio and better in-plane fatigue performance.

A critical aspect of using these bridge decks safely is verifying the fatigue life of the Web-to-Flange Junctions (WFJs), which connect the webs to the facing. Fatigue damage is known to occur in such components with changing cross-sections, leading to stress concentrations. Current design codes lack verification equations or S-N curves for this component, necessitating further research.

This research investigates the static an fatigue performance of the WFJ by performing tests and identifying key parameters influencing this response. Through testing, the static bending moment resistance and the dominant failure mode are determined. Using the safe life approach, an S-N curve is generated by measuring the number of cycles until crack initiation occurred during cyclic loading.

Static tests revealed a constant rotational stiffness followed by a significant reduction due to delamination. Fatigue tests showed progressive stiffness degradation and crack propagation, with some crack retardation indicating a stabilisation phase before ultimate failure. Finite Element Modelling (FEM) accurately predicted initial stiffness but overestimated post-crack rotational stiffness, suggesting the need to incorporate additional parameters like material stiffness degradation or cohesive zone modelling.

This research identified important parameters such as waviness, web thickness, and radius affecting the response of the WFJ. However, testing did not confirm the predicted linear relationships between web thickness, radius and moment resistance as suggested by equations given by Lekhnitskii. Additionally, no direct correlation was found between waviness and moment resistance. It was observed that specimens with greater web thickness often also had higher waviness, and it is hypothesised that these parameters influence each other which would explain the non-linear relationship found from testing. Future research is needed to verify this hypothesis and include methods for quantifying the 'waviness' parameter.

This research enhances the understanding of the static and fatigue behaviour of WFJs in GFRP Web-Core Sandwich Panel bridge decks. The findings reveal that the dominant failure mode of the WFJ subjected to bending is delamination, due to out-of-plane stresses, as predicted by equations given by Lekhnitskii. Therefore, it is suggested that future design codes for FRPs incorporate these equations and delamination S-N curves to verify the fatigue safety of this component. Additionally, the WFJs were observed to be damage-tolerant, suggesting the potential for alternative design concepts to the fatigue life approach. Static tests revealed that although increased web thickness enhances the strength of the WFJs, it is also correlated with increased waviness, which is found from previous research to reduce strength. Future research could explore acceptable levels of crack growth and rotational stiffness degradation for safe bridge design, contributing to the development of design guidelines for GFRP WCSP, making it more viable to use these bridge decks in bridge renovations.

The aim of this project is to benchmark the outcomes of a detailed performance based analysis using CFD and LS-DYNA software against codified methods used more generally on projects, and in particular to demonstrate whether this leads to an increase in the predicted capacity of the bridge under fire loading. The effect and influence of different parameters on the fire resistivity have been investigated. These are the location of the fire, the influence of different live loads, the influence of imperfections, the effect of wind fire interplay, and the effect of internal radiation between surfaces within a structural section. This research shows that doing a detailed thermal structural analysis of fire on a steel bridge can indeed lead to material savings. Performance based analyses show that the bridge does not fail for the considered fire scenarios for at least 30 minutes. When applying temperatures based on Eurocode, failure is reached after 15 minutes. Using a detailed FEM model to determine critical temperature results in four times less protection necessary than when the conservative Eurocode limit of 350 °C limit is used, a critical temperature of approximately 600 °C is found for the case study.

Shell structures are widely favored due to their ability to bear substantial loads with minimal thickness, aligning with contemporary aesthetic sensibilities. This thesis investigates the buckling behavior of thin-shell structures with the aim to refine a knockdown factor formula. Authored by Yuanxi Zhao under the guidance of Dr.ir. P.C.J. Hoogenboom, Ir. A.C.B. Schuurman, and Dr.ir. F.P. van der Meer, this research addresses the critical issue of load-carrying capacity reduction due to shape imperfections leading to buckling.

A complete range of shell shapes and loading has been studied. The shells buckle in ring mode (1-3, 3-3, 2-1, 2-3), column mode (2-2), mixed column-ring mode (1-1) and in-extensional mode (3-2, 3-1, 1-2) (page 19).

Linear buckling analyses were conducted to explore how parameters such as height, boundary conditions and model size influence the buckling load factor. Geometrical nonlinear analyses were conducted using SCIA Engineer, introducing different imperfection amplitudes to simulate real-world conditions. The knockdown factor was calculated as nonlinear buckling load over linear buckling load. This knockdown factor was compared to a knockdown factor obtained from a formula.

The knockdown factor does not depend on the curvature ratio kyy/kxx or the membrane force ratio nxx/nyy. It only depends on the imperfection amplitude and d/t (page 65) and the slenderness a/t (page 6). The knockdown factor formula produces reasonable values. However, the formula is not accurate (page 62). It is recommended to derive a new knockdown factor formula.

Orthotropic steel decks (OSDs) offer structural advantages but are highly sensitive to fatigue cracking, mainly initiated from trough-to-deck plate welds at the intersection between the trough and crossbeam. To mitigate existing fatigue cracks, a high strength concrete (HSC) overlay repair method was developed, which addresses two types of fatigue cracks but does not completely prevent root-weld crack propagation. To avoid damaging the HSC overlay by applying heating in traditional repair methods, the ‘Cold Repair’ method was developed, using a steel angle adhered to the trough-to-deck plate exterior. Recent studies suggest increased effectiveness with a carbon fiber-reinforced polymer (CFRP) angle, created by vacuum infusing carbon fiber fabrics with epoxy reason onto the OSD. However, limited knowledge exists on he use of fiber-reinforced polymer (FRP) to strengthen OSDs and control root crack growth in these weld details. This presents challenges in understanding its behaviour, material properties and design.

This study investigates CFRP-steel adhesive joints through experimental and numerical analyses. Thick-adherend shear tests (TASTs) were conducted to study the adhesive bond’s shear strength, and the failure mechanisms of these adhesive joints subjected to shear loading. Component-level three-point bending tests evaluated bond behaviour under bending loads and the structural performance of OSD strip components strengthened with a CFRP angle. Finite element (FE) models were developed to simulate the adhesive FRP-steel joint, employing both linear tied and non-linear tie-break interface conditions. Experimental and numerical results were compared to assess the FE models’ accuracy.

A comparative analysis was also performed between a full-bridge model, provided by supervising company Arup, and the component-level model developed in this thesis. Significant differences in boundary conditions, loading conditions, element formulation, and the scaling of global dimensions (apart from thicknesses) complicated precise comparisons. The component-level model used tie-break interface conditions to model adhesive interface failure, whereas the full-bridge model employed tied interface conditions, which limited its ability to predict failure.

TASTs results identified debonding between steel and primer -applied to enhance the adherend-adhesive bond- as the primary failure mode. In four samples, this debonding occurred alongside delamination of the first glass-fiber layer. The design value of the average shear bond strength was determined to be 5.42 kN. Component-level three-point bending tests consistently showed crack initiation at the outer edge of the horizontal adhesive bond at a load level of around 82 kN. Crack initiation was followed by linear behaviour up to the onset of yielding of the deck plate, after which full debonding of the horizontal leg of the Cold Repair occurred at an average load of 110 kN.

Numerical studies revealed that linear numerical modelling provides a sufficient approach to model the Cold Repair method up to the point of failure. Developed non-linear numerical models do not contribute to additional reliability of the Cold Repair method, as they were unable to accurately match observed failure behaviour and because adhesive bond failure occurs suddenly. Nonetheless, the additional capacity observed in component strips suggests that non-linear numerical modelling could extend the capacity of the Cold Repair method if its design allows for damage. To improve the accuracy of adhesive bond failure modelling, further experiments, including fracture mechanics tests, are recommended to determine essential adhesive properties, such as fracture toughness.

A novel surrogate model to approximate microscopic behaviour and accelerate concurrent multiscale finite element simulations is proposed. The study serves as a proof of concept, focusing exclusively on 2D, geometric non-linear lattice materials. Despite numerous successful implementations of surrogate modelling techniques in literature, challenges remain, mainly with the black-box nature of most of these models, suffering from lack of interpretability. To tackle these issues, this study reintroduces physics into the model through the use of beam theory in so-called Beam Neural Networks. These networks are tested against a benchmark feed-forward neural network in both interpolation and extrapolation. Although the findings do not satisfy the requirements for practical application, they do indicate that the introduction of beam theory to the model has improved the model's extrapolation ability, suggesting that the proposal has improved robustness and interpretability of the model. Given further optimization, there is promise of Beam Neural Networks to become an useful tool to accelerate concurrent multiscale modelling in the future.

As the structural engineering sector explores innovative materials such as Fibre Reinforced Polymer Composites (FRP), understanding their behavior under static and fatigue is critical. This thesis focuses on developing a numerical method to model the fatigue behavior of FRP composites, reducing the need for extensive experimental testing, resulting in a reduction of costs. Static and dynamic load tests were performed on Glass Fibre Reinforced Polymer (GFRP) coupons extracted from a vacuum-infused sandwich panel deck.

Based on these experimental test results, a numerical model was developed in Abaqus, integrating a VUSDFLD user subroutine to simulate stiffness degradation using a Continuum Damage Mechanics model. The model, which accounts for stress dependent stiffness degradation, was applied to coupons containing imperfections such as dimples from the manufacturing process, and without imperfections.

The research demonstrates promising results for higher load fatigue life predictions, with estimates within 10% of experimental results for both coupons with and without imperfections. However, at lower load levels, the model underestimates fatigue life by 85% for normal coupons and 30% for imperfection ones. These deviations highlight the need for further research, particularly at lower stress levels.

Despite the deviations at lower stress levels, this study presents an advancement in numerically predicting the fatigue life of FRP composites based on stiffness degradation, offering a cost-effective alternative to extensive experimental testing. The numerical model successfully integrates material degradation and manufacturing imperfections, providing valuable insights for the design and evaluation of composite structures subjected to fatigue loads. These findings also highlight the important role that imperfections play in fatigue performance. Future research should focus on optimizing the model, particularly at lower load levels, to enhance accuracy and increase its applicability. In conclusion, this study opens the door to more reliable, efficient, and improved use of FRP in structural applications, particularly in areas where fatigue behavior plays an important role.

Orthotropic steel decks (OSDs) are commonly used in bridge construction due to their material efficiency and strength. However, fatigue issues in welded joints remain a concern. Fatigue cracks often occur due to high stress concentrations, especially under heavy traffic loads. Current approaches of determining damage in a bridge are limited by the computational demands of Finite Element (FE) models to calculate stresses and the complexity of the fatigue verification. Consequently, there has been limited exploration of parametric optimization for OSDs. This research seeks to address this gap by developing a parametric model to assess the fatigue performance of OSDs according to the ROK version 2.0, the new Dutch Guideline, additionally focusing on identifying the influence of key design parameters through a parameter sensitivity analysis (PSA). This study aims to provide insights for optimizing OSDs to enhance fatigue resistance and design. Thereby aiming to increase material efficiency about OSDs and creating a parametric framework to determine damage in an OSD.

This resulted in the following research question: How can a parametric model be developed to assess the fatigue performance of Orthotropic Steel Deck bridges and what insights can be gained from analyzing the influence of key design parameters?

To answer this question, in part 1 a literature study is performed. This began by reviewing the theory of the OSD’s and fatigue, identifying the critical fatigue parameters which were expected to influence the incorporated directly ridden details. Furthermore, the Dutch regulations and state-of-the-art about automatizing of fatigue verifications were explored, after which a parametric model is developed.

Part 2 began by developing this model. Simplifications in the mesh and loading scheme are tested and applied to ensure the model is fast and sufficiently accurate. Utilizing various mesh sizes in different regions helps to reduce computation time by almost 300% while maintaining accuracy. Additionally incorporating symmetry in the loading scheme further reduces the computational time by about 127%. With this model, the first part of the main research question is answered. The model is used to find the governing details in the bridge within the design domain of the ROK [2]. The governing details are: the crack initiating at the weld toe located at the intersection of the trough and the deckplate, and the crack initiating at the weld root located at the intersection between the deckplate, trough and crossbeam. Which are respectively detail 1A and 1C of the ROK[2]. After this, a benchmark model is found to start the PSA and a sensitivity analysis is conducted for these previously mentioned details by systematically altering one parameter at a time (OAT).

Results of the PSA are distinguished for the two aforementioned details. For detail 1C, the deckplate thickness and trough top width influence the damage of the detail primarily, represented by respectively an exponential function and second order polynomial. The crossbeam thickness influences the damage by maximally 30% of the damage number of the benchmark, while this parameter is not included in the analytical solution. Other included parameters show small or negligible influence on the damage of detail 1C. The governing load position within the design domain is the transversal load distribution exactly above the middle of a trough. Furthermore, a difference in stiffness exists between two trough legs of the same
trough for detail 1C, significantly influencing the damage. The governing transversal location of detail 1C is at the trough leg closest to the main girder.

For detail 1A, by far the most influential parameter on the damage of this detail is the deckplate thickness, having a exponential influence. The trough center-to-center distance has the second greatest influence on the damage, this can be represented by a second order polynomial. The top trough width and crossbeam center-to-center account for a maximum influence of the damage number of 20% of the benchmark damage number. The influence of the other included parameters were small or negligible. The governing transversal location of detail 1A is, similarly to 1C, at the trough leg closest to the main girder.

The validation of the model shows a great difference in the difference in damage numbers obtained from version 2.0 of the ROK in comparison with version 1.4. Validation of the Goereese bridges therefore show damage numbers greater than 1 for the 2 aforementioned details. It is suggested to show extra attention to bridges designed with ROK version 1.4, or earlier versions, and to repair occurring cracks in a way that the local damage complies with the verification of ROK version 2.0. The parametric tool can play a useful part in this when expanded. Another future use case can be to support the goal of the Rijkswaterstaat of replacing the current labor-intensive fatigue calculation method with a table that outlines the dimensions of OSDs, by generating a large amount of data.

Welding is a widely used process in various industries for joining materials, but it can introduce several complexities that affect the mechanical properties of the welded components. In particular, the presence of pores within the welded material can have significant implications for fatigue resistance, residual stresses, and overall structural integrity. The primary objective of this thesis is to develop and analyze thermal and mechanical models to understand how various parameters, including geometry, mesh, material properties, boundary conditions, and heat input, influence the behavior of a welded thick plate containing pores. The simulations are conducted with different pore configurations and multiple welding passes to comprehensively explore their impact. Two Finite Element (FE) models were designed. In the first model (Model 1), the objective was to replicate the experimental setup detailed by Qiang et al. in their work "Through-thickness welding residual stress and its effect on stress intensity factors for semi-elliptical surface cracks in a buttwelded steel plate" [41]. This endeavor was accomplished utilizing Abaqus as software. A Dflux subroutine, written in Fortran, was incorporated to effectively emulate the welding procedure. The model was constructed to account for multiple welding passes (up to 7). By extrapolating transverse and longitudinal stresses, a comparative analysis was conducted across five distinct models and the experimental data [41]. The intention was to elucidate variations and similarities in the results. Subsequently, the second model (Model 2) was conceived to exploit the more favorable boundary conditions present in Zhang’s model as described in "Effect of Welding Sequence and Constraint on the Residual Stress and Deformation of Thick Welded Butt Joint Made of Q345qD Steel" [58], when contrasted with the initial experiment. Following a similar procedure, the FE model was developed, with the added feature of an increased number of welding passes (up to 12). Distortions along three distinct paths and transverse and longitudinal residual stresses within two specific regions were extrapolated and subsequently compared. The investigation then progressed to the introduction of pores into Model 2, in the simulation characterized by the lowest number of passes. The aim was to assess the impact of these pores on temperatures, distortions, and residual stresses. By comparing the outcomes of the models both with and without defects, valuable insights were gained into the effect of pores during welding processes. The main findings of this research can be summarized as follows: • Thermal data extracted from a welding experiment conducted at four distinct positions within a 250mm x 200mm x 32mm plate, as documented in Zhang et al.’s publication [58], exhibited inconsistencies when compared to the results obtained through Abaqus simulations in this thesis. These disparities predominantly stem from the absence of accurately specified thermocouple placements in the reference paper [58]. Despite conscientious endeavors to pinpoint the precise thermocouple coordinates, discernible variations of 100°C and a maximum divergence of 25% between the outcomes of the simulations and the reference findings were identified. • Residual stresses obtained in Abaqus (Model 1) trying to replicate Qiang et al. paper [41] in a 700mm x 400mm x30 mm showed good agreement with the reference simulation but deviated from the experimental data. The obtained numerical values peaked around 150 MPa, while the experimental values reached more than double that magnitude (305 MPa), for specific simulations. The number of welding passes significantly influenced the compression at the sides of the plate, with an increasing trend as the number of passes increased. • The simulations (Model 2) created to replicate Zhang et al. experiments [58] demonstrated better agreement with the experimental data for both longitudinal and transverse residual stresses. The number of passes played a crucial role in the results, with the eight to twelve passes simulation showing the closest match to the experimental data. • The presence of the studied configuration of pores in the material did not affect significantly the shrinkage, distortions, and residual stresses in the simulations. Closer to the pores, higher values for residual stresses were found. Based on the findings of this thesis, several recommendations for future research can be made. Laboratory experiments should be conducted to validate the numerical results obtained in this study. Sensitivity analysis considering modifications in the dimensions, boundary conditions, and pores locations of the model can provide further insights. Additionally, incorporating thermally independent properties can reduce the computational time of the simulations. Overall, this thesis contributes to understanding the impact of pores on the thermal and mechanical behavior of thin and thick plates and provides a foundation for future research in this area.

This thesis presents a novel methodology to determine the reliability of cantilever grandstands under dynamic crowd loading. No method currently exists to evaluate this, despite the occurrence of significant vibrations in such structures, for example in the Feyenoord Stadium in Rotterdam. These vibrations can negatively affect both the safety and serviceability of such structures, so a method able to evaluate both is desirable. The methodology consists of four components: a model of a grandstand, a model of the dynamic crowd load, a failure criterion, and a reliability analysis. Of these, the first and third component are case-specific, as a wide range of different grandstands and different criteria could be considered. In this thesis, the methodology is applied on a case study based on the Feyenoord Stadium, with a model of the trusses beneath the main grandstand of this stadium, and a criterion based on the intensity of the vibrations of the upper cantilever of this grandstand, a serviceability issue. The second component represents the most novel aspect of the methodology: a model describing the dynamic crowd load, defined in the frequency domain, and generally applicable regardless of the structure being considered. The core of this model is a parameterisation of the amplitude spectrum of the load applied by a group of jumping spectators. The parameters describing the spectrum are considered as stochastic variables, with distributions fitted using samples from a state-of-the-art database of measured loads. As opposed to the first and third components, this load model should be generally applicable.The parameters of the load model, together with other stochastic variables in the grandstand model, form the input of a Limit State Function. The output of this function determines whether the structure loaded by the crowd meets a certain criterion, and forms the basis of a reliability analysis together with the distribution of the stochastic variables. The probability of \emph{not} meeting the criterion, the failure probability, is calculated through a number of reliability methods in the final component of the methodology. These methods should be generally applicable as well, though which methods fits the best could still depend on the case being considered. This methodology was successfully applied on the case study, and a failure probability was found with two different methods. One of these, Crude Monte Carlo, allowed for a more fluid view of the concept of `failure' when a serviceability criterion based on a subjective limit is considered. The other method, SDARS, returned a slightly larger failure probability, in a much shorter runtime than Monte Carlo. This method is therefore more fit for safety criteria with a small (expected) failure probability, for which Monte Carlo would require an unreasonably long runtime. In addition, the wider applicability of the methodology has been investigated. An important requirement for this is flexibility with regards to the applied reliability methods. Two other methods, Directional Sampling and SDARS, were also attempted but did not yield usable results. This is caused by the manner in which phase angles are defined in the frequency-domain model. Random values are drawn, which causes noise to appear in the limit state function: a constant input does not lead to a constant output. Being able to use different reliability methods is an important requirement for applying the methodology in a wider variety of cases. In order to apply these methods, the phase angles need to be defined in a manner which does not introduce noise. Another important requirement is the ability to consider different failure criteria. While the criterion applied in the case study could be evaluated in the frequency domain, many others will require the results to be transformed to the time domain. Applying this transformation to the frequency-domain results of the models currently does not yield usable results, which is likely also caused by the definition of the phase angles in the load. In conclusion, while the methodology is applicable on the case study, the definition of the phase angles requires attention before it can be applied on other cases.

In the past years, the safety of steel railway bridges has been questioned due to the coped beam connection sensitivity to fatigue and fatigue crack appearance. To ensure the safety of these railway bridges, the propagation of the fatigue crack needs to be analysed by performing regular inspection on the bridges. The frequency of these is required by the defined inspection intervals, which are based on the critical crack length and the number of loading cycles leading to this crack length. Laboratory tests and measurements on the bridges have been performed in the past to define inspection intervals, but had given only an approximation of the real situation. By creating a finite element model of a coped beam, a crack initiation and propagation analysis can be performed. This analysis provides an indication after how many loading cycles the crack will reach a critical length and guides towards revised inspection intervals.

In this thesis, the objective is to take the first steps towards the revised inspection interval by performing a finite element analysis of the crack propagation of steel railway bridges. More specifically, this means an finite element analysis of the coped beam with extended finite element method.

To achieve this goal, first, the location of the fatigue crack initiation has been investigated to understand where exactly in the cope the crack starts. This was performed by creating a local 3D linear elastic FE-model of the coped beam based on the boundary conditions, geometry, and loading from laboratory tests performed by Michael C.H. Yam and J.J. Roger Cheng. The the longitudinal stresses of the model were compared with stresses measured during the laboratory test to validate the crack initiation model. After the model was validated, the location of crack initiation was determined by identifying the location of the peak stresses.

After completion of the crack initiation analysis, the crack propagation analysis can commence. For this, the FE-model was transformed from the crack initiation to the crack propagation model. In the same manner as with the crack initiation model, the propagation model has been based on the boundary conditions, geometry, and loading from the laboratory test. Since no path of the crack was registered during these laboratory tests, and thus could not be implemented in the model, a method for crack propagation analysis called extended finite element method (XFEM) has been used. The accuracy of this method has been confirmed by validating the stress intensity factor (SIF) values obtained for stationary cracks with three different mesh topologies and comparing the results with results from two established methods; J-integral and VCCT.

After the validation of the crack propagation model, a sensitivity study was performed to understand the potential influence of modelling decisions on the number of load cycles versus crack length relation. With the mesh sensitivity analysis, a linear trend has been obtained for models with matching number of elements through the thickness. For the initial crack size sensitivity analysis, the effect of the number of elements through the thickness and the effect of mesh topology have been investigated. One element through the thickness and parallel mesh topology led to lower variation in the results.

Additionally, a new value for the previously assumed Paris law coefficient C has been obtained by calibrating the number of cycles versus the crack length curve from FE-model to match the laboratory test results.

In conclusion, this research provides recommendations for modelling crack propagation in a coped beam. The results are more reliable when keeping at least five finely meshed elements around the crack tip, using a parallel mesh topology, and using one element through the thickness. New value for the C coefficient from the Paris law has been suggested based on this research.

The next step in this research is a continuation of the crack propagation model analysis to reduce the variation in the results. Furthermore, different loading positions and expansion from a simply supported beam model to a model with multiple spans should be analysed to bring us one step closer to the ultimate goal of redefining the inspection interval for coped beam steel bridges based on the models.

Structural elements under compression can fail due to instability. Such type of failure may present itself as flexural buckling, which is the sudden change of configuration of one state to another at a critical compressive load. Actual structure characteristics, such as cracks, real joints, sudden changes of flexural stiffness, bracing, and actual boundary conditions, make current analytical buckling methods inefficient. For this reason, most structures are evaluated using Finite Element (FE) software based on the Finite Element Method (FEM). However, such a numerical method may have a high computational cost when parametric studies need to be performed. The motivation for this thesis was to develop an analytical alternative for the buckling analysis of columns and beam-columns.
The thesis analyses jointed Euler-Bernoulli columns and beam-columns with N discontinuities due to step-changes of flexural stiffness, and influence of open edge cracks, real joints, bracing, and actual support conditions. The approach considered utilizes the Heaviside function to obtain a single piecewise expression for the deflection, slope, moment, and shear of columns and beam-columns. The use of the Heaviside function, along with proposed closed-form expressions, reduce the number of unknown integration constants to only four.
Main findings are listed as following: (i) Linear buckling analysis of a column only depends on solving the determinant of the 4x4 matrix of unknown coefficients, obtained by imposing four boundary conditions. (ii) Solving the four unknown constants of integration results in performing a geometrical non-linear static analysis of the beam-column, which perfectly agrees with results obtained through FE software. (iii) Closed-form expressions reduce the number of unknown constants of integrations to only four, regardless of the number of sections composing a column or beam-column.
Concluding remarks and recommendations include: (i) Closed-form expressions accurately provide linear buckling loads for columns and geometrical non-linear expressions for beam-columns. (ii) Equations solved algebraically can be stored and used for future analysis, saving the computation time of rerunning the analysis for specific columns or beam-columns. Having the equations expressed algebraically allows for the ease of performing parametric analysis and exploring the performance of new designs. (iii) Computational cost (time needed for the computer to obtain the results) may depend on the mathematical software used for the calculations. Other software may result in having lower computational time for the same calculations.

Fiber Reinforced Polymer (FRP) has increased rapidly in popularity in the past few decades. The material's advantageous properties, such as a high strength-to-weight ratio and low required maintenance, gave rise to its popularity in multiple major engineering branches. Buckling behaviour develops due to the notably low stiffness-to-strength ratio and the usual high slenderness of FRP plates. The occurrence of initial imperfections increases the tendency of the material to buckle. The load-carrying capacity of structures with post-buckling behaviour can be determined with progressive failure analysis, which requires a damage model that characterises the onset and evolution of damage. In Abaqus, the Hashin damage model is implemented by default, which considers the four failure modes of the material. Numerical analysis of strain-softening materials with local damage leads to deformation localisation in a single element: a finer mesh will decrease the amount of energy dissipated. To prevent this localisation into arbitrarily small regions, the stress is related to the deformation of a finite volume. The damage evolution is described with a stress-displacement response instead of a stress-strain response. The energy needed to open a unit area of the crack, the fracture energy, is defined as a material parameter and depends on the mesh size of the model. The assessment of fracture energy properties in composite materials is challenging due to specimen geometry and fibre lay-up, and accurate data of GFRP fracture energy is largely unknown. When no actual post-failure behaviour is acquired, the lower bound fracture energy can be determined from the material properties. Numerical analysis of uni-directional coupon experiments is performed to determine the input values and response of the lower bound fracture energy. The lower bound fracture energy implementation results in an abrupt drop in stress when the material strength is reached. Increasing the lower bound fracture energy by a minimum of 2% prevented numerical inconsistencies. Progressive failure analysis of multi-directional coupon experiments validated an increase of 10% for the lower bound values. The use of lower bound fracture energy for non-linear buckling analysis is verified with progressive failure analysis of the buckling experiments. The lower bound fracture energy, increased by 10%, approximates the ultimate strength of six tests with an average difference of 7.7%. To analyse the non-linear buckling behaviour of a GFRP plate, a buckling curve is created by varying the plate thickness. The influence of geometric imperfections on a plate's buckling strength is studied by applying different initial imperfections. Two types of boundary conditions are used to analyse if they result in a different buckling curve. A difference in the buckling strength reduction factor of 0.1 is found. Initial imperfections reduce the buckling strength of the material, which is most apparent for plate slenderness around 1.0. An initial imperfection of B/125 resulted in a 40% strength reduction compared to the elastic buckling strength. The average difference in reduction factor between an initial imperfection of B/1000 and B/125 was 16%, with a maximum difference of 26%.

The orthotropic steel deck (OSD) is nowadays commonly used due to its advantages, such as its lightweight, short construction time, and high capacity to bear the loads. However, fatigue cracks occur in different welded connections in the OSD. In this study, the rib to-deck-plate connection at the crossbeam conjunction has been analysed. This connection has been considered as a very critical connection due to the high-stress concentration under local wheel loading. In addition, the crack initiating at the weld root and propagating through the deck plate thickness cannot be visually inspected until surface cracks appear when the overlay is removed for the investigation. In the Netherlands, deck plate cracks at rib-to-deck plate connections at the crossbeam constitute a significant proportion of investigated cracks. In this thesis, a numerical investigation of the aforementioned cracks is carried out.
First, XFEM is applied to study fatigue crack propagation using compact tension (CT) specimens. Commercial FE software package Abaqus® is used to build 2D and 3D CT models. The corresponding fatigue crack propagation is calculated in the direct cyclic step with strain energy release rate calculated using the virtual crack closure technique (VCCT). A good match is found between analytical calculation and 2D XFEM modeling. For 3D fatigue crack propagation, the number of cycles calculated from the automated crack propagation approach, using the low cycle fatigue step provided by Abaqus®, shows high sensitivity to element sizes, specifically the used element sizes through the thickness of the CT.
Second, 3D crack propagation is applied to OSD with a 20 mm deck plate. For this detail, the fatigue crack initiation under compressive stress states is caused by the local loading on the deck plate. A hypothesis of changing the loading sign from compression to tension to subject the initial crack zone to tension is proposed so that this type of crack can propagate using automated XFEM. This assumption is made because high residual stresses normally exist in the welded connections and fatigue crack can propagate even under compressive stresses induced by loading. Before carrying out crack propagation calculation using VCCT, the stationary crack states were analysed using FEM and XFEM for cracks inserted with different angles. The SIFs obtained from FEM and XFEM are the same; in addition, that the SIF obtained when the detail is loaded in tension or compression has the same absolute value. Subsequently, the propagating crack analysis is carried out as a small initial crack with a depth of 0.5 mm is inserted and Paris’ law parameters C and m of 1∙ 10-13 and 3.0 were selected respectively. The obtained results of strain evolution as a function of loading history came close to that from the experiment with a difference of 7.75% for the initial strain value and 10.95 % for the maximum one. Moreover, the predicted crack shape, angle, and rate were all validated with similar crack shapes obtained from experiments in various literature. As for the crack propagation behaviour in the thickness direction, the crack arresting took place at around 75% of the deck thickness and an angle with the vertical axis of around 30o.
Finally, the deck thicknesses of 16 mm and 10 mm were considered. Their results converged in terms of the crack propagation behaviour with real test specimens from the literature. It is also found that the 16 mm and 20 mm cases had a common crack propagation behaviour in the thickness direction as the crack arrest occurred at around 75% of the deck thicknesses, while for the 10 mm deck case the crack developed more dangerously by penetrating through the deck plate leading to a through-thickness crack. The approach proposed by this thesis proved to be valid for predicting the crack behaviour for the considered OSD deck plate thicknesses. Thus, the structural integrity of the detail can be assessed. This proved that for the 16 mm and 20 mm deck plates, the structural integrity is acceptable, while the 10 mm deck safety is not confirmed.

The offshore wind industry is a quickly growing market because the increasing demand for clean energy sources. Large wind speeds and the abundance of potential wind farm locations make Offshore Wind Turbines an interesting solution. Because of high continuous dynamic loading and extreme environmental conditions, the structural design requires a detailed assessment, especially in the Fatigue Limit State. In this thesis, the focus lies on improving the modeling of monopile foundations for Offshore Wind Turbines, which could pave the way towards more efficient foundation design.

The conventional method of modeling the monopile foundation of an Offshore Wind Turbine is with a nonlinear elastic distributed spring stiffness along the monopile (using p-y curves). Damping related to the soil is considered through either global damping (like Rayleigh damping) or local viscous damping. However, the response of the soil around the monopile under wind and wave loading is better described through a nonlinear hysteretic (rate-independent) model, which is computationally demanding to model in the time domain. Next to that, a conventional frequency domain method can not be combined with any nonlinearity. Therefore, linear elastic models are used to model the soil response in frequency-domain simulations.

The goal of this thesis is to combine a nonlinear hysteretic soil model with a frequency-domain analysis. A response amplitude-dependent linearization of the nonlinear hysteretic element is made. The combination of the response amplitude-dependent element with an iterative solution strategy, the Equivalent Linear method, is shown to approximate a nonlinear time-integration under both harmonic and multiharmonic loading, as long as the nonlinearity is limited.

A nonlinear hysteretic model is fit to available soil reaction data and a response amplitude-dependent linearization is generated. A Finite Element model that can be combined with the Equivalent Linear method is set up and verified with a case study structural model of an Offshore Wind Turbine. The model is subjected to (high) Fatigue Limit State wave loading. The results are compared to both a conventional frequency-domain method (with a linear elastic small-strain soil model) and a nonlinear time-domain method (with a nonlinear elastic soil model). The deflections and deflection spectra in the foundation found through the Equivalent Linear method correspond to results from the nonlinear time-domain method, provided the influence of higher harmonics is limited and the response has a similar amplitude throughout the analyzed time window.

Results from the Equivalent Linear method show that the main frequency of the first resonance peak is around 2% smaller than the first natural frequency of the system, which is consistent with the results found through the nonlinear time-domain method. The identified soil damping in the first mode is 0.64-0.8% critical (4-5% log. dec.), which is similar to other literature. By combining observed system properties with literature about fatigue damage estimation, a hypothesis is stated: the fatigue damage in the foundation calculated through an Equivalent Linear method with a nonlinear hysteretic soil model will be lower than the fatigue damage calculated through a nonlinear time-domain method with a nonlinear elastic soil model.

There are multiple numerical methods for analysing the stability of slopes. Commonly used methods for assessing the slope stability are the slip surface method, strength reduction methods or methods based on load increments. What those methods have in common is that the stability of a slope is assessed by a factor of safety or critical stability number. These dimensionless factors give an indication of the global stability of a slope. A critical stability number is computed through load increments while a factor of safety is based on the strength parameters of the soil. A relatively new XFEM-based method for analysing slope stability is being implemented in the finite element software of Diana FEA. Unique with respect to the other methods is that this method detects onset of localisation and captures the propagation of the slip surface. Therefore, this method is referred to as the propagation method in this work. The propagation method consist of three main procedure steps. First, onset of localisation is detected during incremental loading of the model and the direction of the localisation plain is obtained. In step two, enrichment elements are implemented at the location of localisation, which are able to reproduce a jump in the displacement field. This is followed by a search algorithm for detection of localisation in adjacent elements. From here on, the implementation of the enrichment elements continues till a fully developed slip surface is present, resulting in global failure of the slope. Those procedure steps need to be tested and verified. The objective of this thesis is to verify onset of localisation on element level and to provide a method for verification of the point of global failure in analyses with the propagation method. Onset of localisation is verified with analytical expressions and with numerical results. A critical stability number is used to assess the slope stability in analyses with the propagation method. A relation between the critical stability number and the factor of safety is needed, to be able to compute a factor of safety with the propagation method which is similar to a factor of safety of the slip surface method and a strength reduction method. This relation is obtained through the definitions of those factors. This creates possibilities to asses the stability of a slope with the propagation method by a factor of safety and this factor of safety can be verified with the results of a strength reduction method and a slip surface method. In addition, benchmarks are generated with the aforementioned slope stability analysis methods, which can be used for verification of the factor of safety of the propagation method. The benchmarks are the result of parameter and convergence studies. In the parameter studies, the effect of the Poisson ratio and the dilatancy angle on the factor of safety is studied. This is done by computing the maximum vertical displacements during stability analyses with various values of the Poisson ratio and the dilatancy angle. Those displacements are plotted versus the corresponding factor of safety. The resulting plots provide characteristic information which can be used for verification of the propagation method. The convergence studies are performed in order to obtain reliable factors of safety that can serve as a benchmark. The factors of safety are computed for various mesh sizes and different convergence criteria. From the results, a reliable factor of safety is obtained that can be used as a benchmark for the corresponding finite element model. In the end, a development version of the propagation method is tested and the results are verified with a benchmark which is generated with a finite element model containing interface elements.

In the course of this thesis, a research has been conducted to the application of fracture mechanics on an othotropic steel deck (OSD). Obtaining accurate predictions of crack path and fatigue life assessment were the main objectives for this thesis. As 3D crack propagation modelling in orthotropic steel decks is an arduous task, simpler studies were examined first in order to obtain confidence for the task at hand. These studies are comprised of a through thickness crack in an asymmetrical four point bending specimen and a semi-elliptical crack in a centre cracked plate. Furthermore, studies on computational fracture mechanics and the integration of Python scripting language with Abaqus were conducted for numerical analysis of crack propagation in complex structures. The extended finite element method was used for evaluation of contour integrals of a crack with a constant mesh throughout the propagation analysis. Post-treatment of the results was applied by smoothing stress intensity factors and the shape of the crack front. Moreover, inaccurate contour integral results were excluded from analysis through extrapolation. A Python code was developed for updating the crack front for a given number of loading cycles integrated in Paris' law. The investigated crack was located at the rib-to-crossbeam joint of an OSD. Here, crack propagation occurs along the lower weld toe and in the longitudinal direction of the rib. Validation of results was obtained through experimental studies conducted at the TU Delft laboratory. The weld geometry was incorporated in the model from measurements in order to identify local stresses. Finally, results of strain gauges were used to validate the model. Measurements of the experimental crack growth were obtained at the surface of the crack only. Consequently, assumptions were made of both the depth and shape of the crack in the thickness direction of the rib. A semi-elliptical crack shape was selected with an initial crack depth of 1 mm. Initially, Paris law parameters C and m were selected as recommended by BS7910. The numerical results of crack path complied with those of experimental results, with deviations of no more than 1 mm. Both data sets show that the propagation rate remained somewhat constant. On the other hand, fatigue life assessment results showed stronger deviation. A parametric study was performed to investigate the effect of the initial crack depth. Three different cases were examined for which the initial crack depths were selected as 1, 2 and 3 mm. Varying the initial crack depth did not lead to a significant change in crack path at the surface of the rib, while the depth in the thickness direction was affected. Regarding the fatigue life assessment, the results with respect to an initial crack depth of 1 mm, complied best with experimental results. Given the strong correlation between experimental and numerical results, the methodology followed in this thesis has proven valuable regarding fatigue crack modelling. As the methodology is based on fracture mechanics, an initial crack is required prior to evaluation. Consequently, the application in engineering practices lies in re-evaluation of structures. Moreover, as the parameters in crack propagation relations have a significant influence on the fatigue life assessment, these should be carefully chosen. Therefore, more insights must be obtained regarding the selection of such parameters.

The Rotterdam municipality is constantly busy replacing old footbridges that have reached their lifetime. Lately, this is done using modern materials, such as fibre-reinforced polymers (FRP). FRP is a relatively light-weight material that has a high yield strength, which allows for aesthetically pleasing, very slender designs. Governing for such designs is often the dynamic behaviour of the bridge: its eigenfrequency may very well lie within the `critical range' of common footfall frequencies. If the step frequency of a pedestrian crossing the bridge lies near the eigenfrequency, a high dynamic amplification factor occurs: high vertical acceleration values for the bridge deck will occur, which means discomfort for the pedestrians.

In this thesis, a sustainable solution to that problem was sought. Rather than using pile foundations to clamp the bridgeheads (and thereby increase the eigenfrequency out of the critical range), it was investigated whether the kinetic energy can be harvested from the bridge. Ideally, this both dampens the vibrations and provides free, sustainable energy.

Several theoretical models were developed to describe the behaviour of an existing footbridge for which data is available. Adaptations to these models were made in the form of either extra dashpots or a tuned mass damper (TMD). In both cases, the dampers are regenerative, i.e. able to harvest energy.

It was shown that adding a TMD provides the best energy harvesting performance. From a practical perspective, it has some advantages as well, such as universal applicability. The parameters in the single degree of freedom (SDOF) model were optimized for maximum energy harvesting while still keeping the vertical deck acceleration at reasonable levels. Finite element analysis largely confirmed these design choices, and showed that reducing the vibration levels is certainly possible with only a relatively small TMD. For a single person crossing at near-resonant footfall frequency only leads to a vertical acceleration of about 1.5 m/s.

The amount of energy that can be harvested in such a way is small but non-negligible: about 26 Joules worth of energy is estimated to be gained by an `average' person crossing the bridge. This is taking into account system efficiency as well.

A literature study concerning real-world energy harvesting systems was performed, and showed the possibility to closely emulate the theoretical behaviour that was assumed for the regenerative dashpots. This can be done using electromagnetic dampers in combination with proper power electronics design.