High-precision systems often comprise many individual systems, each operating at its own frequency. However, the vibrations from one system can be transmitted to another, which yields a response. In high-tech applications where precision is crucial, such as compliant transmission systems, these responses are undesired as they result in a loss in precision. Topology optimization can be employed to directly include these unwanted vibrations in the design process of compliant mechanisms. However, the current literature only concerns simple beam structures and suffers from issues such as premature convergence and large intermediate-density areas. This thesis aims to employ topology optimization to design compliant transmission systems whilst simultaneously attenuating the effects of unwanted external vibrations in the form of base excitations. This is done by using an objective function capable of minimizing the displacement response of a structure whilst not suffering from the aforementioned issues. The found objective function relies on the principle of global minimization, which minimizes the largest displacements inside the structure resulting from the applied excitation. An extension of the current research is done by only minimizing a subset of the domain, obtaining a localized minimization whilst other areas of the domain are allowed to exhibit larger responses. These two minimization principles are then applied to the design of a compliant inverter mechanism, with local minimization considering two areas of interest: the entire mechanism area and the regions around the input and output of the mechanism. The results show that global minimization is able to obtain discrete results for a large range of frequencies. Local minimization of the mechanism area yields lower displacement responses and, for higher frequencies, resulting topologies with displacement behaviour similar to the principles of vibration absorption and vibration isolation. Decreasing the response area to be minimized only to cover the input and output regions of the mechanism yields inconclusive results in terms of obtaining lower displacement responses compared to local minimization of the mechanism area. A proof of concept for designing a compliant transmission system whilst minimizing the response to harmonic base excitations is established, demonstrating potential benefits for future research in this domain.

Soft robots, characterised by compliant mechanisms (CMs) made from low-stiffness materials, offer improved adaptability compared to traditional, rigid robots. These CMs are often actuated by pressure loads. Moreover, soft robots provide new possibilities in the area of robotics. They can be used in search and rescue and interact safely in collaboration with humans.

The current state-of-the-art in Topology Optimisation (TO) for design-dependent pressure-actuated CMs (PACMs) relies heavily on linear models. The determination of design-dependent pressure loads involves employing the Darcy method, which integrates Darcy's law with the drainage term to obtain the pressure field. Subsequently, the finite element method (FEM) is used to transform the pressure field into consistent nodal forces. However, it is crucial to acknowledge that these linear models are only valid for small displacements.

This thesis introduces a novel approach by incorporating nonlinearities into the solid mechanics of the TO process for PACMs in conjunction with the Darcy method. Additionally, this work incorporates nonlinearities into the solid mechanics of the TO process for PA multi-material compliant mechanisms, presenting another novel method.

Four nonlinearities in the solid mechanics of PA soft robots may occur, two of which are addressed in this thesis: geometric nonlinearities and a hyperelastic material model. Geometric nonlinearities arise from large deformations caused by high applied pressures. The Neo-Hookean material model is implemented to describe the low-stiffness material accurately.

The TO of pressure-actuated (PA) soft robots is simulated using COMSOL, a commercial software program for multi-physics simulation. This research presents a detailed comparison between theoretical predictions and practical outcomes as realised in COMSOL. Furthermore, this thesis includes a case study validating the successful implementation of the new method, covering a PA inverter, a PA compliant gripper, a PA member of the Pneumatic Networks, and a PA multi-material compliant gripper. The obtained results indicate limitations on the allowable applied pressure loads for the mechanisms, specifically in the case of the PA member of the Pneumatic Networks and a PA multi-material-compliant gripper. However, the PA inverter and PA compliant gripper validate the expectation that incorporating a hyperelastic material model yields significantly different results than the linear elastic material model. Moreover, the TO with the hyperelastic material model can predict displacements more accurately than the linear TO, as the differences between the displacements obtained from the TO and the analysis align more closely.

The Wang method is investigated to observe its influence on the range of the applied pressure loads during the TO of PA soft robots. The Wang method employs an interpolation technique that interpolates between linear and nonlinear theories. In this approach, void elements are described using linear theory, while solid elements are characterised by nonlinear theory. This interpolation method is developed to address distorted elements during large displacements. It effectively extended the range of applied loads during the TO of structures. However, it is found that this method does not influence the range of the applied load during the TO of CMs.

The recent success of - and demand for - compliant mechanisms has increased rapidly within the micro-electromechanical systems-, aircraft-, spacecraft-, surgical-, and precision-instrument industries. Yet, even greater success may be achieved by overcoming the computational cost and instability of the mechanisms' design methodology. This involves large-scale topology optimization, geometrically non-linear structural analysis, and particularly integrating the latter into the former. Therefore, a novel framework is proposed that extends the powerful design freedom of topology optimization with most of the geometrically non-linear qualities, without as much of the computational ramifications. Utilizing a Bayesian-enhanced perturbed analysis, the equilibrium curve is locally approximated by an asymptotic expansion, satisfying the curve's higher-order geometric derivatives at the undeformed state. Each of the latter is recursively and efficiently obtained through a linear solve with the same, Cholesky-factorized stiffness matrix. Furthermore, a tensor reformulation and -decomposition of the four-noded bilinear element's Green-Lagrange strain energy model are successfully exploited. A tight error estimator is derived to govern the Bayesian analysis and balance approximation efficiency and accuracy during optimization. Design-sensitivities of this error-estimator and other design-dependent responses are analytically obtained through the adjoint method, and applied in a few classical density-based topology optimizations; While Bayesian-enhanced perturbed analysis required noticeably less computational effort compared to Newton-Raphson analysis under mildly non-linear conditions, it often resulted in practically identical performance improvements compared to linear analysis.

In conventional aircrafts, lift control is achieved by using flap systems. It would be beneficial if flap systems could be replaced by a variable-camber morphing wing. It has been shown that variable-camber morphing wings can significantly improve the aerodynamic performance of the aircraft due to the smoothness of the surface, making it possible to fly more efficiently, reduce fuel consumption and reduce the impact on the environment. However, the design of such a variable-camber morphing wing is challenging due to the conflicting requirements of the structure. The wing should be flexible so it can morph, stiff so it can withstand aerodynamic pressures and light weight to reduce fuel consumption. The aim of this work is to provide a method for the density-based topology optimization of compliant morphing structures. The method includes a novel formulation for the objective function which compares the deformed shape of the structure with a desired deformed shape by using a dot product. This method is applied to obtain an optimized design of a compliant variable-camber morphing wing. The obtained design was converted to a prototype by 3D printing and an experiment was performed to assess if the deformed shapes of the prototype were similar to the ones predicted by the analysis in the topology optimization. The experiment showed that for small deformations the output shape matched the predicted output shape. For larger deflections, there was a slight difference. However, the obtained shapes were still quadratic-like and so it is expected that for larger deformations the designed trailing edge will still have superior aerodynamic performance than conventional flap systems.

Applications for thermoelastic metamaterials, in which extremely positive, zero or negative thermal expansion is desired, are plentiful. Nevertheless they are rarely applied, due to their poor manufacturability. To enhance their applicability, a topology optimization framework is proposed and verified, able to generate finite thermoelastic metamaterials with tailored unidirectional thermal expansion, manufacturable through automated multi-material additive manufacturing methods. The superelement method is utilized to optimize for finite thermoelastic unit cell arrays connected to solid strips allowing for easy mounting, instead of non-realizable infinite arrays which are optimized in existing frameworks that use the homogenization method. The robust formulation is combined with a filter domain extension approach, to obtain manufacturing tolerant, black and white solutions and minimum length scale control. Uniform material layers are enforced, to obtain layered designs manufacturable with multi-material additive manufacturing methods. Using the proposed framework, a finite thermoelastic unit cell array is optimized for near zero thermal expansion. It is validated that the superelement method is more suitable for the computation of the thermoelastic response of small unit cell arrays, compared to the commonly used homogenization method. A physical sample is manufactured and experimentally validated. Experimental validation confirms numerical predictions and shows that the proposed design approach is able to generate performant and realizable thermoelastic metamaterials.

Density-based topology optimization, when used to design structures that show geometrical non-linear behaviour, currently faces computational effort and stability issues. These issues are caused by the iterative method used in geometric non-linear structural analysis. On top of taking much computational effort to complete, this method encounters instabilities when analyzing low-density elements usually present in the design domain.

This study aims to bypass those issues by proposing approximate analysis in the topology optimization routine, which is an analysis based on an approximation of the geometrical non-linear load-deflection curve of a structure, constructed with equilibrium points close to its undeformed configuration.

To study the performance and the influence of the parameters that govern approximate analysis, three numerical examples are considered. These indicate that using approximate analysis in topology optimization leads to designs that perform over a finite range of motion, similar to when a non-linear analysis is used. The computational effort needed for approximate analysis is closer to the effort needed for linear analysis than non-linear analysis. A limitation of approximate analysis is that its results are only similar to non-linear analysis as long as the deflections stay in the mildly non-linear domain.

When concerning the topology optimization of compliant mechanisms that exhibit mildly geometric non-linear behaviour, we conclude that using approximate analysis is a stable and computationally efficient alternative to non-linear analysis.

The manufacturing freedom of additive manufacturing, and design freedom of topology optimization have proven to be a fruitful combination in creating and manufacturing designs. While research into applications of metal additive manufacturing has advanced from rapid prototyping to end-use components, metal additive manufacturing of compliant mechanisms has only been researched to a limited amount. This is despite the fact that additive manufacturing provides opportunities to manufacture highly advanced, monolithic compliant mechanism considered impossible before. Important considerations regarding geometry during additive manufacturing of compliant mechanisms are what minimum length scale and angle between overhanging features and build plate (the overhang angle) need to be imposed on the design. These considerations determine whether a compliant mechanism is successfully built by additive manufacturing and can ensure that designs are self-supporting. Since these constraints are most relevant in fragile hinge regions of compliant mechanisms where support material removal is unwanted, self-supporting, cross-axis flexural pivots are manufactured using selective laser melting. It is found manufacturability in additive manufacturing does not necessarily guarantee a predictable stiffness and yield strength of these flexural pivots. That is why it is recommended to print self-supporting regions of compliant mechanisms with a minimum length scale 25% greater than prescribed by the manufacturing process used and an overhang angle of at least 5 degrees greater than the prescribed minimum overhang angle. Next, these recommendations are implemented in compliant mechanism design using topology optimization, at locations where these recommendations are most relevant. This is done by redesigning hinge regions of compliant mechanisms, using static condensation to reduce the order of the problem. While adding only 5% extra computation time, small regions of a design can be redesigned successfully. To use the potential of this method fully, an extension to this method is introduced, which allows to redesign domains in more detail. Multi-point constraints are used to couple the original and finer redesign mesh. For a finer mesh, more computation time is needed, but as the design space is enlarged, other, more optimal solutions are found. Next, constraints on overhang angle, minimum length scale and stress are implemented, since these constraints are proven to be meaningful in hinge regions by the experiments with the cross-axis flexural pivots. Implementation is done successfully, and it is seen compliant mechanisms can be designed at relatively low additional computational cost and with minimal loss of mechanism performance. Thus, using this approach, redesigned compliant mechanisms can be manufactured with locally self-supporting hinges and predictable kinematics and stress concentrations can be ensured.

Although the field of structural optimization has undergone substantial growth the last decades, the efficiency of the programs used to generate structurally optimal designs for industrial applications remains questionable. To make matters worse, as structural problems become more complex, e.g. by adding multi-disciplinary optimization targets to the problem formulation, the slow convergence speed associated with the inefficiency of these programs turns into a significant issue. Thus, one can argue that there is a need for improvements in the optimization methods used to address such problems. One of the most prominent methods to tackle structural optimization problems is SAO. This method is comprised of 2 steps: approximating locally the non-analytical functions that describe the studied phenomenon and solving the resultant nonlinear optimization problem. This report is a thorough investigation of the function approximation part on a fundamental level, and an attempt to improve the quality of the generated approximation. We start by conducting a literature survey of the state-of-the-art function approximation methods and evaluating their performance - in terms of convergence speed - under various scenarios. Then, we focus our attention to the most widely applied family of approximations (i.e. the MMA) by locating and understanding their inadequacies. These inadequacies are then addressed by proposing a solution that includes the generation of novel mixed approximation schemes that can outperform their constituent members for a set of small-scale, albeit challenging, test problems. Apart from implementing, validating and evaluating fairly different approximation schemes, we also generate approximation selection criteria, whose output is the 'optimal' approximation method for any given function at an arbitrary point. The outcome of this process is an 'Optimization Laboratory' that offers an in-depth understanding of the behaviour of any function approximation method under examination on a fundamental level. It is effectively an object-oriented software library that can be used to compare different approximation schemes on a set of problems, while offering a detailed insight on the quality of any approximation at any given point. Numerical examples that support our assertions are presented, building a strong case in favor of the possible superiority of a mixed scheme compared to its component members, as far as adaptiveness, robustness and total computational cost of SAO algorithms are concerned. More specifically, all approximations used herein are analyzed with a benchmark profiling method. Different sets of initial points, multiple convergence criteria and several tolerances are used in order to obtain an objective comparison between the considered methods. The results of this thorough comparison are summarized in performance profile plots and discussed thereafter. The results of the present research suggest that the generated mixed schemes are superior to their constituent members for the considered problem set. A significant reduction in the number of iterations required to converge to a local optimum was achieved and overall convergence was improved. Even in the most conservative scenario, the best mixed scheme outperformed all others for 46% of the implemented problems (compared to MMA that did so for just above 15% of them). What is more, improved robustness was also achieved by successfully solving 95% of the considered problems (compared to 72% for MMA). However, this improved performance is accompanied by an increase in the computational cost of the approximation process. To this end, an analysis of the relative computational cost of mixed schemes compared to the state-of-the-art approximation methods - in terms of time spent per iteration on the approximation - follows the performance results and a method to estimate the viability of approximation enhancement is proposed. Finally, conclusions on the relative performance of all methods are drawn from the aforementioned comparison and recommendations for further research on improving the performance and lowering the computational cost of mixed schemes are given.

Auxetic materials exhibit material properties, which are usually not seen in nature. This type of materials belong to the class of mechanical metamaterials and can be used for e.g. energy absorption, cloaking of objects, shape morphing applications and the design of fiber-reinforced composites. They exhibit a negative Poisson’s value and derive their unusual properties from their architecture and are arranged in a pattern of unit cells. However, the design of their architecture is limited by the combination of degrees of freedom and therefore, a topology optimization (TO) procedure is utilized to allow sufficient design freedom. This thesis focuses on the generation, numerical and experimental validation of mechanical metamaterials. Auxetic unit cells are generated using an energy-based TO approach with periodic boundary conditions, with a valid response in the linear elastic regime. A patch of unit cells is numerically investigated for suitable test conditions and auxetic designs are fabricated for testing purposes using the fused deposit modeling (FDM) technique. The possibilities and shortcomings of this print technique are explored and relevant findings came out. Finally, compression tests of the as-printed auxetic designs are conducted to validate the auxetic behavior in practice. This thesis shows that the experimentally tested novel auxetic designs generate new knowledge towards the validation of mechanical metamaterials. It has been shown that the upcoming and user-friendly additive manufacturing technique, (FDM), is suited to generate and validate optimized geometries.