This paper presents a novel damage mechanics based failure model enabling the prediction of low cycle fatigue life and residual strength of isotropic structures under multiaxial loading. The approach herein proposed does not discretize every load cycle but instead takes an envelope loading whereby the numerical load remains constant at a maximum load level and the number of cycles is obtained from a given elapsed time defined within a pseudo-time framework. The proposed formulation is based on the smeared cracking approach accounting for damage propagation due to static and fatigue loadings, where the static component is based on the Von-Mises yield criterion and Prandtl-Reuss stress flow rule; whereas the crack propagation in cyclic loading component is based on the Paris-law. Furthermore, the formulation combines damage mechanics and fracture mechanics within a unified approach enabling the control of the energy dissipated in each loading cycle.

Nondestructive methods, to calculate the buckling load of imperfection sensitive thin-walled structures, such as large-scale aerospace structures, are one of the most important techniques for the evaluation of new structures and validation of numerical models. The vibration correlation technique (VCT) allows determining the buckling load for several types of structures without reaching the instability point, but this technique is still under development for thin-walled plates and shells. This paper presents and discusses an experimental verification of a novel approach using vibration correlation technique for the prediction of realistic buckling loads of unstiffened cylindrical shells loaded under axial compression. Four different test structures were manufactured and loaded up to buckling: two composite laminated cylindrical shells and two stainless steel cylinders. In order to characterize a relationship with the applied load, the first natural frequency of vibration and mode shape is measured during testing using a 3D laser scanner. The proposed vibration correlation technique allows one to predict the experimental buckling load with a very good approximation without actually reaching the instability point. Additional experimental tests and numerical models are currently under development to further validate the proposed approach for composite and metallic conical structures.

Nondestructive methods, to calculate the buckling load of imperfection sensitive thin-walled structures, are one of the most important techniques for the validation of new structures and numerical models of large scale aerospace structures. The vibration correlation technique (VCT) allows determining the buckling load for several types of structures without reaching the instability point, but this technique is still under development for thin-walled plates and shells. This paper presents and discusses an experimental and numerical validation of a novel approach, using the vibration correlation technique, for the prediction of realistic buckling loads on unstiffened cylindrical shells loaded in compression. From the experimental point of view, a batch of three composite laminated cylindrical shells are fabricated and loaded in compression up to buckling. An unsymmetric laminate is adopted in order to increase the sensitivity of the test structure to initial geometric imperfections. In order to characterize a relationship with the applied load, the first natural frequency of vibration and mode shape is measured during testing using a 3D laser scanner. The proposed vibration correlation technique allows one to predict the experimental buckling load with a very good approximation, without actually reaching the instability point. Furthermore, a series of numerical models, including non-linear effects such as initial geometric and thickness imperfection, are carried-out in order to characterize the variation of the natural frequencies of vibration with the applied load and compare the results with the experiment findings. Additional experimental tests are currently under development to further validate the proposed approach for metallic and balanced composite structures.

The importance of taking into account geometric imperfections for cylindrical and conical thin-walled structures prone to buckling had been already recognized by the first authors dealing with new formulations. Nowadays, the analysts still use empirically based lower-bound methods such as the NASA SP-8007 guideline to calculate the required knock-down factors (KDFs), which does include important mechanical properties of laminated composite materials, such as the stacking sequence. New design approaches that allow taking full advantage of composite materials are required. The single perturbation load approach (SPLA), a new deterministic approach first proposed by Hühne, will be investigated with unstiffened composite conical structures varying the geometry, lamina and layup. The SPLA's capability for predicting KDF is compared with the NASA approach. The SPLA was applied to the geometrically perfect structures and to the structure with geometric imperfections of two types, mid-surface imperfections and thickness imperfections. The study contributes to the European Union (EU) project DESICOS, whose aim is to develop less conservative design guidelines for imperfection sensitive thin-walled structures.

Imperfection sensitive structures such as unstiffened or skin-dominant shell structures are commonly used for aeronautic and aerospace applications. Cylindrical shells are dominating satellite launcher structures and a reliable methodology to calculate their behaviour in the early stages of design is fundamental to achieve optimum results. Launcher design requires fast and precise prediction of structural weight as well its weight distribution already in the early design phase, because in that phase different concepts of the whole launcher system have to be evaluated in order to identify the optimal one. The prediction has to be precise, because less reliable ones might lead to basic changes, later in the detailed design phase, which might also influence the design of the whole system. Such changes in later design phases are extremely costly in terms of time and money; they definitely have to be avoided. The dimensioning criterion with the design of launcher structures is buckling not before ultimate load, thus they do not have an exploitable post-buckling area. The most critical aspect for numerical buckling prediction is the structure's sensitivity to geometric and loading imperfections. Currently, imperfection sensitive shell structures prone to buckling are designed according to the NASA SP-8007 guideline [1], from 1968, using its conservative lower bound curve. In this guideline the structural behaviour of composite materials is not appropriately considered, since the imperfection sensitivity and the buckling load of shells made of such materials depend on the lay-up design. There is no specific design guideline for imperfection sensitive composite structures prone to buckling. NASA performed high investments for the last 5 years with one project called "Shell Buckling Knock-down Factor" (SBKF) in order to develop a new guideline to calculate the knock-down factor of cylindrical shells prone to buckling [2], and also the European project DESICOS [3] (New Robust DESign Guideline for Imperfection Sensitive Composite Launcher Structures) is working on new methodologies to estimate the ultimate load of such structures. An example of applicability of these new design guidelines could be the next generation of the European launchers family "Ariane" in order to maintain the actual position in the satellite launchers market [4].

Space and aircraft industry demands for reduced development and operating costs. Structural weight reduction by exploitation of structural reserves in composite space and aerospace structures contributes to this aim, however, it requires accurate and experimentally validated stability analysis. Currently, the potential of composite light weight structures, which are prone to buckling, is not fully exploited as appropriate guidelines in the field of aerospace and space applications do not exist. This paper deals with the state-of-the-art advances and challenges related to coupled stability analysis of composite structures which show very complex stability behaviour. Two types of thin-walled light weight structures endangered by buckling will be considered; imperfection tolerant and imperfection sensitive structures. For both groups improved design guidelines for composites structures are still under development. This paper gives a short state-of-the-art and presents proposals for future design guidelines.

This paper presents the application of the Ritz method for the analysis of laminated composite cylinders and cones using the classical laminated plate theory (CLPT) and the first shear deformation theory (FSDT). The Donnell and Sander kinematic approximations are investigated for the CLPT. It is shown that the equations proposed by Sanders when applied with the CLPT increase the range of applicability of the CLPT in comparison with the Donnell kinematics. The developed models are suitable to obtain linear and non-linear responses of conical and cylindrical shells under displacement or load controlled axial compression and geometric imperfections. This paper brings the investigation of static and buckling responses and the commercial finite element solver Abaqus was used to validate all the linear and non-linear results.

Currently, imperfection sensitive shell structures prone to buckling are designed according to the NASA SP-8007 guideline, from 1968, using its conservative lower bound curve. In this guideline the structural behavior of composite materials is not appropriately considered, since the imperfection sensitivity and the buckling load of shells made of such materials depend on the lay-up design. In this context a numerical investigation about the different methodologies to characterize the behavior of imperfection sensitive composite structures subjected to compressive loads up to buckling is presented in this paper. A comparative study is addressed between a new methodology, called "Single Perturbation Load Approach", adopted by the European project DESICOS, and some classical approaches such as non-linear analyses considering geometric and thickness imperfection obtained from real measurements. An extension of the Single Perturbation Load Approach called "Multiple Perturbation Load Approach" is also introduced in this paper to investigate if one perturbation load is enough to create the worst geometrical imperfection case.The aim of this work is to validate these numerical methodologies with experimental results and point out their limitation, advantage and disadvantage, to calculate less conservative knock-down factors than the obtained with the NASA SP-8007 guideline for unstiffened composite cylinders.

The important role of geometric imperfections on the decrease of the buckling load for thin-walled cylinders had been recognized already by the first authors investigating the theoretical approaches on this topic. However, there are currently no closed-form solutions to take imperfections into account already during the early design phases, forcing the analysts to use lower-bound methods to calculate the required knock-down factors (KDF). Lower-bound methods such as the empirical NASA SP-8007 guideline are commonly used in the aerospace and space industries, while the approaches based on the Reduced Stiffness Method (RSM) have been used mostly in the civil engineering field. Since 1970s a considerable number of experimental and numerical investigations have been conducted to develop new stochastic and deterministic methods for calculating less conservative KDFs. Among the deterministic approaches, the single perturbation load approach (SPLA), proposed by Hühne, will be further investigated for axially compressed fiber composite cylindrical shells and compared with four other methods commonly used to create geometric imperfections: linear buckling mode-shaped, geometric dimples, axisymmetric imperfections and measured geometric imperfections from test articles. The finite element method using static analysis with artificial damping is used to simulate the displacement controlled compression tests up to the post-buckled range of loading. The implementation of each method is explained in details and the different KDFs obtained are compared. The study is part of the European Union (EU) project DESICOS, whose aim is to combine stochastic and deterministic approaches to develop less conservative guidelines for the design of imperfection sensitive structures.

Nondestructive experimental methods to calculate the buckling load of imperfection sensitive thin-walled structures are one of the most important techniques for the validation of new structures and numerical models of large scale aerospace structures. Vibration correlation technique (VCT) allows determining equivalent boundary conditions and buckling load for several types of structures without reaching the instability point. VCT is already widely used for beam structures, but the technique is still under development for thin-walled plates and shells. This paper intends to explain the capabilities and current limitations of this technique applied to two types of structures under buckling conditions: flat plates and cylindrical shells prone to buckling. Experimental results for a flat plate and a cylindrical shell are presented together with reliable finite element models for both cases. Preliminary results showed that the VCT can be used to determine the realistic boundary conditions of a given test setup, providing valuable data for the estimation of the buckling load by finite element models. Also numerical results herein presented show that VCT can be used as a nondestructive tool to estimate the buckling load of unstiffened cylindrical shells. Experimental tests are currently under development to further validate the approach proposed herein.

Some of the knock-down factors applied in design of rocket launcher structures are based on design recommendations which rely on lower-bound curves from experimental data. The best known example is the NASA guideline SP 8007, published in 1965 and revised in 1968, which is applied for cylindrical structures in the space industry. This guideline is based on test data, computational methods and resources from the 1930-1960's. At that time the application of less empirical methods for the design of actual cylindrical shells could not count with the current computational power, and the available methods led to quite large discrepancies between experiments and test observations. Significant improvement on the available analyses approaches and manufacturing techniques since 1960's have not been taken into account in design processes using the NASA SP-8007, and many authors have recognized that for the current standards this guideline is leading to conservative structures. Another aspect for attention regarding application of the NASA SP-8007 for composite shells is that it does not consider the laminate stacking sequence. Moreover, physical observations regarding how does the imperfection sensitivity of unstiffened cylindrical shells change with the presence of an induced geometric imperfection have also suggested that the current applied design rules are too conservative. This conservativeness is confirmed by many tests carried out recently. This study presents an overview of the problem and a detailed description of the physical observations regarding the buckling mechanism of the thin shells under consideration. It is discussed how these observations can be used for less conservative, laminate dependent, knock-down factors accounting for geometric imperfections. The single perturbation load approach is studied in detail and a physically based definition for the minimum perturbation load (P1) is given, paving the way for the development of semi-analytical methods to calculate this minimum perturbation load.