Optimal design and numerical modelling of imperfection sensitive shell structures

Abstract

A brand-new design philosophy tends to harness the load-carrying capacity hidden beyond the onset of buckling phenomena in shell structures. However, when designing in the postbuckling range, among other effects, attention should be given at imperfection sensitivity which may generate catastrophic and unexpected consequences on the optimised structures. Therefore, what would be necessary is an optimisation strategy able to deal with the complex geometries of full-scale structures and, meanwhile, efficiently gather the complexity of their postbuckling response. The aim of this work is to meet this demand by proposing numerical methods that face the problem from different sides, namely the geometrically nonlinear description of the shell, the solution algorithm and the optimisation strategy. As a starting point, a convenient format to describe geometrically nonlinear shell structures is identified in the solid-shell model. On the basis of this model, a discretised environment is constructed using isogeometric analysis (IGA) that, by taking advantage from the high continuity of the interpolation functions, leads to a reduced number of variables with respect to standard finite elements. Afterwards, an IGA-based multimodal Koiter’s method is proposed to solve the geometrically nonlinear problem. This method meets the aforementioned requirements of efficiency, accuracy and is capable of providing information on the worst-case imperfection with no extra computational cost with respect to the analysis of a perfect structure. Additionally, a new strategy for improving the accuracy of the standard version of Koiter’s algorithm in the presence of geometrical imperfections is devised. The last part of the thesis concerns the optimal design of full-scale structures undergoing buckling phenomena. In particular, the design focuses on variable angle tow laminates, namely multi-layered composites in which fibre tows can describe curvilinear paths, thereby providing great stiffness-tailoring capacity. Two optimisation strategies are proposed, both based on the use of Koiter’s method to evaluate the postbuckling response. The first one makes use of a fibre path parameterisation and stochastic Monte Carlo random search as a global optimiser. The second one is based on direct stiffness modelling using lamination parameters as intermediate optimisation variables that lead to a reduction of the nonlinearity of the optimisation problem and remove the direct dependence from the number of layers.