Topology optimization of plate-like structures

Abstract

This thesis deals with the topology optimization of plate and shell structures. The shell structures are modeled as plate-like at facets. Firstly, the formulation of the topology optimization problem is presented in an introductory chapter, which introduces two frequently used topology optimization algorithms (being the optimality criterion and the method of moving asymptotes). Examples of applications are shown, and filtering schemes are introduced. Secondly, the derivation of the finite element formulation and interpolation of plates is presented. Both a shear rigid Kirchoff plate element and a shear flexible Mindlin element are considered. The latter element uses substitute shear strains to overcome locking; hence reduced integration is not necessary, as is normally required when shear flexible plate elements are used in topology optimization. The effect of both element formulations on optimal topology is then illustrated. The results reveal the notable effect of through thickness shear on optimal topolog. Thirdly, a at shell element is constructed by combining the plate elements with a membrane element with drilling degrees of freedom. (The membrane is not discussed in any detail.) To illustrate the topology optimization of shell structures, the so-called Scordelis-Lo roof is then selected as an example problem. The analysis includes an assessment of the effect of eccentric stiffeners or ribs on optimum topology.