Optimal rectangular plate and shallow shell topologies using thickness distribution or homogenization
Abstract
Topological optimization of plates, as well as shallow cylindrical and curved (spherical) shells, are attempted in the present study. For all structures examined, our objective is the minimization of the strain energy function under a volume constraint. An optimum distribution of thickness or microstructural density is sought under the hypothesis that the design variables can only be assigned their extreme allowable bounds, or values very near them, so that material can be removed from low density areas and thus, an optimum topology can be determined. The structural response is computed via a finite element analysis. The analytical formulation is based on a form of linear shallow shell theory with the effects of transverse shear deformation and bending-extensional coupling included. The method of feasible directions is used to perform the optimization task. Numerical examples for various boundary conditions showing similarities or differences of the two methods are presented and discussed. For all structures examined, it is found that the assumption of a repetitious microstructure based on homogenization theory resulted in stronger optima. For clamped plates and shells, both methods converged to nearly identical topologies, an indication of possible global optimal layouts.
- Publication:
-
Computer Methods in Applied Mechanics and Engineering
- Pub Date:
- May 1994
- DOI:
- 10.1016/0045-7825(94)90190-2
- Bibcode:
- 1994CMAME.115..111T
- Keywords:
-
- Cylindrical Shells;
- Dynamic Structural Analysis;
- Microstructure;
- Optimization;
- Rectangular Plates;
- Shallow Shells;
- Spherical Shells;
- Strain Energy Methods;
- Thickness;
- Topology;
- Boundary Conditions;
- Deformation;
- Dynamic Response;
- Finite Element Method;
- Shell Theory;
- Structural Mechanics