Optimization of Laminated Bending Plates

The problems of shape, material, sizing and topology optimization are formulated and solved for thin orthotropic laminated bending plate structures subjected to the in-plane as well as out-of-plane loading. A simple laminated combined finite element that comprises known elements CST for membrane part and DKT for bending part was formulated in the present study. A special numerical-analytical method for structural matrices of the element and analytical sensitivity analysis is used to cope with huge required computer resources for topology optimization. The uniform distribution of deformation energy density over the area of structure is employed as the optimality criterion in all optimization problems. The original algorithms, which may be attributed to the ESO family of algorithms, are suggested for optimization of laminae thicknesses and topology optimization. A number of numerical examples are provided.