Compliance Minimization of Two-Material Elastic Structures
Minimum compliance problem set for a structure made of two elastic, isotropic materials is tackled in this paper. The relaxation by homogenization technique is used for obtaining its mathematically well-posed formulation. The problem is first discussed in general two-material context. Derivation of main results is recalled and supplemented with some explanations and remarks. Next, an important topic of one-material layout optimization (or shape optimization) is addressed. It is hampered by the non-smoothness of formula for relaxed stress energy hence its approximation is proposed which in turn makes the FEM easier to apply in solving the equilibrium problem. Shape optimization is then linked to a wellknown Michell problem of the lightest, fully stressed structures. Possible extension of the relaxation by homogenization method to other structures like thin or moderately thick plates in bending as well as thin plates or shells submerged to simultaneous in-plane and bending load are also commented.
KeywordsTopology Optimization Shape Optimization Sandwich Plate Stress Energy Layout Optimization
Unable to display preview. Download preview PDF.