Compliance minimization of thin plates made of material with predefined Kelvin moduli. Part II. The effective boundary value problem and exemplary solutions

Abstract

The compliance minimization of transversely homogeneous plates with predefined Kelvin moduli leads to the equilibrium problem of an effective hyperelastic plate with the hyperelastic potential expressed explicitly in terms of both the membrane and bending strain measures, as derived in Part I of the present paper. The aim of this second part of the paper is to show convexity of this potential and, consequently, uniqueness of solutions of the minimum compliance problem considered. Theoretical results are illustrated by numerically calculated optimal trajectories of the eigenstate corresponding to the largest Kelvin modulus.