The Free Material Design in Linear Elasticity

Abstract

The Free Material Design (FMD) is a branch of topology optimization. In the present article the FMD formulation is confined to the minimum compliance problem within the linear elasticity setting. The design variables are all elastic moduli, forming a Hooke tensor C at each point of the design domain. The isoperimetric condition concerns the integral of the p-norm of the vector of the eigenvalues of the tensor C. The most important version refers to p = 1, imposing the condition on the integral of the trace of C. The paper delivers explicit stress-based formulations and numerical solutions of the FMD problems in the case of a single load case as well as for a general case of a finite number of load conditions.