Material orientation design of planar structures with prescribed anisotropy classes. Study of rhombic systems

Abstract

A heuristic approach to optimization of structural topology including self-weight AIP Conference Proceedings 1922, 020001 (2018) Abstract. The paper deals with the minimum compliance problem of 2D structures made of a non-homogeneous elastic material.In the first part of the paper a comparison between solutions of Free Material Design (FMD), Cubic Material Design (CMD) and Isotropic Material Design (IMD) is shown for a simply supported plate in a shape of a deep beam, subjected to a concentrated in-plane force at its upper face. The isoperimetric condition fixes the value of the cost of the design expressed as the integral of the trace of the Hooke tensor. In the second part of the paper the material design approaches are extended to rhombic system in 2D. For the rhombic system the material properties of the structures are set, the design variables being the trajectories of anisotropy directions which in 2D are described by one parameter. In the Orthotropic Orientation Design (OOD) no isoperimetric condition is used.