Optimal topology of retaining wall

This paper intends to present an approach the problem of optimal cross-section topology a retaining wall. We use Solid Isotropic Material with Penalization (SIMP) method solve this problem. An isotropic solid is divided into n quadrilateral finite elements, and each such element e associated design variable xe which might be regarded as material density. The notion virtual Young's modulus introduced, for it can approximated follows: , where p penalty, usually equal 3; Emin small value modulus, we in order avoid singularity stiffness matrix; E0 material. Thus when condition 0 ≤ xep 1 satisfied Ee varies between certain minimum usual E0. regard wall form rectangle height base ratio 3:1 demonstrate proposed approach. Along its entire under pressure soil, linearly from 1. In general, corresponds hydrostatic pressure. From standpoint theory elasticity considered planar. shrinks mathematical programming conditions (here F vector external forces, u(x) displacements, x densities). objective function interpreted work done by forces deform system, thus tend find stiffest body volume. To Python language, Numpy Scipy packages. eliminate “checkerboard problem” (alternation black white cells) apply Gaussian filter Skimage package. parameters obtained model are described ANSYS Parametric Design Language exported Ansys Mechanical further analysis. It determined that maximum von Mises stress structure prescribed volume fraction 60% does not exceed rectangular cross section.