OPTIMIZATION OF ELASTIC STRUCTURES USING BOUNDARY ELEMENTS AND A TOPOLOGICAL-SHAPE SENSITIVITY FORMULATION

Abstract

THE OBJECTIVE OF THIS WORK IS TO PRESENT THE IMPLEMENTATION OF A HARD KILL MATERIAL REMOVAL ALGORITHM IN A STANDARD BEM FORMULATION. A TOPOLOGICAL-SHAPE SENSITIVITY APPROACH IS USED TO SELECT THE POINTS SHOWING THE LOWEST SENSITIVITIES, WHERE MATERIAL IS REMOVED BY OPENING A CAVITY. AS THE ITERATIVE PROCESS EVOLUTES, THE ORIGINAL DOMAIN HAS HOLES PROGRESSIVELY PUNCHED OUT, UNTIL A GIVEN STOP CRITERIA IS ACHIEVED. BENCHMARKS OF TWO-DIMENSIONAL ELASTICITY ARE PRESENTED AND ANALYZED. BECAUSE THE BEM DOES NOT EMPLOY DOMAIN MESHES IN LINEAR CASES, THE RESULTING TOPOLOGIES ARE COMPLETELY DEVOID OF INTERMEDIARY MATERIAL DENSITIES. THE RESULTS OBTAINED SHOWED THAT THE MATERIAL REMOVAL STRATEGY PLAYS A KEY ROLE IN THE GENERATION OF QUALITY RESULTS. ALTHOUGH THE DRAWBACKS OF HARD-KILL METHODS ARE STILL PRESENT, THE PRESENT APPROACH OPENS AN INTERESTING FIELD OF INVESTIGATION FOR INTEGRAL EQUATION METHODS, SO FAR ACCOMPLISHED ONLY WITHIN THE FINITE ELEMENT METHODS CONTEXT.