Optimal variable support size for mesh-free approaches using genetic algorithm

Abstract

The main difficulty of the meshless methods is related to the support of shape functions. These methods become stable when sufficiently large support is used. Rather larger support size leads to higher calculation costs and greatly degraded quality. The continuous adjustment of the support size to approximate the shape functions during the simulation can avoid this problem, but the choice of the support size relative to the local density is not a trivial problem. In the present work, we deal with finding a reasonable size of influence domain by using a genetic algorithm coupled with high order mesh-free algorithms which the optimal value depends on the accuracy and stability of the results. The proposed strategy provides guarantees about the growth of approximation errors, monitor the level of error, and adapt the evaluation strategy to reach the required level of accuracy. This allows the adaptation of the proposed algorithm with problem complexity. This new strategy in meshless approaches are tested on some examples of structural analysis.

Towards adaptation of the NURBS weights in shape optimization

“…Shape optimization problems try to find the shape which is optimal in that it minimizes a certain cost functional while satisfying given constraints, see [3][4][5]. To improve a shape optimization process, authors, in [6], use the adaptation of Bézier parametrizations.…”