TOPOLOGY OPTIMIZATION OF CONTINUUM TWO-DIMENSIONAL STRUCTURE UNDER VOLUME CONSTRAINT

Resumo

This work presents the Topology Optimization Method where the objective is to minimize
compliance with lateral and volume constraints of a rib from aircraft wings profile leading edge. The
problem is solved by a Topology Optimization Method technique, formulated as finding the best
material distribution into the domain. The static problem is solved with the Finite Element Method were

the structural response is given as nodal displacements. The Optimality criteria are based in the power-
law approach, also known as Solid Isotropic Material with Penalization that uses a “fictitious” density

to represent the material distribution into each finite element that defines the elastic properties of
isotropic porous material. The solution is implemented with a didactic algorithm. No linear
programming is used and a heuristic updating scheme is used as standard optimality criteria. Besides,
sensitivity and densities filters are used to minimize the occurrence of numerical instabilities:
checkerboards, mesh-dependencies, and local minima. The results are evaluated in three criteria: first,
the occurrence of these instabilities and filter performance, second the convergence and implementation
time and the last one a brief comparison with the literature and a general analysis of the results.