Note on topology optimization of continuum structures including self-weight

Abstract

This paper proposes to investigate topology optimization with density dependent body forces and especially self-weight loading. Surprisingly the solution of such problems can not be based on a direct extension of the solution procedure used for minimum compliance topology optimization with fixed external loads. At first the particular difficulties arising in the considered topology problems are pointed out: non-monotonous behaviour of the compliance, possible unconstrained character of the optimum and parasitic effect for low densities when using the power model (SIMP). To get of rid of the last problem requires to modify the power law model for low densities. The other problems require to revisit the solution procedure and the selection of appropriate structural approximations. Numerical applications compare the efficiency of different approximation schemes of the MMA family. It is shown that important improvements are achieved when the solution is carried out when using the Gradient Based Method of Moving Asymptotes (GBMMA) approximations. Criteria for selecting the approximations are suggested. In addition, the applications are also the opportunity to illustrate the strong influence of the ratio between the applied loads and the structural weight onto the optimal structural topology.

Worst-case topology optimization of self-weight loaded structures using semi-definite programming

“…Topology optimization including self-weight was studied by Bruyneel and Duysinx (2005), who noticed that for design variables approaching the lower bound, the ratio between the load and the (SIMP-based) stiffness becomes infinite, leading to unbounded displacements and thus also unbounded compliance. This causes the optimization to converge to a design with intermediate design variable values.…”

Application of a bi-level scheme including topology optimization to the design of an aircraft pylon

“…Here the Conlin approximation (Fleury and Braibant, 1986) is used in conjunction with efficient dual solvers (Fleury, 1993) in a multi-objective formulation. The GCM approximation (Bruyneel et al, 2002) is also available in TOPOL for problems including body forces and presenting non-monotonous behaviors (Bruyneel and Duysinx, 2005;Bruyneel, 2006). …”

Topology optimization of multiphase material structures under design dependent pressure loads

“…Within this scope, optimal support locations were found by Rozvany [1], Mroz and Rozvany [2], Prager and Rozvany [3], Szelag and Mroz [4] to improve elastic and plastic responses of beams. Likewise, Rozvany and Mroz [5], Olhoff and Taylor [6], Olhoff and Akesson [7] discussed the column support optimization for buckling load maximization.…”

“…In other words, no material, no load. Bruyneel and Duysinx [7] investigated the topology optimization of structures under self-weight loading with SIMP and different MMA (Method of Moving Asymptotes) approximation schemes. Yang et al [24] applied the ESO/BESO method to solve the same problem.…”