Complexity control in the topology optimization of continuum structures

Abstract

A general mesh independent filter as a mean to control the complexity of topology optimization designed structures is discussed. A new mesh-independent filter, applied over the move-limits of the sequential linear programming is proposed, and it is shown that its use alleviates common problems in the continuum topology optimization, like checkerboarding, mesh dependency, as well as effects associated to non-structured meshes, like numerical anisotropy. The structural optimization formulation adopted in this work is the minimization of a penalized function of the volume, with constraints on the compliance of each load case. Aspects of this penalized objective function are discussed, and several numerical examples are shown

Morphology-based black and white filters for topology optimization

“…The alternative methods in group 3 are mostly still in their infancy and have yet to be successfully applied to advanced problems with many constraints. There are also methods that are hybrids between categories 1 and 2 (Zhou et al, 2001;Cardoso and Fonseca, 2003). Here, the box-constraints of the optimization algorithm are modified according to a filtering scheme, resulting in local gradient controllike behavior.…”

Optimization of Functionally Graded Materials Considering Dynamical Analysis

“…Currently, there is a need of efficient engineering methodologies to design parts and structures in order to save material, time and costs [11]. Thus, in recent years, there has been increasing interest in methods that automatically obtain optimized structures from performance conditions specified by the designer [12].…”

“…Even though these methods are useful, the number of design variables used in the optimization problem are higher than those used in the SIMP model. Additionally, homogenization models require a dependence model for the material properties with respect to the geometric parameters of the unit cell, which complicates their implementation [11].…”

Topology Optimized Design, Microfabrication and Characterization of Electro-Thermally Driven Microgripper

“…The procedure converges when the changes in design variables from iteration to iteration are below than 10 À3 (Rubio, 2005). Moreover, in order to avoid the traditional mesh dependency and checkerboard (regions with alternating solid and void element) problems in topology optimization (Bendsøe and Sigmund, 2003), a filter (Cardoso and Fonseca, 2003) is implemented by using a filter radius of eight neighboring elements.…”