Structural optimization using sensitivity analysis and a level-set method

Abstract

In the context of structural optimization we propose a new numerical method based on a combination of the classical shape derivative and of the level-set method for front propagation. We implement this method in two and three space dimensions for a model of linear or nonlinear elasticity. We consider various objective functions with weight and perimeter constraints. The shape derivative is computed by an adjoint method. The cost of our numerical algorithm is moderate since the shape is captured on a fixed Eulerian mesh. Although this method is not specifically designed for topology optimization, it can easily handle topology changes. However, the resulting optimal shape is strongly dependent on the initial guess.

Topology optimization of acoustic–structure interaction problems using a mixed finite element formulation

“…This procedure has been widely used to calculate responses of acoustic-structure interaction problems [23]. For the procedure, the interfacing boundaries should be exactly or at least approximately defined with parametric curves such as splines, which, for optimization, can be controlled by design variables [8,29]. Thus, shape optimization has become a natural choice with this analysis procedure [10,12,17,18,19,20,21,25,26,30].…”

Vibration design of laminated fibrous composite plates with local anisotropy induced by short fibers and curvilinear fibers

“…The expression in Eq. (4) is based on the level set function used in topology optimization and makes it possible to accommodate topology changes simply [36].…”

The bidirectional improvement of level set method topology optimization

“…Atpresent,continuousstructuretopologyoptimizationhasbecomeanimportantresearchfieldof engineeringapplication.LevelsetmethodwasproposedbyOsherandSethian [1]andusedtostudy thedynamicinterfacetrackingasanumericalmethod.AsshowninFig.1,themainideaofthis methodistousezerolevelsurface(lines)ofhighdimensionlevelsetfunctiontoexpresstherepresent evolutionofsurface(curve)implicitly,andcurveorsurfaceboundarymotionanalysisandtracking willbeobtainedbysolvingthelevelsetequation.Usingsensitivityanalysisofthelevelsetfunctionto solvethestructureoptimizationwhichhasbeenproposedbyAllaire [2].Thelevelsetfunctionis firstlyintroducedintothefieldofstructuraltopologyoptimizationbySethian [3].Anoptimization modelwasproposedbyWang [4],whichestablishedtheobjectivefunctionbythemostminimized structurecomplianceandbuildthevolumelimitastheconstraintcondition.Challis [5]usinga discretelevel-setmethodtosolvestructuraltopologyoptimizationandpresentamatlabcode.The reactiondiffusionequationswasintroducedtosolvethelevelsetfunctionmethodforstructural topologyoptimizationbyMasakiOtomori [6]andcreateanewtopologyoptimizationmethod,this articleisbasedonthemethodtocarryoutrelevantbidirectionalimproveoptimization. …”