Theory Research And Application On Topology Optimization Of Engineering Structures

Optimization is the procedure of obtaining the best results under givenconditions. The purposes of structure optimization are economical materials usageand reasonable stress distribution. Structure optimization usually includes sizeoptimization, shape optimization and topology optimization. As is known to all that thefield of the application of structural topology optimization is steadily growing, forthe efficient use of structures and mechanical components is more important thanthat of sizing or shape optimization. It extends the abilityof engineer to master theforce-transmitting or thermo-transmitting path in the early design stage, andshorten the design cycle. An improved structure topology could enhance thestructureperformanceordecreaseweightofit,andthisleadtomorebenefit.Topologyoptimizationisnowamost challengingtopicinthefieldofstructuraloptimization. Topology optimization aims at finding the optimal distribution ofmaterials in a prescribed design domain and the optimal way of componentconnection in a discrete structure. It is a valuable tool for designers since it canprovide novel conceptual designs. Topology optimization that is one of the majorsubjects ofoptimizationresearchuptodate,usuallyneeds todeterminemanymoreparameters than size optimization and shape optimization. However, it can beobtainedmorebenefitsothatitismoreattractivefordesignengineer.It iswellknownthattopologyoptimizationofcontinuumstructureisoneofthemajor challenges because of difficulty to establish a good geometric model whichcomprising a large number of design variables, and complexity of optimizationalgorithm. During the past two decades, theory of topology optimization has beendeveloped for structural and mechanical systems, including micro-structure andmacro-structure methods. Additionally, many optimization techniques have beendeveloped and applied, such as Mathematical Programming, Genetic Algorithm,and EvolutionaryOptimization. Although a lot of achievements have been made intopologyoptimization,therearestillsomeproblemsneedfurtherexplorations.The following five aspects are deeply investigated in this paper: topologymaterial interpolationschemefor continuum structure,optimizationalgorithms, themethods to overcome numerical instabilities in calculation, the applications inengineeringstructuredesign.Theconceptoftopologyis firstintroducedinthearticle,andthen,thetopologyoptimization principle, the method as well as the optimized algorithm etc havecarriedontheconcreteintroduction.Secondly, the material interpolation schemes- SIMP method are deeplyresearched, an optimization model based on SIMP method of continuum structureisestablished. After that, aneffectivesolvingmethod-optimizationcriteriamethodis adopted, and the update scheme for the density is deduced. Finally, a series ofstructure analyses and topology optimization designs are implemented byprogramminginMATLAB.Following, the numerical instabilities such as porous, checkerboard,mesh-dependency and local minima which exist in topology optimization areanalyzed. Some methods are studying and comparing. The numerical instabilitiesintopologyoptimizationcanbeeffectivelyeliminatedwiththesealgorithms.At last,the above theoryandalgorithm fortopologyoptimizationof continuumstructure is applied on the study of engineering structure component by usingHyperworks,the structure Finite Element Method software which is supplied byAmerican Altair Software Corporation. The simulation results show that theresearchiscorrectandeffective,andithasaverybroadapplicationprospects.