The Research Of Structure Topology Optimization Based On Variable Density Method

Structure optimization usually includes size optimization, shape optimizationand topology optimization. The purposes of structure optimization are economicalmaterials usage and reasonable stress distribution. Topology optimization extendsthe ability of engineer to master the force-transmitting or thermo-transmitting pathin the early design stage, and shorten the design cycle. An improved structuretopologycouldenhancethestructureperformance ordecreaseweight ofit,andthisleadtomorebenefit.Sotopologyoptimizationis moreimportantthanthatofsizingorshapeoptimization.Topology optimization is now a most challenging topic in the field ofstructural optimization. Topology optimization of continuum structure is the mostchallenging and difficult, as well as hot research topic in structure optimizationbecauseofdifficultytoestablish agoodgeometricmodel whichcomprisingalargenumber of design variables, and complexity of optimization algorithm. Theresearch to topology optimization has the count for much theory significance andtheprojectapplicationprospect.Thereinafter,fivepartsofcontentareresearchedinthispaper.The first part, the current domestic and foreign research present situation arediscussedindetail.The second part, introduced thefinite element analysis and it's basic mentality,thesolutionstep,theanalysis flowas wellas thefiniteelement model criterionandtheperformanceindex,whichhavelaidthefoundationforthenextchapteroffiniteelementanalysis. The third part, the material interpolation schemes- SIMP method are deeplyresearched, an optimization model based on SIMP method of continuum structureis established. After that, optimization criteria method is adopted, and the updatescheme for the density is deduced. Following, the numerical instabilities such ascheckerboard, mesh-dependency and local minima which exist in topologyoptimizationareanalyzed.The fourth part, the above theory and algorithm for topology optimization ofcontinuum structure is applied on the study of optimization design with the finiteelement optimization procedure to the plane and the three dimensional simplestructure, the result has indicated this optimized method is validity and theaccuracy.Finally,thelastsectionissummarizationandexpectation.