Research Of Theory And Application About Topology Optimization Of Continuum Structure

This whole paper is focused on topology optimization of continuum structure, which isthe most challenging and difficult, as well as hot research topic in structure optimization. Thefollowing five aspects are deeply investigated in this paper: topology depicting method andmaterial interpolation scheme for continuum structure, optimization algorithms, the methodsto overcome numerical instabilities in calculation, the applications in MEMS design, and amodeling method including engineering constrains for topology optimization. On the contrastof different depicting methods of structural topology, a generalized formulation of topologyoptimization about continuum structure is provided and is used to find the optimal structuretopology with some structure response. Together with the method to eliminate numericalinstabilities, appropriate optimization algorithm is applied to solve the topology optimizationproblem stably and effectively. These algorithms are used in the design of MEMS componentsand solution of engineering problem. Topology depicting method and material interpolation schemes are basis of topologyoptimization and its application. The material interpolation schemes includinghomogenization method and SIMP method are deeply researched and the related formulationsare deduced. An optimization model based on SIMP method of continuum structure isestablished for the further research in theory and applications. Optimization solution algorithm is the most important in topology optimization.Algorithms fit for discrete structure and continuum structure are all investigated. Thecharacteristic and different using limit of both optimization criteria (OC) method andmathematics programming (MP) method are all analyzed in this paper. OC algorithm and theseries MMA (method of moving asymptotes) algorithm based on SIMP approach are deducedand used for the topology optimization problem of continuum structure. MMA algorithm hasa bad convergence but it has a high computational efficiency, while GCMMA is excellent onconvergence and stability with bad calculation efficiency. Aim to deal with thesedisadvantages of both MMA and GCMMA, some calculation control parameters in GCMMAis properly adjusted and modified. Meanwhile, a new hybrid MMA-MGCMMA algorithm isproposed. Numerical examples show that: the virtue of this mixed algorithm exists on that thecalculation efficiency can be greatly improved meanwhile the bad convergence or stabilitycan be avoided. The numerical instabilities exists in topology optimization is analyzed. A new mixedalgorithm combing local filter of convolution integral factor with whole filter of wavelet is IIintroduced on the base of studying and comparing some conventional methods to eliminatenumerical instabilities nowadays. The numerical instabilities, such as porous, checkerboardand mesh-dependency in topology optimization can be effectively eliminated with this mixalgorithm. This mixed algorithm is very concise in theory and convenient for programming,Therefore,it can be widely used in application. The above theory and algorithm for topology optimization of continuum structure isapplied on the study of MEMS component. Some design theory for special domains includingcompliant micro-mechanisms, coupling multi-physics problem and thermal conductionstructure are deeply researched. The related topology optimization models are establishedwhile the related algorithms are programmed and then realized with numerical examples.These topology algorithms for compliant micro-mechanisms, coupling multi-physicsproblems and thermal conduction structure are successfully used to study some typicalmicro-components. An optimization model including engineering constrains is proposed andis applied into some projects. With this method, an engineering-accepted topology result canbe achieved.