Topology Optimization Of Continuous Structure With Frequency Constraints And Software Development

Topology optimization of continuum structure has more design freedoms thanshape and size optimization, it can save material as more as possible and realizeoptimal distribution of material. Dynamic topology optimization of continuumstructure has widely application, such as aerospace, vehicle and bridge engineering.And dynamic topology optimization can reduce noise and vibration and improve themechanical properties of structure. Therefore, the research of dynamic topologyoptimization for continuum structure has not only theoretical significance but alsowide application. Based on Independent Continuous and Mapping method (ICM)proposed by Professor Sui Yunkang, in this paper we studied dynamic topologyoptimization problem of continuum structure, which is considering weight asobjective and eigenfrequencise as constraints. The main contents are summarized asfollows:(1) Based on ICM method, we studied the effect of filter function and therelationship between power function and exponential function. And the parameter inexponential function was determined according to power function. In the end, thetopology optimization formulation of continuous structure was established based onICM method, where the weight was considered as objective.(2) Combining with the power function and exponential function, the dynamictopology optimization formulation was established based on ICM method, whichconsidering minimizing the weight of structure and fundamental eigenfrequency asconstraint. The objective function was simplified by second-order Taylor expansion ofeigenvalue, and constraint function was explicitly expressed by first-order Taylorexpansion of eigenvalue. Then, the quadratic programming formulation that can besolved was formed. Finally, the effects of two types of filter functions to optimizationresult were compared by numerical examples.(3) We studied the dual sequence quadratic programming (DSQP) algorithm andthe global convergence method of moving asymptotes (GCMMA) algorithm. Then,the two algorithms were adopted to solve the quadratic programming formulation, andcompared the effects of two types of optimization algorithms to optimization result bynumerical examples.(4) As for numerical instabilities, the filter method was adopted to avoid checkerboard and grid dependency, localized eigenmodes was avoided by choosingproper filter parameters, the mode switch problem was eliminated by adding thedynamic constraint in dynamic optimization process. Numerical examples indicatedthat the method above can deal with the problem of numerical instability, effectively.(5) According to the theory above, we developed the optimization program usingPCL language based on Patran platform. And the GCMMA algorithm was integratedinto Patran, realized connection between Patran and Matlab. Then, the continuumstructure topology optimization program which considering weight as objective andfrequency as constraint is obtained. Numerical examples indicated that clear topologyconfiguration and optimization result can obtain through the optimization program.