Topology Optimization Of Continuum Structures Based On Discrete Wavelet Transform Compression

When applying structural topology optimization in large-scale engineering projects such as bridges,automobiles,airplanes,etc.,in order to obtain a clear and non gray scale topology diagram,it is necessary to set very fine meshes,resulting in too many degrees of freedom in the finite element model.However,in the variable density method of topology optimization,the number of design variables is equal to the number of degrees of freedom in the finite element model,which leads to a large increase in the calculation of the finite element analysis and optimization solution process,and the efficiency of topology optimization is low.In this paper,the projection function of variable density method for topology optimization is first studied,and a modified density filtering method based on Heaviside projection function is proposed;the mathematical model of topology optimization based on discrete cosine transform is discussed,and the efficiency of optimization process is improved by compressing the number of design variables;based on the fast algorithm of discrete wavelet transform in digital image compression,the mathematical model of topology optimization is established and verified by a typical numerical example.The projection function of variable density method for topology optimization is analyzed and discussed,and a modified density filtering method based on Heaviside projection function is proposed for improving a projection function.Compared with the problem of volume change before and after filtering in the original projection function,the formula is modified by introducing a threshold parameter to suppress the instability in the iterative process.The numerical results of the MBB beam and short cantilever show that the modified method can effectively suppress the volume change in the iterative process when using the method of moving asymptotes and sequential quadratic programming,thus reducing the running time,making the boundary of the optimized topology clear and improving the objective function value.The mathematical model of topology optimization based on discrete cosine transform is discussed.The design variables are compressed,and the distribution of virtual density is corrected by using the modified Heaviside projection function.The range of design variables and the selection of initial values are determined,and the influence of the number of design variables on the optimization results is analyzed.The numerical example results show that for the topology optimization problem of static compliance,compared with the traditional variable density method,the variable density method based on discrete cosine transform compression can reduce the calculation time by 95.5% when the number of design variables is reduced by 98.75%,and it can replace the numerical filtering method.Based on the fast algorithm of discrete wavelet transform compression,the mathematical model of topology optimization is established to compress the design variables,and the numerical instability is suppressed by the modified Heaviside projection function.The range of design variables is derived,and the influence of compression ratio and wavelet function on the optimization results is analyzed.The numerical examples of the MBB beam and short cantilever show that,for the topology optimization problem of static compliance,compared with the traditional variable density method,when the number of design variables is reduced by 98.44%,the variable density method based on discrete wavelet transform compression can reduce the calculation time by 95.6%,obtain the topological optimization results with clear boundary,accelerate the convergence of the optimization process,and replace the numerical filtering method.At the same time,the overall effect is equivalent to the variable density method based on discrete cosine transform compression.