STRUCTURAL TOPOLOGY OPTIMIZATION METHOD BASED ON MATERIAL-FIELD REDUCTION SERIES EXPANSION

摘要

Provided is a structural topology optimization method based on material-field reduction series expansion; the invention solves the problem of conventional density method topology optimization wherein computational efficiency is low because of excessive design variables, relative density requirements, or sensitivity filtering measures. By means of defining a bounded material field which takes relevance into account, a spectral decomposition method is used for transformation into a series of linear combinations of undetermined coefficients, and, taking those undetermined coefficients to be design variables, an optimization model is constructed on the basis of a cell density interpolation model; a gradient or non-gradient optimization algorithm is used to solve the topology optimization problem, and thus a topological configuration having clear boundaries is obtained efficiently. The method greatly reduces the number of design variables in density-based topology optimization, and also has the natural advantage of completely avoiding mesh dependency and checkerboard pattern problems. The method also inherits the advantages of the density method, such as its simple form and convenience in promotion in engineering, has a rapid speed of optimization solution, and ensures efficiency in the research and development of innovative topological designs of complex equipment structures.