A material-field series-expansion method for topology optimization of continuum structures

Abstract This paper proposes a new topology optimization method based on a material-field topology description and a reduced series expansion. Not only does the proposed method greatly reduce the number of design variables, it also inherently avoids checkerboard patterns and the mesh dependency of conventional density-based topology optimization methods. In the present method, the structural topology is represented by a bounded material field with spatial dependency. The correlation length is introduced here to control the length-scale of the topology distribution. After approximating the bounded material field as a linear function of a reduced set of undetermined coefficients by using a series expansion, the topology optimization problem is constructed in the form of finding the optimal coefficients of the material field with the minimum structural compliance. A standard, gradient-based algorithm incorporating the design sensitivity information is then used to solve the optimization problem effectively. Several examples are given to demonstrate the effectiveness and applicability of the proposed topology optimization method.

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