High-order complex Fourier numerical manifold method for improving the optimization of cracked structures

Abstract

In this paper, a combination of the high-order numerical manifold method with material interpolation is established with the goal of improving the optimization of cracked structures. Complex Fourier shape functions, known for their inherent advantages, are utilized as weight functions in the numerical manifold method. By implementing high-order analysis, the occurrence of checkerboard patterns is effectively avoided. In addition, a modified sensitivity filtering technique is introduced to address the issue of mesh dependency and minimum length scale in the final topology. This technique is based on the notion of a manifold element. Furthermore, a methodology is introduced to represent void regions within the design domain without the need for passive elements. This methodology involves describing an algorithm to accurately determine the manifold element and the corresponding element area within the final topology. Numerical problems of topology optimization are presented to examine all the aforementioned advantages. The findings indicate that the proposed algorithm for topology optimization does not exhibit any instances of checkerboard patterns. Moreover, the final topology of the curved void regions does not show any zigzag patterns. The above method demonstrates a commendable rate of convergence, and the final topology of the cracked regions can be conveniently simulated.