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In this study, the numerical manifold method (NMM), coupled with material interpolation, is applied to the topology optimization of continuum structures. Quadrilateral element (Q4) meshes are used in the NMM for mathematical cover. The order of the local approximation function is increased to improve the accuracy of the analysis. This method usually leads to linear dependency of the global degrees of freedom, as reflected in the rank deficiency of the global approximation space. However, using Q4 elements, the rank deficiency value is not fixed with mesh refinement. The presented solution handles this problem, and the efficiency of the proposed method is investigated with four examples. The results indicate that the high-order numerical manifold method (HONMM) has great accuracy in the analysis and works well for topology optimization problems. One advantage of using the combined HONMM with material interpolation in topology problems is chequerboard-free patterns, owing to mathematical cover and high-order analysis.

Topology optimization based on the high-order numerical manifold method by implementing a four-node quadrilateral element