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<p>In this paper, a smoothed nodal density-based topology optimization approach, that uses the Finite Element method as an analysis tool, is presented. The overall smoothness of the nodal density distribution is achieved following Shepard interpolation technique. These refined nodal densities are mapped spatially using material interpolation scheme to form the Density Distribution Function (DDF), rendering sufficient smoothness and continuity. Here the DDF is constructed using the B-spline basis functions of different degrees, as they possess non-negativity and range-bounded properties. Subsequently, the DDF is utilized to formulate the necessary elements of topology optimization related to structural problems. A variety of topology optimization problems, both in two and three dimensions, are solved to demonstrate the effectiveness of the proposed method in obviating islanding and mesh-dependency issues. Additionally, the effects of the degree of material interpolation function on the optimum topology of the structural problems are also studied.</p>

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Smoothed nodal density based structural topology optimization with B-spline-based material interpolation

  • 期刊论文

  • 发表日期：

    2026年1月28日

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  • Umesh Mishra,
  • Tejdeep Ganekanti,
  • Atanu Banerjee

摘要

In this paper, a smoothed nodal density-based topology optimization approach, that uses the Finite Element method as an analysis tool, is presented. The overall smoothness of the nodal density distribution is achieved following Shepard interpolation technique. These refined nodal densities are mapped spatially using material interpolation scheme to form the Density Distribution Function (DDF), rendering sufficient smoothness and continuity. Here the DDF is constructed using the B-spline basis functions of different degrees, as they possess non-negativity and range-bounded properties. Subsequently, the DDF is utilized to formulate the necessary elements of topology optimization related to structural problems. A variety of topology optimization problems, both in two and three dimensions, are solved to demonstrate the effectiveness of the proposed method in obviating islanding and mesh-dependency issues. Additionally, the effects of the degree of material interpolation function on the optimum topology of the structural problems are also studied.