Topology optimization has developed rapidly in the past three decades; as a creative and efficient optimization technique, it has been applied in engineering fields of aerospace and mechanical. However, there are a few attempts in bridge form design. In this paper, the parametric level set method is utilized to solve the form finding of arch bridges. The optimization model for minimizing the structural compliance under the volume constraint is built. Three numerical examples of form finding of arch bridges are studied. Results show that the optimal structures which have well-distributed stress and smooth force transmission are almost identical with the actual forms of arch bridges. The optimal forms can be treated as alternatives in the preliminary design stage, and topology optimization has a bright prospect in form finding of arch bridges.

This paper presents a parametric level set-based method (PLSM) for multimaterial topology optimization of heat conduction structures with volume constraints. A parametric level set-based optimization model of heat conduction structures is built with multimaterial level set (MM-LS) model, which describes the boundaries of different materials by the combination of all level set functions. The heat dissipation efficiency which means the quadratic temperature gradient is conducted as the objective function. The adjoint method is utilized to calculate the sensitivities of the objective function with respect to expansion coefficients of the compactly supported radial basis functions (CSRBFs). The optimal configuration is achieved by updating the expansion coefficients gradually with the method of moving asymptotes (MMA). Several numerical examples are discussed to demonstrate effectiveness of the proposed method for multimaterial topology optimization of heat conduction structures.

As an implementation form of basis function, interpolation matrices (IMs) have a crucial impact on parametric level set method (PLSM)-based structural topology optimization (STO). However, there are few studies on compressing IM into triangular matrix (TM) with less storage and computation. Algorithm 1 using LU decomposition and Algorithm 2 using innovative asymmetric basis functions that transform the IMs of compactly supported radial basis functions (CSRBFs) into highly sparse TMs are proposed. Theoretical derivation and numerical experiments show that they effectively improve computational efficiency.

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