An isogeometric-analysis-based stiffness and mass spreading method for topology optimization of trusses subjected to dynamic loads in time domain

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Journal of Vibration and Shock ›› 2024, Vol. 43 ›› Issue (20) : 85-93.

JIANG Xudong1，NIU Qiancheng1，TENG Xiaoyan2，WU Ziwang1，WU Hao1，LIAN Shanli3

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Abstract

This paper proposes the isogeometric-analysis-based stiffness and mass spreading method for topology optimization of trusses under transient loads to achieve their lightweight design with high load-bearing capability. Through the energy equivalence principle, both the stiffness and the mass matrixes are projected to the isogeometric background mesh, respectively. Subsequently, the isogeometric FEM of trusses is developed for transient analysis, which is effectively solved by unconditionally stable implicit Newmark’s scheme. We model the dynamic layout optimization of trusses for compliance minimization while constraining the volume of trusses. Based on the discretize-then-differentiate approach, the corresponding adjoint equations are derived for the transient problem, such that the sensitivity analysis is consistently computed on the discretized system in both space and time. Then, several 2D and 3D numerical examples are presented to verify the proposed method. The numerical results demonstrate that this approach has the potential to perform the layout design of trusses for the maximal dynamic stiffness, and thereby provides the wide application prospects in practical engineering.

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topology optimization / compliance minimization / elastodynamics / isogeometric analysis / stiffness and mass spreading method / truss

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JIANG Xudong1, NIU Qiancheng1, TENG Xiaoyan2, WU Ziwang1, WU Hao1, LIAN Shanli3. An isogeometric-analysis-based stiffness and mass spreading method for topology optimization of trusses subjected to dynamic loads in time domain[J]. Journal of Vibration and Shock, 2024, 43(20): 85-93

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