基于等几何刚度与质量扩散法的桁架结构动力学拓扑优化方法

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振动与冲击 ›› 2024, Vol. 43 ›› Issue (20) : 85-93.

论文

基于等几何刚度与质量扩散法的桁架结构动力学拓扑优化方法

江旭东1，牛乾成1，滕晓艳2，武子旺1，吴昊1，连善立3

作者信息 +

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

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

Author information +

文章历史 +

摘要

针对瞬态激励下桁架式结构的高承载轻量化设计问题，提出了基于等几何刚度与质量扩散法的桁架结构动力学拓扑优化方法。通过能量等效原理，将杆件单元的刚度与质量矩阵投影到弱材料等几何背景网格，构建桁架结构的等几何有限元动力学分析模型，利用无条件稳定的隐式Newmark时间积分方案求解结构的动态响应。以动柔度最小化为目标，以材料体积用量为约束，建立了桁架结构动力学布局优化模型。基于先离散-后微分敏度分析策略，推导了瞬态优化问题的伴随方程，在时-空离散的动力学系统上实施了一致性灵敏度分析。最后，通过2D和3D数值算例验证了所提方法的有效性。数值结果表明，提出方法可实现桁架式承力结构的动刚度性能优化设计，在实际工程中具有广阔的应用前景。

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.

导出引用

江旭东1, 牛乾成1, 滕晓艳2, 武子旺1, 吴昊1, 连善立3. 基于等几何刚度与质量扩散法的桁架结构动力学拓扑优化方法[J]. 振动与冲击, 2024, 43(20): 85-93

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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