The finite particle method (FPM), a novel numerical analysis approach for simulating structural statics and dynamics, is introduced into the field of structural optimization through the development of a new structural sensitivity analysis procedure. Using FPM, we can analyze static and dynamic structural responses, including typical nonlinear behaviors, based on a system composed of a finite number of particles. The new sensitivity analysis procedure integrates seamlessly with the general time-difference scheme of FPM. In the initial application of this sensitivity analysis procedure, we focus on the static optimization of truss structures. Optimization strategies tailored to truss structures are developed by predicting static responses via FPM. The positions of improperly placed particles are adjusted through particle fusion and projection strategies to achieve a reasonable configuration, enabling collaborative size, shape, and topology optimization. Various 2D and 3D numerical examples demonstrate the effectiveness and efficiency of the static optimization framework, made possible by the new sensitivity analysis procedure and FPM.

中文翻译：

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通过有限粒子法优化桁架结构的尺寸、形状和拓扑


有限粒子法 （FPM） 是一种用于模拟结构静力学和动力学的新型数值分析方法，通过开发新的结构敏感性分析程序，被引入结构优化领域。使用 FPM，我们可以基于由有限数量粒子组成的系统来分析静态和动态结构响应，包括典型的非线性行为。新的灵敏度分析程序与 FPM 的一般时差方案无缝集成。在这个敏感性分析程序的初始应用中，我们专注于桁架结构的静态优化。为 Truss 结构量身定制的优化策略是通过 FPM 预测静态响应来开发的。通过粒子融合和投影策略调整放置不当的粒子位置，实现合理的配置，实现协同大小、形状和拓扑优化。各种 2D 和 3D 数值示例证明了静态优化框架的有效性和效率，这得益于新的灵敏度分析程序和 FPM。