【摘要】 基于物质导数概念和直接微分法,将再生核质点法应用于形状设计灵敏度分析(DSA)中。导出了基于无网格近似的灵敏度方程,特别强调了在考虑形状函数关于设计变量的物质导数时无网格方法与有限元法的不同。通过对RKPM形状函数及其物质导数进行矩式显式表述,提高了无网格方法的计算效率。对两个二维线弹性问题进行了位移灵敏度和应力灵敏度分析,计算结果与解析解吻合的很好;同时通过对通常的RKPM和改进的RKPM计算耗时的比较,显示了该方法不仅有效,而且可以显著地提高计算效率。更多还原

【Abstract】 Based on the material derivative approach and the Direct Differentiation Method (DDM), the Reproducing Kernel Particle Method (RKPM) is developed further for shape design sensitivity analysis (DSA). DSA formulations based on meshless approximation are derived, and in particular, the differences between meshless method and FEM are stressed when taking material derivatives of shape functions with respect to design variables. A unique approach is presented to improve the efficiency of meshless methods, in which RKPM shape functions and their material derivatives are expressed explicitly in terms of kernel function moments. Two 2-D elasticity DSA examples are given. There is good agreement between the numerical results and the analytical results with regard to displacement sensitivities as well as stress sensitivities. In addition, comparison of time-consuming between the classic RKPM and the improved RKPM demonstrates that the present method can improve the efficiency of DSA markedly.更多还原