固体静力学边值问题的光滑粒子解法  

Smooth particle method for the static boundary value problem of solids

作　　者：陈丁[1] 黄文雄[1] 张旭明[1] CHEN Ding;HUANG Wenxiong;ZHANG Xuming(College of Mechanics and Materials,Hohai University,Nanjing 211100,China)

机构地区：[1]河海大学力学与材料学院

出　　处：《河海大学学报（自然科学版）》2018年第4期329-336,共8页Journal of Hohai University(Natural Sciences)

基　　金：国家自然科学基金(11172088);江苏省普通高校研究生创新计划项目(KYZZ16_0268)

摘　　要：针对固体静力变形边值问题的特点,基于SPH的区域粒子离散原理构建了一种光滑粒子静力学(SPS)解法,并从2个方面入手,在保持一定计算量的同时提高了数值方法的精度。其一是应用最小势能原理来取代强形式的平衡方程,建立控制方程,能够降低对位移连续性的要求,避免了位移二阶导数的计算以及由此带来的数值误差;其二是提出一种新的边界处理方法,能够完全摆脱通过布置虚粒子的处理方式。最后,通过数值算例表明了数值方法的有效性。With respect to the property of static boundary value problem of solids,a smooth particle static(SPS)method is developed based on the particle discretization of spatial domain.To increase the accuracy of numerical method and maintain the amount of calculation,the governing equations are established through the application of principle of minimum potential energy,rather than using the strong form of equilibrium equation.The approach avoids the use of second-order derivatives of displacement and reduces related errors.An alternative integration method over the supportive domain is proposed which allows a direct treatment of boundary condition without virtual particles along boundary.Numerical examples are presented to demonstrate the good performance of the proposed method.

关 键 词：光滑粒子静力学法 固体变形 边值问题 最小势能原理 边界条件处理 

分 类 号：O34[理学—固体力学] O242[理学—力学]