基于Kriging插值无网格法的动力弹塑性分析  

Dynamic elastoplastic analysis by using meshless Kriging interpolation method

作　　者：熊勇刚[1,2] 田万鹏[1] 陈科良[1] 陈云飞[2] 杜民献[1] 吴吉平[1] 

机构地区：[1]湖南工业大学机械工程学院,湖南株洲412007 [2]东南大学机械工程学院,江苏南京210000

出　　处：《中南大学学报（自然科学版）》2014年第2期435-440,共6页Journal of Central South University:Science and Technology

基　　金：国家自然科学基金资助项目(51345005);江苏省博士后基金资助项目(1202003B);湖南省自然科学基金资助项目(13JJ9014)

摘　　要：为了克服移动最小二乘近似难以准确施加本质边界条件的缺点,将滑动Kriging插值引入无单元Galerkin法中,与非线性瞬变动态理论相结合,提出动力弹塑性分析的Kriging插值无网格法,推导Kriging插值无网格法在动力弹塑性问题中的理论公式,给出求解方案。研究结果表明:采用所提方法计算仅需要离散节点的信息,因而处理变得简单;采用预校正形式的Newmark法进行时间离散,计算效率提高;通过2个经典数值算例与有限元软件ABAQUS的计算结果对比,验证了所提理论和方法的正确性与可行性。Because the shape fimctions constructed by the moving least squares approximation do not possess the Kronecker delta property, accurate imposition of essential boundary conditions in the traditional element free Galerkin （EFG） method is often difficult, the moving Kriging interpolation procedure was introduced into EFG method to be the meshless Kriging interpolation method （MKIM）. On the basis of MKIM and nonlinear transient dynamic theory, the MKIM for dynamic elastoplastic analysis was presented. The results show that only a group of discretized nodes is needed and therefore the preprocessing of this method is very simple. The predictor-corrector form of the Newmark algorithm is employed for the time integration scheme. Several numerical examples are presented to verify the validity and accuracy of the presented method.

关 键 词：无网格法 滑动Kriging插值 动力响应 弹塑性 

分 类 号：O344[理学—固体力学]