Reproducing kernel particle methods for large deformation analysis of non-linear structures
Reproducing kernel particle methods for large deformation analysis of non-linear structures
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DOI：
10.1016/s0045-7825(96)01083-3
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发表时间：
1996-12-15
影响因子：
7.2
通讯作者：
Liu, WK
中科院分区：
文献类型：
--
作者：
Chen, JS;Pan, CH;Liu, WK
提出了基于再现核颗粒方法（RKPM）的非线性弹性和非弹性结构的大型变形分析。该方法在计算中不需要明确的网格，因此在大变形分析中避免了网格失真困难。当前的配方考虑了超弹性和弹性塑料的材料，因为它们分别代表与路径无关和路径依赖性材料行为。在本文中，引入了材料内核函数和RKPM材料形状函数，以进行大型变形分析。 RKPM材料形状函数的支持覆盖了材料变形过程中相同的颗粒集，因此在大型变形计算中没有遇到张力不稳定。基本边界条件是通过使用转换方法引入的。如果使用RKPM材料形状函数，则在初始阶段仅形成一次转换矩阵。从再现条件的角度研究了目前矩阵及其导数的适当集成程序。在具有显式时间整合方法的瞬态问题中，在节点坐标上构建了总质量矩阵，以使质量在颗粒处集成。研究了几种超弹性和弹性性问题，以证明该方法的有效性。数值结果表明，由于其更平滑的形状函数，RKPM比有限元更有效地处理大型材料失真，因此在较大的变形下提供了更高的溶液精度。与常规的有限元方法不同，rkpm中的节点间距不规则性不会导致不规则的网格形状，从而显着恶化了溶液的精度。在将非线性RKPM应用于几乎不可压缩的超弹性和完美的可塑性问题时，未观察到容积锁定。此外，可以简单地通过在高度变形的区域中添加更多点而不会重新安排来实现RKPM中的模型适应性。
Large deformation analysis of non-linear elastic and inelastic structures based on Reproducing Kernel Particle Methods (RKPM) is presented. The method requires no explicit mesh in computation and therefore avoids mesh distortion difficulties in large deformation analysis. The current formulation considers hyperelastic and elasto-plastic materials since they represent path-independent and path-dependent material behaviors, respectively. In this paper, a material kernel function and an RKPM material shape function are introduced for large deformation analysis. The support of the RKPM material shape function covers the same set of particles during material deformation and hence no tension instability is encountered in the large deformation computation. The essential boundary conditions are introduced by the use of a transformation method. The transformation matrix is formed only once at the initial stage if the RKPM material shape functions are employed. The appropriate integration procedures for the moment matrix and its derivative are studied from the standpoint of reproducing conditions. In transient problems with an explicit time integration method, the lumped mass matrices are constructed at nodal coordinate so that masses are lumped at the particles. Several hyperelasticity and elasto-plasticity problems are studied to demonstrate the effectiveness of the method. The numerical results indicated that RKPM handles large material distortion more effectively than finite elements due to its smoother shape functions and, consequently, provides a higher solution accuracy under large deformation. Unlike the conventional finite element approach, the nodal spacing irregularity in RKPM does not lead to irregular mesh shape that significantly deteriorates solution accuracy. No volumetric Locking is observed when applying non-linear RKPM to nearly incompressible hyperelasticity and perfect plasticity problems. Further, model adaptivity in RKPM can be accomplished simply by adding more points in the highly deformed areas without remeshing.