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Development of a nodal natural element method with applications to classical and gradient plasticity.

机译：开发了节点自然元素方法，并将其应用于经典可塑性和梯度可塑性。

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摘要

The method of natural neighbors was recently introduced as a means of generating a surface interpolating between various specified point values. In this study, we exploit a node-based natural element method resulting from the natural neighbor approximations constructed on the basis of a mixed formulation centered at nodes.; A stabilized conforming nodal integration scheme is implemented in the natural element method in conjunction with non-Sibsonian interpolation. In this approach, both the shape functions and the integration scheme are defined through use of first order Voronoi diagrams. The method illustrates improved performance and significant advantages over previous natural neighbor formulations; notably, patch tests are satisfied to near machine precision, and computational difficulties are overcome in near incompressible elasticity. A discussion on higher-order gradient calculations and a solution process for geometrically non-linear problems are also presented.; A variational principle of generalized Hu-Washizu type is established for strain-gradient plasticity, and its numerical implementation is presented. The higher-order stresses as well as the conventional ones are taken as Lagrange multipliers. The fields of primary unknowns, displacement and consistency parameter, are approximated by use of non-Sibsonian interpolants, and the gradients of the primary variables are represented by discontinuous interpolations over a nodal domain. The method enables the relaxation of continuity requirements and incompressibility constraints in strain-gradient elastoplastic problems. A solution algorithm with consistent linearization and discrete Kuhn-Tucker conditions is presented. An implementation for generalized strain-gradient plasticity with three material length parameters is also illustrated.
机译：最近引入了自然邻域方法，作为在各种指定点值之间生成曲面插值的方法。在这项研究中，我们利用基于节点的自然元素方法，该方法是基于以节点为中心的混合公式构造的自然邻居近似结果。结合非Sibsonian插值的自然元法实现了一种稳定的顺应性节点积分方案。在这种方法中，形状函数和积分方案都是通过使用一阶Voronoi图定义的。该方法比以前的天然邻苯二甲酸酯制剂具有更高的性能和明显的优势。值得注意的是，贴片测试满足了接近机器的精度要求，并且克服了不可压缩弹性附近的计算难题。还讨论了高阶梯度计算和几何非线性问题的求解过程。建立了广义Hu-Washizu类型的变分原理以求应变梯度塑性，并给出了其数值实现方法。高阶应力与常规应力一样，被视为拉格朗日乘数。主要未知数，位移和一致性参数的字段通过使用非西伯逊插值来近似，主要变量的梯度由节点域上的不连续插值表示。该方法可以缓解应变梯度弹塑性问题中的连续性要求和不可压缩性约束。提出了具有一致线性化和离散Kuhn-Tucker条件的求解算法。还说明了具有三个材料长度参数的广义应变梯度可塑性的实现。

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  • 作者

    Yoo, Jeong Wahn.;

  • 作者单位

    Northwestern University.;

  • 授予单位 Northwestern University.;
  • 学科 Engineering Civil.; Engineering Mechanical.
  • 学位 Ph.D.
  • 年度 2003
  • 页码 108 p.
  • 总页数 108
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 建筑科学;机械、仪表工业;
  • 关键词

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