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A finite element formulation in boundary representation for the analysis of nonlinear problems in solid mechanics

机译：边界表示中的有限元公式，用于分析固体力学中的非线性问题

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The contribution is concerned with a numerical element formulation in boundary representation. It results in a polynomial element description with an arbitrary number of nodes on the boundary. Scaling the boundary description determines the interior domain. The scaling approach is adopted from the so-called scaled boundary finite element method (SBFEM), which is a semi-analytical formulation to analyze problems in linear elasticity. Within this method, the basic idea is to scale the boundary with respect to a scaling center. The boundary, which is denoted as circumferential direction, and the scaling direction span the parameter space. In the present approach, interpolations in scaling direction and circumferential direction are introduced. The interpolation in circumferential direction is independent of the scaling direction. The formulation is suitable to analyze problems in nonlinear solid mechanics. The displacement degrees of freedom are located at the nodes on the boundary and in the interior element domain. The degrees of freedom located at the interior domain are eliminated by static condensation, which leads to a polygonal finite element formulation with an arbitrary number of nodes on the boundary. The element formulation allows per definition for Voronoi meshes and quadtree mesh generation. Numerical examples give rise to the performance of the present approach in comparison to other polygonal element formulations, like the virtual element method (VEM). Some benchmark tests show the capability of the element formulation. A comparison to standard and mixed element formulations is presented. The present approach is perfectly suitable to model heterogeneous structures with inclusions and voids. It avoids also staircase approximation of curved boundaries. (C) 2018 Elsevier B.V. All rights reserved.
机译：该贡献与边界表示中的数字元素公式化有关。结果是在边界上具有任意数量的节点的多项式元素描述。缩放边界描述可确定内部区域。缩放方法是从所谓的缩放边界有限元方法（SBFEM）中采用的，该方法是分析线性弹性问题的半分析公式。在这种方法中，基本思想是相对于缩放中心缩放边界。边界（表示为圆周方向）和缩放方向跨越参数空间。在本方法中，引入了在缩放方向和圆周方向上的插值。圆周方向上的插值与缩放方向无关。该公式适合分析非线性固体力学中的问题。位移自由度位于边界上的节点和内部元素域中。静凝聚消除了位于内部区域的自由度，这导致边界上具有任意数量节点的多边形有限元公式。元素公式允许对Voronoi网格和四叉树网格生成进行定义。与其他多边形元素公式（例如虚拟元素方法（VEM））相比，数值示例可以提高本方法的性能。一些基准测试表明了元素配方的能力。介绍了与标准和混合元素配方的比较。本方法非常适合对包含夹杂物和空隙的异质结构进行建模。它还避免了曲线边界的阶梯近似。 （C）2018 Elsevier B.V.保留所有权利。

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