C 1 Discretizations for the Application to Gradient Elasticity
C 1 Discretizations for the Application to Gradient Elasticity
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C 1 离散化应用于梯度弹性
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
P. Steinmann
中科院分区：
文献类型：
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作者：
P. Fischer;J. Mergheim;P. Steinmann
对于梯度弹性力学的数值解，由于平衡方程中弱形式的应变梯度的出现，需要采用C1连续离散化方法。在本工作中，各种C1连续单元以及C1自然单元法的性能进行了研究，应用于非线性梯度弹性。在次参数三角形单元方面，采用了Argyris、Hsieh-Clough-Tocher和Powell-Sabin分裂单元。采用Bogner-Fox-施密特单元作为等参四边形单元。所有这些方法被应用到两个不同的数值例子和收敛行为的L2，H1和H2误差范数进行检查。
For the numerical solution of gradient elasticity, the appearance of strain gradients in the weak form of the equilibrium equation leads to the need for C 1-continuous discretization methods. In the present work, the performances of a variety of C 1-continuous elements as well as the C 1 Natural Element Method are investigated for the application to nonlinear gradient elasticity. In terms of subparametric triangular elements the Argyris, Hsieh–Clough–Tocher and Powell–Sabin split elements are utilized. As an isoparametric quadrilateral element, the Bogner–Fox–Schmidt element is used. All these methods are applied to two different numerical examples and the convergence behavior with respect to the L 2, H 1 and H 2 error norms is examined.