IUTAM Symposium on Multi-Functional Material Structures and Systems
IUTAM Symposium on Multi-Functional Material Structures and Systems
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IUTAM 多功能材料结构与系统研讨会
DOI：
10.1007/978-90-481-3771-8_30
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Natarajan S
中科院分区：
文献类型：
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作者：
Natarajan S
这一贡献在有限元不连续逼近的公式方面提出了两个进展。第一种方法依靠Schwarz-Christoffel映射在任意多边形域上进行积分[1]。当一个元素被分段连续的不连续分成两个子域时，每个多边形域被映射到一个使用体积规则的单位圆盘上。这样就不需要通常的两级等参贴图。第二种方法依赖于应用于间断有限元近似的应变光滑化。通过将应变场写成协调应变场的非局部加权平均，将有限元表面上的积分转化为边界积分，从而不需要对积分单元进行通常的细分，不需要等参映射，也不需要计算形(浓缩)函数的导数。给出了断裂力学和复合材料的计算结果，并从精度和简单性两方面对这两种方法进行了比较。感兴趣的读者可参考[1，6，13]了解更多细节，并应与作者联系，以获得用于获得本文结果的MatLab代码的版本。
This contribution presents two advances in the formulation of discontinuous approximations in finite elements. The first method relies on Schwarz-Christoffel mapping for integration on arbitrary polygonal domains [1]. When an element is split into two subdomains by a piecewise continuous discontinuity, each of these polygonal domains is mapped onto a unit disk on which cubature rules are utilized. This suppresses the need for the usual two-level isoparametric mapping. The second method relies on strain smoothing applied to discontinuous finite element approximations. By writing the strain field as a non-local weighted average of the compatible strain field, integration on the surface of the finite elements is transformed into boundary integration, so that the usual subdivision into integration cells is not required, an isoparametric mapping is not needed and the derivatives of the shape (enrichment) functions do not need to be computed. Results in fracture mechanics and composite materials are presented and both methods are compared in terms of accuracy and simplicity. The interested reader is referred to [1,6,13] for more details and should contact the authors to receive a version of the MATLAB codes used to obtain the results herein.