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裂纹扩展过程模拟的无网格流形MSIM方法

ISSN号：1672-7207
期刊名称：《中南大学学报：自然科学版》
时间：0
分类：TU411[建筑科学—岩土工程;建筑科学—土工工程]
作者机构：[1]中国电建集团华东勘测设计研究院有限公司,浙江杭州310014, [2]浙江中科依泰斯卡岩石工程研发有限公司,浙江杭州310014, [3]同济大学地下建筑与工程系,上海200092
相关基金：国家自然科学基金资助项目（10972161）;国家重点基础研究发展计划（“973”计划）项目（2011CB013800）

关键词：无网格方法, 数值流形方法, 单位分解法, 有限覆盖理论, 裂纹扩展, Shepard函数, meshless method, numerical manifold method, partition of unity, finite cover theory, crack propagation, Shepard function

中文摘要：

采用一种新的无网格流形MSIM方法来进行裂纹扩展过程的模拟分析。该方法利用单位分解法和有限覆盖技术来构造插值函数，该插值函数的建立不受域内不连续面的影响，可较好地求解裂纹扩展问题；此外，该插值函数还具有高阶完备性、一致性，且可以在需要的节点处具备delta属性，能够方便、准确地施加各种边界条件。与通常的无网格方法相比，该方法由于采用了有限覆盖技术，试函数的构造不受域内不连续面的影响，克服了传统的无网格方法在处理不连续问题时由于采用光线法所遇到的困难；与数值流形方法相比，该方法用一系列节点的影响域来建立有限覆盖和单位分解函数，具有无网格方法的特性，摆脱了传统数值流形方法中在处理复杂非连续问题时网格所带来的困难，且其覆盖系统的生成远比数值流形方法中覆盖系统的生成简单。数值算例结果表明本文方法用于追踪复杂应力状态下裂纹扩展过程的正确性和有效性。

英文摘要：

A newly proposed meshless Shepard interpolation method （MSIM） interpolation was employed for the simulation of crack growth. The shape functions in this method were formed by the partition of unity and the finite cover technology, so the shape functions are not affected by discontinuous domains and crack problems can be more properly treated. This MSIM shape function possesses three distinguished features： the interpolation property, the arbitrarily high order consistency, and satisfy delta property at any desired node. Thus the essential boundary conditions can be treated as easily as they are in finite element method （FEM）. Compared with the conventional meshless methods, the shape functions are not influenced by the discontinuities in the solution domain because finite cover technology is used. Compared with the numerical manifold method, the finite covers and the partition of unity functions are formed by using the influence domains of a series of nodes with advantages over the mesh-based numerical manifold method, and the algorithm for the finite covers of the MSIM is much simpler than the popular finite cover method based on the finite meshes. Numerical examples indicate the advantages and the accuracy of the present method for the analysis of cracks propagation.

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