Hansbo类有限单元法的非连续分片试验  

Discontinuous patch tests in Hansbo and Hansbo's type of methods

作　　者：凌道盛[1,2] 石吉森[1,2] 张如如[1,2] 王云岗[3] 

机构地区：[1]浙江大学软弱土与环境土工教育部重点实验室,浙江杭州310058 [2]浙江大学岩土工程研究所,浙江杭州310058 [3]浙江大学城市学院,浙江杭州310015

出　　处：《浙江大学学报（工学版）》2015年第11期2142-2150,共9页Journal of Zhejiang University：Engineering Science

基　　金：国家"973"重点基础研究发展计划项目(2014CB047000);国家自然科学基金资助项目(51278451);浙江省自然科学基金面上资助项目(LY12E08011);浙江省自然科学基金重点资助项目(LZ12E09001)

摘　　要：为了研究Hansbo和Hansbo类有限单元法的数值分析精度和稳定性,基于增强有限元法,对该类有限单元法进行非连续分片试验.结果表明,采用3节点三角形数学单元的网格能够以机器精度通过分片试验,采用4节点四边形数学单元的网格一般不能以机器精度通过分片试验,且计算精度与数学单元形状和刚度矩阵积分方法有关.理论分析证明,数学单元与物理单元分离引入数学单元与物理单元母单元间的非线性坐标变换和不同于数学单元的物理单元Jacobi行列式,导致单元刚度矩阵被积函数比常规有限单元复杂,降低数值积分精度.在非连续变形区域采用三角形或平行四边形数学单元、或将含裂纹物理单元精细划分成积分子域是保证Hansbo和Hansbo类方法高精度通过非连续分片试验的合理和有效方法.The discontinuous patch test designed by element method in order to study the computational of methods. The test results show that the meshes pass the discontinuous patch test in machine precisi lateral mathematical element generally fail, and the Dolbow etc. was conducted with the augmented finite precision and stability of the Hansbo ＆ Hansbo＇s type which adopted 3 node triangular mathematical element on, whereas the meshes which computational precision is highl metrical shape of mathematical element and the integration methods of stiffness ma adopted 4 node quadri y depended on the geo trix of the cracked ele ments. Further theoretical analysis reveals that the geometrical separation of mathematical and physical el- ement introduces the nonlinear natural coordinate transformation from physical element to mathematical el- ement and the Jacobi determinant of physical element. The integrand of element stiffness matrix is more complicated than that of standard finite element. The numerical integration accuracy was reduced, and the failure of the discontinuous patch test was induced. The theoretical and numerical analysis show that adop- ting triangular or parallelogram mathematical elements within the potential discontinuous deformation re- gion, and subdividing each cracked physical element into fine integrating subdomain are reasonable and effective ways to ensure the Hansbo ＆ Hansbo＇s type of methods to pass the discontinuous patch test in high precision.

关 键 词：非连续变形 分片试验 Hansbo和Hansbo类方法 增强有限单元法 数值积分 

分 类 号：TU411[建筑科学—岩土工程] TU472[建筑科学—土工工程]