摘要
为了提高在网格畸变时的数值计算精度,基于非对称有限单元的概念,提出US-FE-LSPIM四边形单元。该单元是利用传统的四节点等参元形函数集和FE-LSPIM四边形单元形函数集分别作为检验函数和试函数而构成。前者用于满足单元间和单元内的位移连续性要求,后者用于满足位移完备性要求。该单元结合了有限单元法和无网格法的优点,能方便地施加整段长度的位移边界条件。在分析几何非线性问题时,使用修正拉格朗日格式建立有限元方程,采用牛顿迭代法求解,编制了FORTRAN程序。数值算例表明,在规则网格和畸变网格下,US-FE-LSPIM四边形单元都具有很高的计算精度对网格畸变不敏感,性能优于传统的四节点等参元和QM6单元。
In order to improve precision of numerical calculation for distorted meshes, the US-FE-LSPIM QUAD4 element is developed based on the concept of unsymmetrie finite element formulation. This element is formed by using two different sets of shape functions for the trial and test functions, viz. sets of FE-LSPIM QUAD4 element shape functions and sets of classical isoparametrie shape functions. The former is used for requirements of intra-element and inter-element continuity in displacement field, and the latter is for requirements of completeness in displacement field. This element combines the strengths of finite element and meshfree methods, and could easily fulfil exact essential boundary condition along the entire length of the edge. ＂In the analysis of the geometrically nonlinear problems, the formulation is derived based on the updated Lagrangian formulation. An incremental and iterative solution procedure u-ing Newton-Raphson iterations is used to solve the problems. FORTRAN programme is made. Numerical examples show that the US-FE-LSPIM QUAD4 element exhibits superiority to classical four node isoparametric element and QM6 element, and possesses good precision for both regular and distorted meshes, insensitiveness to mesh distortion.
出处
《计算力学学报》
EI
CAS
CSCD
北大核心
2011年第5期785-791,共7页
Chinese Journal of Computational Mechanics
