Two-Dimensional Fixed Grid Based Finite Element Structural Analysis
Two-Dimensional Fixed Grid Based Finite Element Structural Analysis
复制标题
基于二维固定网格的有限元结构分析
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
G. Mullineux
中科院分区：
文献类型：
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作者：
Peter D. Dunning;H. Kim;G. Mullineux
本文介绍了一种新的基于经典有限元等参公式的固定网格结构分析方法。固定网格法在基于边界的优化中很流行，因为它们避免了网格扭曲问题，而且重分析简单有效。基于面积比的固定网格法因其实现简单而常被采用。然而，由于刚度的均匀化，最大误差出现在边界上。此外，误差与面积比有关，从而在边界上产生不希望看到的误差变化。等参数固定网格法的目的是在不显著降低面积比公式效率的情况下减少误差对面积比的依赖。二维等参法根据边界单元的内部区域形状将边界单元分为三类。采用双线性等参列式建立了四边形单元，并利用单元形状的先验信息导出了单元刚度矩阵的代数表达式。将三角形单元表示为常应变三角形，用四边形单元矩阵和内部单元矩阵的线性插值法逼近单元刚度矩阵。用数值算例比较了以拟合网格为基线的等参固定网格法和面积比固定网格法在位移误差计算中的应用。算例表明，等参数固定网格法在精度上有一定的优势，但也揭示了有待改进的地方。
This paper introduces a new fixed mesh structural analysis technique based on isoparametric formulations from classic finite element analysis. Fixed mesh methods are popular in boundary based optimisation as they avoid mesh distortion problems and reanalysis is simple and efficient. The area ratio based fixed grid method is often employed due to its favourable simplicity in implementation. However, maximum errors occur along the boundary due to homogenization of stiffness. Also errors are area ratio dependant, producing an undesirable variation of errors along the boundary. The aim of the isoparametric fixed grid method was to reduce the error dependency on area ratio without significantly reducing the efficiency of the area ratio formulation. The two dimensional isoparametric method divides boundary elements into three types depending on their inside area shape. Quadrilateral elements were formulated using a bilinear isoparametric formulation and an algebraic expression for the stiffness matrix was derived using a priori information about the element shape. Triangular elements were formulated as constant strain triangles and pentagonal element stiffness matrices were approximated by linear interpolation of quadrilateral and inside element matrices. Numerical examples were used to compare the isoparametric to the area ratio fixed grid method using a fitted mesh as a baseline for displacement error calculation. The examples showed some promising benefits in accuracy of the isoparametric fixed grid method, but also revealed areas for improvement.