A mixed least squares method for solving problems in linear elasticity: formulation and initial results
A mixed least squares method for solving problems in linear elasticity: formulation and initial results
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解决线弹性问题的混合最小二乘法：公式和初始结果
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
S. Sture
中科院分区：
文献类型：
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作者：
M. Tchonkova;S. Sture
摘要 本文提出了一种求解线弹性问题的混合最小二乘有限元方法。 The developed numerical technique allows the use of separate unknowns for displacements and stresses, discontinuous interpolation functions for displacements, and the resulting linear system has a symmetric and positive definite coefficient matrix.线弹性问题的近似解是通过基于本构方程和平衡方程的最小二乘函数的最小化而获得的。所提出的方法是用 C 编程语言编写的原始计算机代码来实现的。其性能通过弹性理论的经典示例和众所周知的精确解析解进行测试。讨论了恒定位移双线性应力单元和双线性位移双线性应力单元的实施结果。
Abstract In this paper a mixed least squares finite element method for solving problems in linear elasticity is proposed. The developed numerical technique allows the use of separate unknowns for displacements and stresses, discontinuous interpolation functions for displacements, and the resulting linear system has a symmetric and positive definite coefficient matrix. The approximate solution of the linear elasticity problem is obtained by minimization of a least squares functional based on the constitutive equations and equations of equilibrium. The proposed method is implemented in an original computer code written in C programming language. Its performance is tested on classical examples from theory of elasticity with well-known exact analytical solutions. Results from the implementation of a constant displacement-bilinear stress element and bilinear displacement-bilinear stress element are discussed.