Modified Mixed Variational Principle and the State-Vector Equation for Elastic Bodies and Shells of Revolution
Modified Mixed Variational Principle and the State-Vector Equation for Elastic Bodies and Shells of Revolution
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DOI：
10.1115/1.2893764
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发表时间：
1992-09
期刊：
影响因子：
--
通讯作者：
C. Steele;Y. Kim
中科院分区：
文献类型：
--
作者：
C. Steele;Y. Kim
针对一类以一个空间变量为自变量的问题，建立了一种改进的混合变分原理。具体应用于弹性体的三维变形和旋转壳的非对称变形。可能的新颖特征是在变分公式中消除了不能在边界上规定的应力分量。其结果是一个完全类似于动力系统经典力学的形式，其状态方程完全是汉密尔顿标准方程的形式。利用该方法可以很容易地确定使系统自伴随的场变量的正确尺度因子，并且可以有效地处理包括复合材料在内的各向异性材料。对考虑和不考虑横向剪切变形的旋转壳进行了分析。
A modified mixed variational principle is established for a class of problems with one spatial variable as the independent variable. The specific applications are on the three-dimensional deformation of elastic bodies and the nonsymmetric deformation of shells of revolution. The possibly novel feature is the elimination in the variational formulation of the stress components which cannot be prescribed on the boundaries. The result is a form exactly analogous to classical mechanics of a dynamic system, with the equations of state exactly in the form of the canonical equations of Hamilton. With the present approach, the correct scale factors of the field variables to make the system self-adjoint are readily identified, and anisotropic materials including composites can be handled effectively. The analysis for shells of revolution is given with and without the transverse shear deformation considered.