层合结构Hamiltonian元弱形式的辛方法

Symplectic algorithm for weak formulation of Hamiltonian element in laminated structure

文章基于力学平衡方程,在柱坐标系下,导出正交各向异性层合柱壳混合方程和边界条件算子的弱形式,继而给出层合结构的Hamilton正则方程,建立半离散半解析的Hamiltonian元的微分方程,用弱形式给出的微分方程和边界条件对函数的连续性要求降低了,用于解决实际的工程问题常常比原始的微分方程更逼近真正解;针对其Hamiltonian元的矩阵结构,构建分析计算Hamiltonian元弱形式的辛方法,Hamilton结构在辛约化过程中得到充分保证,文中提出的辛方法简易可行,具有较强的有效性和稳定性。

It was presented of weak formulations of mixed equations including boundary conditions of laminated cylindrical shell in a cylindrical coordinate system based upon the mechanical equilibrium equation.Hamilton canonical equation of laminated structure was established,and then semi-discrete and semi-analytical differential equation of Hamiltonian element was set up.The differential equations and boundary conditions given in weak formulation make the requirements for the continuity of functions relaxed,and for the actual physical problem,it often more approaches the true solution than the original differential equations.The symplectic algorithm for testing Hamiltonian matrix structure was established in the process of reducing Hamiltonian matrix.This method works with symplectic similarity transformation which reflects the structure of the Hamiltonian matrices.This algorithm is simple and feasible,and has preferable validity and stability.