By using new dual vectors,dual differential matrix and orthogonality relationship,a new solution method by igenfunction expansion for an elastic system with one continuous coordinate is establishen based on the theory of ordinary differential eguations.
以常微分方程的理论为基础,利用新的对偶变量、对偶微分矩阵和正交关系,以单连续坐标弹性体系为例,建立了与弹性力学求解新体系平行的特征函数展开解法。
While Hamiltonian system was led to solution of elastic theory a new systematic methodology for theory of elasticity was established and a symplectic orthogonality relationship was presented (Zhong Wanxie, 1995).
利用平面弹性与板弯曲的相似性理论,将弹性力学新正交关系中构造对偶向量的思路推广到各向同性薄板弹性弯曲问题,由混合变量求解法直接得到对偶微分方程并推导了对应的变分原理。
We studied the links between orthogonality relations and inverse formulas.
对正交关系与反演公式之间的联系进行了一些探讨 ,并对其几种具体表现形式进行了讨
The new orthogonal relationship is generalized for orthotropic elasticity of three_dimensions.
新的正交关系被推广到正交各向异性三维弹性力学· 将弹性力学新正交关系中构造对偶向量的思路推广到正交各向异性问题· 将弹性力学求解辛体系的对偶向量重新排序后,提出了一种新的对偶向量· 由混合变量求解法直接得到对偶微分方程· 所导出的对偶微分矩阵具有主对角子矩阵为零矩阵的特点· 由于对偶微分矩阵的这一特点,对于正交各向异性三维弹性力学发现了2个独立的、对称的正交关系· 采用分离变量法求解对偶微分方程· 从正交各向异性弹性力学求解体系的积分形式出发,利用一些恒等式证明了新的正交关系· 新的正交关系不但包含原有的辛正交关系,而且比原有的关系简洁· 新正交关系的物理意义是对偶方程的解关于z坐标的对称性的体现· 辛正交关系是一个广义关系,但辛正交关系可以在一定的条件下以狭义的强形式出现· 新的研究成果将为研究正交各向异性三维弹性力学的解析解和有限元解提供新的有效工具·
In a new systematic methodology for two\|dimensional elasticity, a new dual differential matrix L is presented by the dual vectors over again sorted in the paper of Zhong Wanxie and a new orthogonal relationship is discovered for isotropic plane problems.
在平面弹性力学求解新体系中,将文献[2]对偶向量进行重新排序后,提出了一种新的对偶微分矩阵L,对于各向同性平面问题发现了一种新的正交关系。
Orthogonality of proper function and its derivative from second imension green s indentity in pole form guide are proved and the conclusion is got that whether between proper functions or between field components, certain orthogonality exists.
无论是本征函数之间或是场分量之间,都存在着一定的正交关系。
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