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 引用本文: 侯国林 阿拉坦仓. 平面扇形域问题的新正交关系和变分原理[J]. 力学学报, 2011, 43(4): 731-736.
Guo-lin Hou Alatancang Chen. New orthogonality relationship of plane elasticity in sectorial region and its variational principle[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(4): 731-736.
 Citation: Guo-lin Hou Alatancang Chen. New orthogonality relationship of plane elasticity in sectorial region and its variational principle[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(4): 731-736.

## New orthogonality relationship of plane elasticity in sectorial region and its variational principle

• 摘要: 通过构造新的对偶向量, 用空间的环向坐标数学上比拟Hamilton体系的时间变量,在平面弹性扇形域问题中导出了一个斜对角Hamilton算子. 该算子具有主对角元为零,斜对角元是非零对称算子的结构特性. 得到两个独立的、对称的子正交关系.恰当选择对偶向量后, 直角坐标系下各向同性平面弹性问题的新正交关系被推广到极坐标情形. 根据控制微分方程的弱(积分)形式及相应的边界条件,建立了对应边值问题的变分原理, 并提出了相应的泛函表达式.

Abstract: In the plane elasticity sectorial region problem, an off-diagonal Hamiltonian operator is obtained by constructing new dual vectors and using virtual circumferential coordinate in spatial domain to mathematically analogize the time variable in temporal domain of Hamiltonian system. The operator possesses some structural characteristics that the elements of main diagonal are zero and skew diagonal entries are symmetric operators. Two independent and symmetrical orthogonality sub-relationships are discovered. By selecting dual vectors appropriately, the new orthogonality relationships in the rectangular coordinates are generalized into the polar coordinates for isotropic plane elasticity problems. By using integral form, a variational principle which is relative to differential form is derived, and moreover, a complete functional expression is proposed.

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