On dual conservation laws in planar elasticity
On dual conservation laws in planar elasticity
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平面弹性的对偶守恒定律
DOI：
10.1016/j.ijengsci.2004.01.002
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发表时间：
2004
影响因子：
6.6
通讯作者：
Shaofan Li
中科院分区：
文献类型：
--
作者：
Shaofan Li
基于应力函数形式，系统地研究了线平面弹性力学的对偶守恒律。基于Noether定理及其Bessel-Hagen推广，利用广义对称变换或Lie-Bäcklund变换，得到了平面弹性力学中一类新的对偶守恒律.这些对偶守恒律代表了互补势能的变分对称性，而这种变分对称性源于二维双调和方程的相容性条件的对称性。这些对偶守恒律的物理意义进行了简要的讨论。特别地，构造了一个对偶Eshelby张量，并与Eshelby能量动量张量进行了比较。
Dual conservation laws of linear planar elasticity theory have been systematically studied based on stress function formalism. By employing generalized symmetry transformation or Lie–Bäcklund transformation, a class of new dual conservation laws in planar elasticity have been discovered based on Noether theorem and its Bessel–Hagen generalization. These dual conservation laws represent variational symmetry properties of complementary potential energy, which stems from the symmetry properties of compatibility conditions––a biharmonic equation in two dimension. The physical implications of these dual conservation laws are discussed briefly. In particular, a dual-Eshelby tensor is constructed and compared with the Eshelby's energy momentum tensor.