弹性力学的一种正交关系

A ORTHOGONALITY RELATIONSHIP FOR THEORY OF ELASTICITY

在弹性力学求解新体系中,将对偶向量进行重新排序后,提出了一种新的对偶微分矩阵,对于有一个方向正交的各向异性材料的三维弹性力学问题发现了一种新的正交关系。将材料的正交方向取为z轴,证明了这种正交关系的成立。对于z方向材料正交的各向异性弹性力学问题,新的正交关系包含弹性力学求解新体系提出的正交关系。

While the theory of Hamiltonian system was led to solution of elastic theory a new systematic methodology for theory elasticity was established. In the field of theory of elasticity a work platform was opened on which the solution methods was parallel to traditional solution methods and a series of results had be achieved. In a new systematic methodology for theory of elasticity a new dual differential matrix is presented by the dual vectors over again sorted and a new orthogonality relationship is discovered for anisotropic materials problems for three-dimensional theory of elasticity in which a direction is an orthogonal direction of materials. The orthogonal direction of materials is put on this direction of coordinate z and the new orthogonality relationship is proved. For anisotropic materials problems for theory of elasticity in which this direction of coordinate z is an orthogonal direction of materials the new orthogonality relationship includes the orthogonality relationship that is presented in a new systematic methodology for theory of elasticity. The orthogonality relationship of the system of dual vectors is a generalized relationship. The research of this paper indicates that the orthogonality relationship of the system of dual vectors may be appeared in a strong form with narrow sense in certain condition.