Abstract
Since the transversely isotropic elastic materials have been widely used in the fields of architecture, aviation and so on, the related mechanical calculation has become an important research topic. One of the most commonly used method is the semi inverse method with displacement or stress as the basic variable. However, this method can not describe the local deformation. In this paper, based on the variational principle and the method of separating variables, the basic equations of symplectic system are established. According to the characteristics of Hamiltonian matrix operators, all analytical solutions of transversely isotropic elastic plane are found, and a complete solution space is established. In the example, the boundary problem is studied, and the first five non-zero eigenvalue are obtained.
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