Dual Method for Problems of Transversely Isotropic Elastic Solids

For problems of transversely isotropic elasticity, the semi inverse method is usually adopted according to the Saint Venant principle in Euclidean space. However, the result of this method is not accurate since the local effect is neglected in the computation. In this paper, the governing equations of Hamiltonian system are constructed by using dual variables. According to the characteristics of Hamiltonian matrix operators and the method of variable separation, all the analytical solutions of transversely isotropic elastic plane is obtained, and the complete solution space is established. In fact, the solution of any problem can be expressed as a linear combination of these basic solutions. In the numericl calculation, the problem of fixed end constraints is studied, and the stress concentration caused by boundary constraints is described.