STUDY ON SCALED BOUNDARY FINITE ELEMENT METHOD FOR PLATES AND SHELLS UPON SCALING FACE AND HAMILTON SYSTEM

Based on a Hamiltonian system, a scaled boundary finite element method (SBFEM) is established for the numerical simulation of plates and shells. Unlike the classical SBFEM, which takes a point as the scaling center, the method proposed takes a circumferential boundary face as the transformation center of the plates and shells. And, in the novel SBFEM, the surface of structures is discretized with two-dimensional spectral elements. The transformation relationship between the boundary face and the scaling face are established, and the governing equations with the scaling face based on the Hamiltonian system are derived. At the same time, for the coefficient matrix with local radial parameter as the variable, the Hamiltonian coefficient matrix of the equation is determined by quadratic polynomial fitting, and the expressions of the stiffness matrix and the nodal displacement function of the structures are obtained. The proposed SBFEM based on scaling face is established and solved upon three-dimensional solid theory, which effectively overcomes the locking problem of traditional finite element in the plates and shells. The method proposed is suitable for plates and shells with varying thickness and arbitrary shapes. The accuracy and correctness of the model are verified by classical numerical examples.