A high-order polygonal element in structural dynamics

Abstract eng:
A high-order polygonal element of arbitrary order and geometry is developed for the dynamic analysis in computational solid mechanics. This polygonal element may have any number and shape of edges as long as a point from which the entire boundary is visible can be identified. Only the boundary is discretized into elements. An edge can also be subdivided into arbitrary number of elements of any order. The inertial effect within the polygon is represented by a high-order mass matrix. No internal mesh is required. The high-order polygonal element is constructed by applying the scaled boundary finiteelement method. An equation for the dynamic stiffness matrix with respect to the degrees of freedom on the boundary is formulated. A continued fraction solution of the dynamic stiffness matrix is obtained recursively. The equation of motion of the polygonal element is formulated by introducing auxiliary variables. A high-order static stiffness matrix and a high-order mass matrix are defined. This polygonal element can also be seamless coupled with standard finite elements when the same shape functions are used on the common edges. A parametric study of the convergence of the solution with increasing order of continued fraction is carried out. Rapid convergence is observed. It is shown that 3-4 terms of continued fraction is sufficient to model one wavelength. Numerical examples demonstrate that the high-order polygonal element of arbitrary order and geometry reduces both the effort in mesh generation and the computer running time.

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