Improvement of the solution convergence rate for an elastic shell driven by a vibratory constraint using analytical-numerical matching

Abstract

A three-dimensional elastic shell is driven by the motion of an attached support and the solution is constructed using the method of analytical-numerical matching (ANM) with finite-element analysis and the structural-acoustic scattering code sonax. First, the area around the structural constraint is resolved in great detail as a separate local three-dimensional FEA solid model. Second, a Love–Timoshenko shell-type model of the local region is solved analytically for a set of smooth forces that will be applied to the full three-dimensional shell in place of the constraint. Third, the model of a full three-dimensional shell with end caps is analyzed in sonax, with the smooth forces applied on a mode-by-mode basis. The complete solution to the original problem is the superposition of the solutions of each of the subproblems described. Note that the high modal content of the original problem is contained in the high-resolution separate local problem (small domain), leaving only low modal content in the global (large domain) problem that is solved using sonax. This sample problem demonstrates the ability of ANM to enhance the capabilities of sonax and to improve the convergence rate (and overall computation time) for problems of this type. [Work sponsored by ONR.]