Abstract

ABSTRACT This paper deals with an adaptive refinement technique of a B-spline degenerate shell finite element model, for the free vibration analysis of curved thin and moderately thick-walled structures. The automatic refinement of the solution is based on an error functional related to the density of the total potential energy. The model refinement is generated by locally increasing, in a sub-domain R of a local patch domain, the number of shape functions while maintaining constant the functions polynomial order. The local refinement strategy is described in a companion paper, written by the same authors of this paper and presented in this Conference. A two-step iterative procedure is proposed. In the first step, one or more sub domains to be refined are identified by means of a point-wise error functional based on the system total potential energy local density. In the second step, the number of shape functions to be added is iteratively increased until the difference of the total potential energy, calculated on the sub domain between two iteration, is below a user defined tolerance. A numerical example is presented in order to test the proposed approach. Strengths and limits of the approach are critically discussed. INTRODUCTION Finite Element (FE) techniques are widely used for modeling the vibration behavior of industrial component and structures. Within the FE method, the infinite dimensional solution space is approximated with a finite dimensional one, consequently the obtained solution is usually approximated. In order to reduce the error, the user is usually involved in an iterative,time consuming process, in order to improve the accuracy of FE analysis results and keep low its computational cost. Efficient adaptive procedures can help users improving the accuracy of computed eigensolutions, by means of automatic, optimal, mesh refinement.