SUPERCONVERGENT PATCH RECOVERY SOLUTIONS AND ADAPTIVE MESH REFINEMENT ANALYSIS OF FINITE ELEMENT METHOD FOR THE VIBRATION MODES OF NON-UNIFORM AND VARIABLE CURVATURE BEAMS

It presents a superconvergent patch recovery method for the superconvergent solutions of modes in the finite element (FE) post-processing stage of non-uniform and variable curvature curved beams. An adaptive method for the in-plane and out-of-plane free vibration of curved beams with variable cross-section is also proposed. In the post-processing stage of the displacement-based finite element method, the superconvergent patch recovery method and the high-order shape function interpolation technique are introduced to obtain the superconvergent solution of mode (displacement). Using the superconvergent solution of mode to estimate the error of the FE solution of mode in the energy form under the current mesh, an adaptive mesh refinement is proposed by mesh subdivision to derive the optimized mesh and accurate FE solution to meet the preset error tolerance. Numerical examples show that the proposed algorithm is suitable for solving the continuous orders for frequencies and modes in the in-plane and out-of-plane free vibration of different kinds of curve shapes, boundary conditions, non-uniform cross-section, and variable curvature forms of the non-uniform curved beams. The computation procedure can provide accurate solutions. The analysis process is efficient and reliable.