变截面变曲率梁振型的有限元超收敛拼片恢复解和网格自适应分析

该文提出变截面变曲率梁振型的有限元后处理超收敛拼片恢复方法，建立各阶振型的超收敛解，并基于振型超收敛解进行变截面曲梁面内和面外自由振动的自适应分析。在位移型有限元后处理阶段，引入超收敛拼片恢复方法和高阶形函数插值技术，得到振型(位移)的超收敛解。利用振型超收敛解估计当前网格下振型有限元解的能量模形式下的误差，并指导网格进行自适应细分加密分析，获得优化的网格和满足预设误差限的高精度解答。数值算例表明该算法适于求解不同曲线形态、多类边界条件、变截面、变曲率形式的曲梁面内和面外自由振动连续阶频率和振型，解答精确、分析过程高效可靠。

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.