Study On New Superconvergent Recovery Methods For Fe Analysis On Member’s Free Vibration

Free vibration is a typical eigenvalue problem in structural engineering. Efficiently solving of its modes and frequencies is a challenging task. This thesis proposes two new superconvergent alogrithms to recover the FE solutions, named p-version algorithm and “sub-dividing element method” respectively. These two algorithms are applied to several members’ free vibration computation, and greatly enhanced the convergence rate of the solutions. This article shows that the proposed method is efficient, reliable and accurate. The main research work in this thesis is as followings:(1) These two superconvergent algorithms are applied to the FE recovery on the rod axial free vibration problem. Corresponding formulae are derived. Numerical examples show that both algorithms are efficient and reliable, and both can give superconvergent results effectively.(2) These two superconvergent algorithms are applied to the FE recovery on Euler beam’s free vibration problem. Numerical examples show that both algorithms can enhance the quality and accuracy of all results completely and effectively.(3) These two superconvergent algorithms are applied to the FE recovery on Timoshenko beam’s free vibration problem. Numerical examples show that both algorithms can enhance the accuracy of all frequencies and modes effectively.(4) These two algorithms are compared. Their advantages and weaknesses are analyzed. Finally, their forecastings are studied. They can be applied to structural elastic stability analysis, as well as the FE adaptive analysis.