新型p型板單元及其在結構振動分析中的應用

Abstract

利用Legendre正交多項式作為形函數基底函數，開發了兩種新型的通用p型板單元。單元矩陣的解析積分保證了p型有限單元解的精確性及單調收斂性，計算實例表明所開發的p型有限單元計算結果隨基底函數中附加項數量的增加而快速收斂，且它們的計算精度遠高於一般線性單元。另外，p型板單元不使用縮減積分也能分析薄板的振動問題，利用它們收斂率高的特點，分析了結構破壞的時頻特性。p型有限單元仿真結果與實測結果良好的吻合證明了它們用於結構振動響應分析的有效性。

Using Legendre orthogonal polynomials as shape functions,two versatile p-version plate elements are developed.The element matrices are integrated analytically to guarantee the accuracy and monotonic convergence of the predicted solutions of the proposed p-version elements.The analysis results show that the convergence rate of the present elements is very fast with respect to the increasing number of additional polynomial terms in shape functions,and their solutions are much more accurate than those of the linear finite elements for the same number of degrees of freedom.Additionally,the new elements without the reduced integration can be applied for the free vibration analyses of thin plates over the conventional h-version ones.Due to the fast convergence of the proposed p-version elements,the structural damage is simulated to study its time-frequency characteristic.Good agreement between the simulated and the experimental results verifies the present p-version finite elements for the structural vibration analyses.