新型p型板单元及其在结构振动分析中的应用

利用Legendre正交多项式作为形函数基底函数,开发了两种新型的通用p型板单元.单元矩阵的解析积分保证了p型有限单元解的精确性及单调收敛性,计算实例表明所开发的p型有限单元计算结果随基底函数中附加项数量的增加而快速收敛,且它们的计算精度远高于一般线性单元.另外,p型板单元不使用缩减积分也能分析薄板的振动问题,利用它们收敛率高的特点,分析了结构破坏的时频特性.p型有限单元仿真结果与实测结果良好的吻合证明了它们用于结构振动响应分析的有效性.

New p-version plate elements and applications in structural vibration analyses

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.