新型 p 型板单元及其在结构振动分析中的应用

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.