Impact Response Analysis of Multi-layered Surface Structures with Composite Material

第一部分：将本征函数展开法发展到具有简支边的横向各向同性厚矩形板在冲击压力载荷作用下的弹性动力响应分析。将弹性动力学解分解为准静态和动态两部分。通过对具有时变边界条件的拟微分方程进行精确分析，得到了拟静力解。而动力部分则是由满足齐次边界条件的相关问题的精确自由振动分析得到的特征函数（正模态）的无穷级数给出的。用图形表示了应力和位移响应，然后讨论了各向异性对动力响应的影响。第二部分：基于三维弹性动力学理论，采用本征函数展开法对横向各向同性圆柱壳的冲击响应进行了分析。圆柱壳在其端面简单支承，外表面突然受到部分分布的均布荷载。文中给出了一些感兴趣位置的应力和位移响应的数值结果，并讨论了各向异性对冲击响应的影响。纵向弹性模量越大的方向应力响应越大。

Part1: The method of eigenfunction expansion is developed to the elestodynamic response analysis of a transversely isotropic, thick rectangular plate with simply supported edge conditions under impact pressure loadings. The elastodynamic solution is decomposed into their quasi-static and dynamic components. The quasi-static solution is obtained by an exact analysis of the quasi-differential equations with the time-dependent boundary conditions. While the dynamic part is given in an infinite series of the eigenfunctions (normal modes) which are derived from the exact free vibration analysis of the associated problem satisfying homogeneous boundary conditions. Stresses and displacements responses are shown graphically, and then influences of anisotropy on the dynamic response are discussed.Part2 : An impact response analysis for a transversely isotropic circular cylindrical shell is carried out using the method of eigenfunction expansion based on the theory of 3D elastodynamics. The circular cylindrical shell is simply supported at its end surfaces, and a partially distributed uniform load is suddenly applied to its outer surface. Numerical results for stress and displacement responses at some locations of interest are shown graphically, and then the influences of anisotropy on the impact response are discussed. The higher stress response will be occurred in the direction with higher longitudinal elastic modulus.