非轴对称移动载荷下有限长圆柱厚壳的动力响应

本文在介绍圆柱厚壳应力与位移理论分析发展的前提下，建立了有限长圆柱厚壳在非轴对称移动载荷作用下的三维力学模型，假设沿厚度方向径向剪切应变二次分布、径向正应变线性分布，且建立了为满足边界条件待定的位移表达式，采用Heaviside函数和Dirac函数表达移动和作用变化着的移动载荷的基础上，用最小势能原理建立了该圆柱厚壳的动力学微分方程组，应用Galerkin法和修正的Runge–Kutta–Fehlberg法，求得了非轴对称移动载荷作用下的圆柱厚壳的动力响应。通过具体算例，对有限长圆柱厚壳的位移响应和应力状态进行了分析，并将动态响应的理论解与ANSYS数值解进行了对比，从而相互印证了解的可靠性。

Dynamic Response of of Length-limited Cylindrical Thick Shellsunder Non-axisymmetric Moving Loads

The theoretical research history of cylindrical thick shells’ stress and displacement is firstly reviewed, and a 3D mechanical model of length-limited cylindrical thick shells under non-axisymmetric moving loads is established. Then based on the assumption of radial shear strains with quadratic distribution and radial normal strains with linear distribution through the radial coordinate, displacement expressions satisfying boundary conditions are established. The non-axisymmetric loads are expressed by Heaviside function and Dirac function, and equilibrium differential equations containting unkowns are derived according to the minimum potential energy principle. After application of the Galerkin Method and the Modified Runge–Kutta–Fehlberg Mehtod, dynamic response of cylindrical thick shells under non-axisymmetric moving loads is obtained. This method is verified by a comparative analysis of the theoretical solutions with ANSYS numerical results from an example.