热冲击下的复合材料壳刚柔耦合动力学研究

研究了在热冲击下任意形状(仅一个方向有曲率)复合材料壳的非线性刚柔耦合动力学响应。根据Mindlin理论,建立了任意形状的复合材料壳的非线性应变-位移关系。借助于数学理论以及几何关系,描述了壳上任意点的变曲率。用虚功原理建立了动力学变分方程,并采用等参单元对壳的连续动力学方程进行离散,建立了中心刚体-复合材料壳的刚-柔耦合动力学方程。用高斯积分计算常值阵,为了提高计算效率,采用广义-α法结合Newton-Raph-son迭代法对动力学方程进行积分。将采用该方法计算得到的频率与ANSYS软件计算得到的作对比,验证了模型的正确性。通过算例分析了在热冲击作用下复合材料壳的线性、非线性的动力学特性,以及曲率、材料特性对动力学响应的影响。

Rigid-Flexible Coupling Dynamics of Composite Shell Considering Thermal Shock

The nonlinear dynamical response of composite shell with arbitrary shape in one direction that is suddenly exposed to a heat flux is investigated using the finite element method. With the help of basic mathematic knowledge, the variable curvature radius of shell is derived. According to Mindlin shell theory, the nonlinear strain-displacement relationship is showed. variation equations of a composite shell are derived by means of the principle of virtual work. The isoparametric elements are used to discrete the variation equations to obtain the rigid-flexible coupling dynamic equations for hub-composite shell system. Gauss quadrature is introduced for calculating the constant matrix. Implicit time integration generalized-α method associated Newton-Raphson is employed for integration. Comparison of the present frequency results with that obtained by ANSYS verifies the correctness of the present formulation. The linear and nonlinear dynamical characteristics are concluded considering heat flux. Influences of curvature and material behavior on the dynamical responses are studied.