对边简支对边滑支三维矩形层合板的精确解

Exact Solutions for Rectangular Laminates in Cylindrical Bending by Three-dimensional State Space Approach

在状态空间体系下,研究四边简支层合板壳精确解的文献较多,而关于其它边界条件问题的文献却不多见。根据矩形板一对对边简支(simply supported)另一对边滑移(slippery surface)的边界条件特征,构造了状态变量三角函数形式表达式。然后,基于三维的状态空间方法,将状态变量以级数形式展开,推导了相应的三维状态方程。借助四边简支矩形层合板的求解方法,给出了矩形层合板表面受均布压应力作用下的数值实例。从数值结果和位移图形可以看出,本文的矩形层合板弯曲变形具有明显的圆柱弯曲特征,其数值结果可作为其它数值法的标准解。

In state-space framework,there exist many references for exact solutions of laminates with four sides simply supported,and the literature on the other boundary conditions is rare. For rectangular laminates with two opposite sides simply supported and other sides slippery surface,the state variables are expressed in appropriate trigonometric form according to the boundary conditions. Then,after expanding the state variables in the form of series,three-dimensional state equation of rectangular laminates corresponding to the boundary conditions is derived by three-dimensional state space approach. By combining method of analyzing rectangular laminates with four sides simply supported,numerical examples under uniform pressure are investigated for rectangular laminates with two opposite sides simply supported and other sides slippery surface. The numerical results and displacement distribution diagram demonstrate that the laminates investigated have obvious cylindrical bending characteristics. The results of this paper can be used as standard solutions for other numerical methods.