纵横荷载共同作用下斜置矩形板的解析解

Analytical solution of inclined rectangle board under vertical and horizontal load

针对3边固支1边自由,受纵横荷载共同作用的斜置矩形板力学模型,充分考虑中面内力对弯曲的影响,确定了相应的荷载势能,将弹性力学边值问题转化为能量原理的形式,得到板的挠度、应力和内力的解析表达式;应用解析式研究了薄板挠曲变形和内力变化规律。研究表明:板的挠曲变形及内力与荷载、板体材料、结构几何特征及倾角有关,并呈现明显的非线性特征。

To the mechanical model of inclined rectangle board subjected to forces acting vertically and horizontally with fixed ends on three edges and free end on one edge,corresponding loading potential energy and the analytical solution of deflection,stress and inner force,considering the influence of inner force in central surface on the bend of the board,were given by transforming boundary value problem of elasticity into energy principle form.The deflected deformation and inner force rules of the board and evol...