纵横载荷联合作用下弯曲薄板的功的互等定理

Reciprocal Theorem Applied for the Bending Thin Plates under Loading in the Plan and Forces Vertical to the Plane

本文将功的互等定理应用于形状、大小和材料均相同且处于真实状态的两个薄板系统之间,得出了纵横载荷联合作用下弯曲薄板的功的互等定理,并给出了简洁的数学表达式。该式既可以用于横向载荷作用下弯曲薄板问题的求解,又可以用于薄板稳定问题的求解。定理推导过程中没有对薄板的形状和边界条件加以限制,因而使该定理具有较广的适用范围。

In this paper, the authors applied reciprocal theorem to two thin plate system which have the same shape, same material and the same status, worked out the explicit equation of this theorem for thin plates under loading in the plan and forces vertical to the plane. This agnation can be used for the bending and eaten buckling of thin plates. Because of the deduction of this equation, we don't confine the plates' shape and boundary condition, its application can be generalized to many cases.