纯余能原理在杆系大变形中的应用

将高玉臣提出的弹性大变形的纯余能原理(即只含有未知的内力分量)用于杆件系统的内力计算.在杆系变形后的位置建立平衡方程,根据节点的平衡条件,将杆系中的某几个未知力用其余未知力表示,此时应用余能原理无需考虑各杆在相邻边界上的力平衡条件,将有条件驻值转化为无条件驻值问题.在算例中假设各杆变形量与内力呈线性关系,即只考虑几何大变形,将算例所得结果与理论值对比可知二者非常接近,故将纯余能原理用于杆系大变形的计算是切实可行的.

The Application of Pure Complementary Energy Principle in Large Deformation of Rods System

It was applied to rods system that the pure complementary energy principle presented by Gao Yuchen, which is only involving unknown internal forces. Constructing equilibrium equations after deformation, substituting some unknown internal forces with other unknown ones in terms of the equilibrium conditions at nodes, under this condition it was no necessary to consider the force equilibrium condition on the neighbor boundary of rods when the complementary energy principle was used. So it changed the conditional stationary problems into unconditional ones. The hypothesis of linear relationship was used between internal force and deformation in the example, i.e. only geometrically large deformation was considered. The computational results and theoretical values were compared, from which it can be known that they are close, so it is feasible for this pure complementary energy principle to apply to large deformation of rods system.