用于大位移情形的杆系结构虚功原理

通过典型示例揭示了传统杆系结构虚功原理在“微小位移”假定下,忽略挠度的一阶导数,用二阶导数代替曲率,造成的近似计算的假象,以及引起的概念上的混乱. 论证了虚功原理实质上是一组精确的数学恒等式,只是通过定义“力”和“位移”使其中每一项都赋予了虚功的物理意义,并不存在近似的问题. 提出了用截面转角的正切值定义截面的转动位移,并将虚功中力和位移的关系描述为力不随位移拖动的模式. 由此澄清了传统虚功原理可能引起的“近似计算,只适用于小位移”的假象,使虚功原理可以抛弃小位移假定,精确地适用于大位移情形.

Principle of virtual work for framed structures with large displacement

The feint of approximate treatment and the confusion of conception in the conventional principle of virtual work, in which the assumption of small displacement was introduced and the first derivative of the deflection was neglected and the curvature was represented by the second derivative, were disclosed by a typical example structure in this paper. It was demonstrated that the principle of virtual work was essentially an identical mathematics equation with no any approximation, but each item in the equation was endowed special physical meaning of virtual work by defining the patterns of forces and displacements. The conception of virtual work was modified by defining the tangent of a rotating angle of a cross-section as the rotational displacement and explaining the relationship of forces and displacements as forces not dragging along the displacements. It therefore clarifies the confusion that the virtual work principle is approximate and just suitable for the situation of small displacement, and makes the virtual work principle can put away "the assumption of small displacement" and can be applied to the situation of large displacement.