用最小势能原理求解支承系统问题

摘要

利用弹性力学中的叠加原理和等效原理，将支撑系统看作一个整体来研究，基于弹性力学中的能量守恒原理，以约束力为桥梁，假定各个约束力是依次作用于支撑系统，借助多个位移的叠加，推导出了支承系统的势能泛函公式，并利用最小势能原理，给出了求解支承系统问题的一种新算法。该算法简便、准确，能够较为广泛地应用于各类工程计算。%Using the superposition principle and equivalence principle of elastic mechanics,take the supporting system as a whole to study it,based on the priciple of energy conservation of elastic mechanics,the potential energy functions for the supporting system are derived by applying the theo-rem of superposition for multiple displacements under the assumption that every internal force is act-ing on the supporting system in turns. A new algorithm for the supporting system is also obtained by using the principle of minimum potential energy. This algorithm is simple,accurate ,and can be widely used in various types of engineering calculations.