基于能量原理的空间结构无应力状态平衡方程推导

Derivation of equilibrium equation of space beam element based on principle of potential energy

为探讨分阶段成形空间梁结构成形状态影响因素,基于最小势能原理推导空间梁结构无应力状态法平衡方程,分析结构最终状态的影响因素,并通过算例验证平衡方程的正确性和可靠性。研究结果表明:所推出的空间梁单元无应力状态法平衡方程正确可靠,可直接应用于分阶段成形空间梁结构任意阶段状态计算;对于由空间梁单元组成的分阶段成形结构,无论是否考虑结构的几何非线性效应,结构的最终状态只与结构体系、外荷载、边界条件以及空间梁单元的无应力状态量有关,而与结构具体的成形过程无关。

In order to explore the influencing factors of the final state of the space beam element based on the shape structure,this study was aimed to derive the equilibrium equation of space beam structure of unstressed state control method based on the principle of minimum potential energy.The influencing factors of the final state of the structure,and the correctness and reliability of the equilibrium equation were analyzed and then verified by an example.The analysis results show that the equilibrium equation of unstressed state control method on space beam element is correct and reliable,which can be directly applied to the calculation of the state of any stage inthe shape space beam structure.The final state of the structure formed in stage is only related to the structural system,external load,boundary condition,the unstressed lebgth and the unstressed curvature of the spatial beam element,but not with the specific forming process.