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该文提出并初步探讨了空间索桁体系上下弦曲线形状确定问题。首先,基于节点平衡关系建立了单榀索桁体系在外荷载无自内力的情况下连续化平衡方程,并将其推广到存在自内力的情况。在无自内力的情况下,该文从数学的角度添加优化条件,归结为基于上下弦索曲线的总拉压应变能泛函和仅包含二阶导数的具有非整型约束条件和固定边界条件的变分极值问题,可由欧拉方程组求得其解。该文的工作可供建筑、结构设计人员和有关学者参考。
This paper presents and preliminary discusses the space truss system upper and lower chord curve shape problem. First, based on the node equilibrium, the continuous equilibrium equation of a single cable truss system under the condition of external load without self-internal force is established and generalized to the case of self-internal force. In the absence of self-internal force, this article adds the optimization conditions from the mathematical point of view, boils down to the total tensile and compressive strain functional based on the upper and lower chord lines and the non-integer constraints and the fixed boundary conditions The extreme variational problem can be solved by Euler’s equations. The work of this paper can be used for reference by architects, structural designers and relevant scholars.