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中文摘要：
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。
英文摘要：
In the present paper, a basic shape determination problem of cable frames is put forward and discussed. At first in the case of no self-equilibrated internal forces but with external loads, the continuous equilibrium equation of a single planar cable frame is given out on the basis of the balance of nodal forces. Then, this equation is extended to the case of exiting self-internal forces but without external loads. In the case of there are no self-internal forces within a cable frame, It will be necessary to assume a functional as the total strain energy of the upper and lower chord of a planar cable frame, the shape determination problem of cable frames will be a calculus of a variational problem with fixed boundary conditions and non-integral constraints. Then on the basis of Euler’s equation group the solution of this constrained calculus of variation can be derived out. Hopefully the work in the present paper could be helpful for practicing engineers and researchers.
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