用条件极值法求解静不定空间桁架

Solving statically indeterminate space truss by using condition limit method

求静不定空间桁架内力的余能函数取最小值问题,是满足桁架节点平衡方程的条件极值问题,可利用静不定空间桁架的余能函数及节点平衡方程,构造一个新的能量泛函数.把新的能量泛函数对桁架内力求一阶偏导数且令一阶偏导数等于零,可得到桁架的变形协调条件,再结合桁架节点平衡方程,即可求得静不定空间桁架的内力,然后把静不定空间桁架势能函数对作用在桁架节点的外力求一阶偏导数,可以求得该节点的变形位移.

It is the condition limit problem meeting the equilibrium equation of truss nodes that obtains the minimum value through solving complement energy function of internal forces in statically indeterminate space truss.New energy function is constructed on the basis of complement energy function and equilibrium equation of truss nodes in statically indeterminate space truss.Taking the new energy function’s first partial derivative of truss internal force and making it equal to zero,the deformation compatibility condition of the truss is obtained.Combining equilibrium equation of truss nodes,the internal forces in statically indeterminate space truss are achieved.Using potential energy function in statically indeterminate space truss to take the first partial derivative of external forces acting on truss nodes,the deformation displacement of the nodes is obtained.