用余能原理求解非线性静不定结构的支承反力  

Solving Support Reaction of Nonlinear Statically Indeterminate Structures by Using the Residual Energy Principle

作　　者：肖珍 李政 欧成 Xiao Zhen;Li Zheng;Ou Cheng(School of Intelligent Building,Changde College,415000,China)

机构地区：[1]常德学院智能建筑学院,415000

出　　处：《特种结构》2024年第2期7-11,共5页Special Structures

基　　金：国家自然科学基金青年基金项目(52008164);湖南省教育厅项目(HNJG-2022-1365)。

摘　　要：根据余能原理,结构的余能对任一外力的偏导数,等于外力作用点沿该力方向位移。由于非线性静不定结构支承处的支承反力方向位移为零或转角为零,可直接把结构的余能对外力求一阶偏导数来求支承反力,克服了有关文献采用广义变分原理求非线性静不定结构支承反力时,存在增加计算量的不足。算例分析表明,采用本方法计算的支承反力与相关文献结果一致,梁截面曲率正负号判定对支承反力计算有着较大的影响。According to the principle of complementary energy,the partial derivative of the complementary en-ergy of the structure with respect to any external force is equal to the displacement of the point of application of the external force in the direction of the force.Because the displacement of the bearing reaction direction at the bearing of the nonlinear statically indeterminate structure is zero or the rotation Angle is zero,and the supporting reaction could be obtained by directly applying the coenergy of the structure to the first partial derivative.It was overcomed the shortage of increasing the calculation amount while the generalized variational principle was used to calculate the bearing reaction of the nonlinear statically indeterminate structure in relevant literature.Examples shown that the bearing reaction calculated by the method was consistent with the results of relevant literatures,and the determination of beam section curvature sign had great influence on the calculation of bearing reaction.

关 键 词：余能原理 非线性 静不定 支承反力 

分 类 号：O341[理学—固体力学] TU13[理学—力学]