求解工程中静不定结构内力的通用方法

发布时间：2018-05-06 21:39

  本文选题：静不定 + 结构　； 参考：《中南大学学报(自然科学版)》2016年01期

【摘要】：基于材料力学、结构力学工程中静不定结构内力的求解多采用力法、位移法等方法,静不定结构在外载荷作用下的平衡状态是一个稳定的平衡状态,其应变能存在极小值,故利用静不定结构的多余约束力列出其应变能表达式,引入拉格朗日乘数并结合静力平衡方程,构造拉格朗日函数,对拉格朗日函数求一阶导数并令一阶导数等于0,即可求得静不定结构的内力,并通过算例予以证明。研究结果表明:此方法适用于求解平面或空间静不定梁、弧形结构、刚架、桁架(包括非线性材料)的约束反力、内力及位移;采用拉格朗日乘数法求解静不定桁架内力的通用性较强,不但可以克服常规方法需利用几何关系建立协调方程的缺陷,而且具有力学概念清晰直观、计算过程简洁、便于工程设计人员在实际中掌握和计算的优点;其所得结果是精确解析解,故可以用于检验其他方法的计算精度。
[Abstract]:Based on the mechanics of materials, the internal forces of statically indeterminate structures in structural mechanics engineering are solved by force method and displacement method. The equilibrium state of statically indeterminate structures under external loads is a stable equilibrium state, and the strain energy of statically indeterminate structures is minimized. Therefore, the strain energy expressions of statically indeterminate structures are presented by using superfluous binding force, and Lagrange multipliers are introduced and combined with static equilibrium equations to construct Lagrange functions. If the first order derivative of Lagrange function is obtained and the first order derivative is equal to 0, the internal force of the statically indeterminate structure can be obtained and proved by an example. The results show that this method is suitable for solving the constrained reaction forces, internal forces and displacements of plane or spatial statically indeterminate beams, curved structures, rigid frames and trusses (including nonlinear materials). The Lagrange multiplier method is widely used to solve the internal force of statically indeterminate truss. It can not only overcome the defect that the conventional method needs to use geometric relations to establish the coordination equation, but also has a clear and intuitive mechanical concept and a simple calculation process. It is convenient for engineering designers to grasp and calculate the advantages in practice, and the results obtained are exact analytical solutions, so it can be used to test the calculation accuracy of other methods.
【作者单位】： 湖南文理学院机械工程学院;
【基金】：湖南省科技计划项目(2011SK3145) 湖南“十二五”重点建设学科项目(湘教发[2011]76号) 湖南省自然科学基金资助项目(2015JJ6073)~~
【分类号】：O34
，

本文编号：1854005