用拉格朗日函数计算材料非线性桁架的变形

发布时间：2018-05-08 17:58

本文选题：拉格朗日 + 乘数　；参考：《湘潭大学自然科学学报》2016年03期

【摘要】：利用桁架材料应力与应变的非线性本构关系,得到了外载荷作用下材料非线性静不定桁架应变能函数及余能函数的表达式.引入拉格朗日乘数结合静不定桁架应变能函数、桁架节点静力平衡方程,构造了拉格朗日函数,求得了材料非线性静不定桁架的内力,再采用材料非线性静不定桁架余能函数,即可求出材料非线性静不定桁架的位移.研究结果表明:采用拉格朗日函数求解材料非线性静不定桁架的内力及位移通用性较强,所求的结果是精确解析解.采用拉格朗日函数求解材料非线性静不定桁架的内力及位移方法,不但克服了常规方法需利用几何关系建立协调方程的缺陷,且具有力学概念清晰直观、计算过程简便等优点.
[Abstract]:By using the nonlinear constitutive relation of stress and strain of truss material, the expressions of strain energy function and complementary energy function of material nonlinear statically indeterminate truss under external load are obtained. By introducing Lagrange multiplier and strain energy function of statically indeterminate truss and static equilibrium equation of truss joint, Lagrange function is constructed, internal force of material nonlinear statically indeterminate truss is obtained, and complementary energy function of material nonlinear statically indeterminate truss is adopted. The displacement of the material nonlinear statically indeterminate truss can be obtained. The results show that the Lagrange function is widely used to solve the internal force and displacement of the material nonlinear statically indeterminate truss, and the exact analytical solution is obtained. The Lagrangian function is used to solve the internal force and displacement of the material nonlinear statically indeterminate truss, which not only overcomes the defect that the conventional method needs to use geometric relations to establish the coordination equation, but also has the advantages of clear and intuitive mechanical concept, simple calculation process, and so on.
【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项目(2015JJ6073)
【分类号】：O341

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