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.
Using the nonlinear constitutive relation between stress and strain of truss material,the strain energy function and the complementary energy function of statically indeterminate truss with material nonlinearity under external load are obtained.Lagrange function is constructed by combining Lagrange multiplier with the strain energy function of statically indeterminate truss and the static equilibrium equations of truss nodes,and the internal force of statically indeterminate truss with material nonlinearity is obtained.Then based on the complementary energy function expression of statically indeterminate truss with material nonlinearity,its displacement is found out.The result shows that the above method of solving the internal force and displacement of statically indeterminate truss with material nonlinearity is universal and the obtained solutions are accurate analytical ones.This method not only overcomes the defects of conventional methods to establish the coordination equations by using the geometric relationships,and has clear and intuitive the mechanics concept,and the simple calculation process.
出处
《湘潭大学自然科学学报》
CAS
北大核心
2016年第3期17-22,共6页
Natural Science Journal of Xiangtan University
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)
关键词
拉格朗日
乘数
材料
非线性
静不定
桁架
内力
位移
Lagrange
multiplier
materials
nonlinear
statically indeterminate
truss
internal force
displacement
