用拉格朗日函数分析不同模量静不定桁架内力

Analysis on the Different Modulus Statically Indeterminate Truss Internal Force by Lagrange Function

在外载荷作用下的不同模量静不定桁架平衡问题,是任意有限多个自变量的多元函数在任意有限多个约束条件下的极值问题,对采用拉格朗日乘数法求解此类极值问题进行了数学证明.通过求解不同模量静不定桁架极限载荷的几个算例,阐述拉格朗日乘数法在计算不同模量静不定桁架极限载荷中的应用.研究结果表明:采用拉格朗日乘数法求解不同模量静不定桁架极限载荷的通用性较强,用拉格朗日乘数法求解不同模量静不定桁架极限载荷的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、便于工程设计人员在实际中掌握和应用.

Equilibrium problems in the different modulus statically indeterminate truss by external load is an extremal problem of any finite number of the independent variable multivariate function, which is restrained by any finite number of conditions. Mathematical proof by Lagrange multiplier rule to solve this kind of extremal problem was given. The application in calculation of the different modulus statically indeterminate truss limit load by Lagrange multiplier rule was described through several examples solved by different modulus statically indeterminate truss limit load. The conclusions of our research show that we solve the different modulus statically indeterminate truss limit load by Lagrange multiplier rule, this method has a strong versatility, and the result is accurate. The method for solving the different modulus statically indeterminate truss internal force by Lagrange multiplier rule not only can overcome the defects of conventional method which needs to establish the compatibility equation by using geometric relation, but also has the advantages of clear mechanics concept, simple in calculation procedures, easy to master and convenient for calculating by engineering designers in actual engineering.