用广义变分原理求解多节点双模量静不定桁架

Solving Multi-Node Double Modulus Statically Indeterminate Truss by Using Generalized Variational Principle

在外载荷作用下的多节点双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,采用广义变分原理可以方便求解多节点双模量静不定桁架内力.通过求解多节点双模量静不定桁架内力的几个算例,阐述广义变分原理在计算多节点双模量静不定桁架内力中的应用.研究结果表明:采用广义变分原理求解多节点双模量静不定桁架内力的通用性较强,所求的结果是精确解析解.采用广义变分原理求解多节点双模量静不定桁架内力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计算等优点.

Equilibrium in multi-node double modulus statically indeterminate truss under external loading is an extreme problem of multivariate function with arbitrary limited multiple independent variables under the condition of arbitrary limited multiple constraints. The internal forces of multi-node double modulus statically indeterminate truss can be easily solved by using generalized variational principle. Several examples solving the internal forces illustrate the applicability of the generalized variational principle in calculating the internal forces of the multi-node double modulus static truss. The research result shows that it is of strong generality and high precision to use the generalized variational principle to solve the internal forces of multi-node double modulus statically indeterminate truss. This method not only overcomes 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, simplicity in calculation procedures, easy to apply and convenience in calculating by engineers in practical application.