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工程结构中结构或构件之间存在接触摩擦现象是较为普遍的,接触协同作用使得结构非线性屈曲问题的数值求解变得困难。该文从这一实际问题出发,采用子结构凝聚自由度的有限元方法得到基于接触界面问题的非线性有限元平衡方程,通过增广拉格朗日乘子法对接触问题的约束条件进行处理,并与柱面弧长法结合,对非线性屈曲问题进行全过程跟踪求解。算例结果表明接触协同作用对结构的非线性屈曲过程影响明显,有必要在实际工程结构设计中考虑接触协同作用的影响。
The phenomenon of contact friction between structures or components in engineering structures is more common. Contact synergies make the numerical solution of nonlinear buckling problems of structures more difficult. Based on this practical problem, this paper presents a nonlinear finite element equilibrium equation based on the contact interface problem by using finite element method of sub-structure cohesion degree of freedom, and treats the constraint of contact problem by augmented Lagrange multiplier method , And combined with the cylindrical arc length method, the entire process of nonlinear buckling problem tracking solution. The results show that the contact synergy has obvious effect on the nonlinear buckling process of the structure, and it is necessary to consider the influence of the contact synergy in the actual engineering design.