大变位下多体系统摩擦接触问题线性规划求解方法

建立了多体系统中摩擦接触问题的整体控制方程，在大变位情况下将其分解成两个线性互补问题，一般通过两次线性规划求解可完成一次接触问题的求解，大大地减少了接触问题求解的迭代次数和计算量，并且可直接得到系统中接触界面上的接触应力，从而克服了对于多体系统求解接触问题需要多次迭代和难于直接得到接触应力的缺陷．数值算例表明了该方法的合理性和有效性，为大变位下多体系统中接触问题的求解提供了有效的手段．

Linear programming algorithm for solving friction-contact problems of multi-body systems under large displacements

The global control equations of the friction contact problem of the multi-body systems are developed and the corresponding numerical formulations are given based on the generalized finite elements and the contact-force elements presented by the authors. In order to consider the effect of variation of configuration including the contact position and the contact area during large-scale deformation on the equilibrium of forces, the resulting mathematical programming is partitioned into two linear complementary problems of mathematical programming. The numerical procedure for solving these linear programming problems is given. Accordingly, the configuration and the contact forces or stresses under the condition of large displacements can be defined accurately. It is shown by a numerical example that the proposed method is reasonable, effective and powerful for solving the contact problem of the multi-body system under large displacements.