Solution And Optimization Of Nonlinear Contact Problems Based On Multipole Boundary Element Method

The boundary element method is an important numerical calculation method,which has the advantages of high precision and dimensionality reduction.For the three-dimensional elastic friction contact problem,the boundary element method can better deal with such nonlinear problems on the basis of meeting the contact conditions.Therefore,according to the optimization theory,the penalty function idea,and the principle of minimum poten-tial energy,the three-dimensional elastic point-surface friction contact problem is analyzed,a mathematical programming model of penalty factors is established,and the penalty opti-mization IGMRES(m)algorithm is proposed,which is verified by numerical examples.The effectiveness and practicability of the method.Finally,according to the optimization of the truncation technique of the IGMRES(m)algorithm,the WIGMRES(m)algorithm is pro-posed based on the weighted GMRES(m)(WGMRES(m))algorithm,and the feasibility of the method is verified by numerical examples.The main content of the paper is as follows:Firstly,the friction contact analysis is carried out for the three-dimensional elastic fric-tion contact problem,and the constraint conditions are given.For the case of non-penetration,the least square method is used to linearize the nonlinear contact constraint.For the case of penetration,the penalty function is used according to the principle of minimum potential en-ergy.The method introduces the non-penetrating condition into the system as a penalty term,analyzes the influence of the choice of penalty factors on the calculation results,establish-es a mathematical programming model of penalty factors,and transforms the point-surface friction contact problem into an unconstrained optimization problem.Secondly,for the mathematical programming model of penalty factors,the optimali-ty condition of the model solution is analyzed.For the solution of the model,a penalty-optimized IGMRES(m)algorithm is proposed to analyze the convergence of the algorithm.Finally,through numerical examples,the two The object is numerically simulated,and the calculation results of displacement,pressure,friction and friction slip in the contact area are given.The results show that the multi-pole boundary element penalty function numerical method proposed in this paper is not only effective and practical,but also has advantages such as easy implementation,fast convergence and good stability.Finally,according to the truncation technique of the penalty-optimized IGMRES(m)algorithm,based on the WGMRES(m)algorithm,using the incomplete orthogonal weighted Arnoldi process,a new algorithm,namely the weighted truncated GMRES(m)algorithm,is proposed.(WIGMRES(m)algorithm),through theoretical proof of the convergence of the algorithm,numerical examples verify the feasibility of the algorithm,the results show that the algorithm greatly improves the calculation efficiency on the premise of ensuring accuracy.