Abstract
In this paper, a kind of node_face frictional contact FM-BEM penalty function method is presented for 3D elastic frictional contact nonlinear problems. According to the principle of minimum potential energy, nonpenetrating constraints are introduced into the elastic frictional contact system as a penalty term. By using the least square method and penalty function method, an optimization mathematical model and a mathematical programming model with a penalty factor are established for the node_face frictional contact nonlinear system. For the two models, a penalty optimization IGMRES (m) algorithm is proposed, and the influences of different penalty factors on the solution of the whole system are analyzed. Finally, a numerical simulation is carried out for two elastic frictional contact objects, and some important results including displacements, pressures, friction forces, and friction slips in the contact area are presented. Theoretical analysis and numerical experiment show that the newly presented FM-BEM penalty function method not only is efficient and practical but also has much superiority. It is easy to implement, and it is fast convergent with good stability.
Highlights
Elastic frictional contact is a multiple nonlinear problem [1, 2], and it is necessary to accurately track the motion of the object before contact and the interaction between objects after contact, which includes the correct simulation of friction and deformation behavior between contact surfaces and the analysis of the possible energy conversion problem
Only very few of them can be solved by analytical methods, and most of them need to be simulated by numerical methods such as the Finite Element Method (FEM) [3, 4] and the Boundary Element Method (BEM) [5, 6]. e FEM is relatively mature and widely used [7,8,9,10]
By using the superiorities of Fast Multipole Boundary Element Method (FM-BEM) such as high precision, high computational efficiency and being suitable for large-scale computing, we have successfully applied it to the numerical analysis of elastic frictional contact problems and have completed some simulations [35,36,37,38], for example, the interference fit between taper sleeve and roll neck of an oil film bearing and a surface force field of screw pair in a rolling mill
Summary
Elastic frictional contact is a multiple nonlinear problem [1, 2], and it is necessary to accurately track the motion of the object before contact and the interaction between objects after contact, which includes the correct simulation of friction and deformation behavior between contact surfaces and the analysis of the possible energy conversion problem. By using the superiorities of FM-BEM such as high precision, high computational efficiency and being suitable for large-scale computing, we have successfully applied it to the numerical analysis of elastic frictional contact problems and have completed some simulations [35,36,37,38], for example, the interference fit between taper sleeve and roll neck of an oil film bearing and a surface force field of screw pair in a rolling mill. According to the abovementioned analysis, we will present a kind of FM-BEM penalty function method to solve the elastic node_face frictional contact problems. We will establish a mathematical programming model with a penalty factor and propose a penalty optimization algorithm In this method, some important factors will be synthetically considered, which include the deformation and stress condition in a contact process, the nonlinearity of boundary condition for the contact surface, the size and mutual position of the contact area, the change of contact state, and so on.
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