On the decision of contact problems of structural mechanics with unilateral constraints and friction by step-by-step analysis

Lukashevich, A. A.; Rozin, L.A.

doi:10.5862/mce.36.9

Cited by 11 publications

(4 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The signs' rule for interaction forces x and mutual displacements z maintained their popularity until the present [16][17][18][19][20]. These problems are stated in the form of variational inequalities [21][22][23][24], and the following numerical methods were used to solve them: Lagrange multipliers [25][26][27], penalty functions [28; 29] and their combinations [30][31][32]. And other methods using contact finite elements [32][33]; quadratic programming approach [34][35][36]; finite element methods (Spigot-algorithms) [37][38][39]; and other [40][41][42][43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

Algorithm for calculating the problem of unilateral frictional contact with an increscent external load parameter

Popov,

Lovtsov

2023

Struct. Mech. of Eng. Const. and Build

View full text Add to dashboard Cite

The subject of the study is the contact interaction of deformable elements of linear complementarity problem (LCP). To solve the linear complementarity problem, the Lemke method with the introduction of an increasing parameter of external loading is used. The proposed approach solves the degenerated matrix in a finite number of steps, while the dimensionality of the problem is limited to the area of contact. To solve the problem, the initial table of the Lemke method is generated using the contact matrix of stiffness and the contact load vector. The unknowns in the problem are mutual displacements and interaction forces of contacting pairs of points of deformable solids. The proposed approach makes it possible to evaluate the change in working schemes as the parameter of external load increases. The features of the proposed formulation of the problem are shown, the criteria for stopping the stepwise process of solving such problems are considered. Model examples for the proposed algorithm are given. The algorithm has shown its efficiency in application, including for complex model problems. Recommendations on the use of the proposed approach are given.

show abstract

Section: Introductionmentioning

confidence: 99%

Algorithm for calculating the problem of unilateral frictional contact with an increscent external load parameter

Popov,

Lovtsov

2023

Struct. Mech. of Eng. Const. and Build

View full text Add to dashboard Cite

show abstract

“…The stresses are secondary and can be calculated by numerically differentiating the displacements. The finite element method in displacements is widely used to solve geometrically and physically nonlinear problems [3][4][5], constructively nonlinear problems with unilateral constraints [6][7][8][9], problems of stability and dynamics of structures [10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Finite elements for problems of the elasticity theory with the discontinuous stress approximation

Lukashevich

Kobelev

2020

E3S Web Conf.

View full text Add to dashboard Cite

The paper deals with the development of the finite element models on the basis of stress approximation. At present, the displacementbased finite element method is mainly used for engineering calculations. Finite element formulations in stresses are not so widely spread, but in some cases these formulations can be more effective in particular with respect to the calculating stresses and also obtaining a two-sided estimate of the exact solution of the problem. The finite element models based on the approximation of discontinuous stress fields and the use of the penalty function method to satisfy the equilibrium equations are considered. It is shown that the continuity of both normal and tangential stresses only on the adjacent sides of the finite elements contributes to the expansion of the class of statically admissible stress fields. At the same time, the consistent approximation is provided, both of the main part of the functional of additional energy, and its penalty part. The necessary matrix relations for rectangular and triangular finite elements are obtained. The effectiveness of the developed models is illustrated by numerical studies. The calculation results were compared with the solution on the FEM in displacements, as well as with the results obtained using other schemes of approximating the stresses in the finite element. It is shown that the model of discontinuous stress approximations gives the bottom convergence of the solution, both in stresses and in displacements. At the same time, the accuracy on the stresses here is much higher than in the displacement-based FEM or when using conventional stress approximation schemes.

show abstract

“…Thus, in [6], in the study of a constructively nonlinear problem with unilateral constraints and friction with an unknown contact zone, an iterative approach was applied to model the bonds using special contact elements in a thin friction layer in combination with a finite element model of a plane problem. In [7], on the basis of the domain decomposition method, contact interaction was studied by the method of penalty functions, which are the conditions for kinematic admissibility of displacements.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Identification of the additional exposure zone for ensuring a complete contact of the two-layered system

Ободан

Гук

Kozakova

2017

EEJET

View full text Add to dashboard Cite

On the decision of contact problems of structural mechanics with unilateral constraints and friction by step-by-step analysis

Cited by 11 publications

References 0 publications

Algorithm for calculating the problem of unilateral frictional contact with an increscent external load parameter

Algorithm for calculating the problem of unilateral frictional contact with an increscent external load parameter

Finite elements for problems of the elasticity theory with the discontinuous stress approximation

Identification of the additional exposure zone for ensuring a complete contact of the two-layered system

Contact Info

Product

Resources

About