A Scaled Boundary Finite-Element Method with B-Differentiable Equations for 3D Frictional Contact Problems
Open Access
- 27 February 2022
- journal article
- research article
- Published by MDPI AG in Fractal and Fractional
- Vol. 6 (3) , 133
Abstract
Contact problems are among the most difficult issues in mathematics and are of crucial practical importance in engineering applications. This paper presents a scaled boundary finite-element method with B-differentiable equations for 3D frictional contact problems with small deformation in elastostatics. Only the boundaries of the contact system are discretized into surface elements by the scaled boundary finite-element method. The dimension of the contact system is reduced by one. The frictional contact conditions are formulated as B-differentiable equations. The B-differentiable Newton method is used to solve the governing equation of 3D frictional contact problems. The convergence of the B-differentiable Newton method is proven by the theory of mathematical programming. The two-block contact problem and the multiblock contact problem verify the effectiveness of the proposed method for 3D frictional contact problems. The arch-dam transverse joint contact problem shows that the proposed method can solve practical engineering problems. Numerical examples show that the proposed method is a feasible and effective solution for frictional contact problems.Keywords
This publication has 31 references indexed in Scilit:
- Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBSComputer Methods in Applied Mechanics and Engineering, 2012
- A practical and efficient numerical scheme for the analysis of steady state unconfined seepage flowsInternational Journal for Numerical and Analytical Methods in Geomechanics, 2011
- A contact algorithm for 3D discrete and finite element contact problems based on penalty function methodComputational Mechanics, 2011
- Contact treatment in isogeometric analysis with NURBSComputer Methods in Applied Mechanics and Engineering, 2011
- Sensitivity analysis for frictional contact problems in the augmented Lagrangian formulationComputer Methods in Applied Mechanics and Engineering, 2010
- A Stabilized Lagrange Multiplier Method for the Finite Element Approximation of Frictional Contact Problems in ElastostaticsMathematical Modelling of Natural Phenomena, 2009
- Non-smooth Nonlinear Equations Methods for Solving 3D Elastoplastic Frictional Contact ProblemsComputational Mechanics, 2006
- Contact algorithm for non-linear elastic problems with large displacements and friction using the boundary element methodComputer Methods in Applied Mechanics and Engineering, 1999
- Adaptive finite element techniques for frictional contact problems involving large elastic strainsComputer Methods in Applied Mechanics and Engineering, 1998
- A mixed formulation for frictional contact problems prone to Newton like solution methodsComputer Methods in Applied Mechanics and Engineering, 1991