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.
Highlights
Contact problems are among the most difficult issues in mechanics and are of crucial practical importance in engineering applications
This paper presents an extension of the SBFEM with B-differentiable equations (BDEs) to 3D frictional contact problems with small deformation in elastostatics
In the framework of the SBFEM–BDEs, the contact body is discretized by using the SBFEM, and the frictional contact conditions are enforced by BDEs
Summary
Contact problems are among the most difficult issues in mechanics and are of crucial practical importance in engineering applications. The SBFEM has been widely used in the fields of fracture mechanics [14–16], seepage problems [17–19], dam–reservoir interactions [20,21] and contact problems [22–26] Another key problem in contact analysis is how to enforce the contact constraint conditions. When the penalty function method, the Lagrange multiplier method or the augmented Lagrange multiplier method is used to enforce the contact constraint conditions, and the classical Newton–Raphson method is often used in contact iterative calculations. The B-differentiable equations (BDEs) method [2], as one of the mathematical programming methods, can accurately impose the contact constraint conditions, which are initiated from the augmented Lagrange approach [32]. In the framework of the SBFEM–BDEs, the contact body is discretized by using the SBFEM, and the frictional contact conditions are enforced by BDEs. The B-differentiable Newton method is used to solve the governing equation of 3D frictional contact problems.
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