A Scaled Boundary Finite-Element Method with B-Differentiable Equations for 3D Frictional Contact Problems

• Published in: Fractal and fractional Vol. 6; no. 3; p. 133
• Main Authors: Xue, Binghan, Du, Xueming, Wang, Jing, Yu, Xiang
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.03.2022
• Subjects: Arch dams; B-differentiable equations; Boundary conditions; boundary discretization; Elastostatics; Finite element analysis; Finite element method; Friction; frictional contact; Lagrange multiplier; Mathematical analysis; Mathematical programming; Newton methods; Numerical analysis; scaled boundary finite-element method
• ISSN: 2504-3110; 2504-3110
• DOI: 10.3390/fractalfract6030133

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.