A Scaled Boundary Finite-Element Method with B-Differentiable Equations for 3D Frictional Contact Problems
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 elastostat...
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Published in | Fractal and fractional Vol. 6; no. 3; p. 133 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Basel
MDPI AG
01.03.2022
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 2504-3110 2504-3110 |
DOI: | 10.3390/fractalfract6030133 |