A scaled boundary finite element based node-to-node scheme for 2D frictional contact problems

Xing, Weiwei; Song, Chongmin; Tin‐Loi, F.

doi:10.1016/j.cma.2018.01.012

Cited by 51 publications

(22 citation statements)

References 43 publications

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“…The scaled boundary finite-element method [12,13] is a semi-analytical numerical method that only discretizes the outer boundary of the computational domain, reduces the problem dimension by one, accurately simulates the infinite domain, and does not need a fundamental solution. The SBFEM has been widely used in the fields of fracture mechanics [14][15][16], seepage problems [17][18][19], dam-reservoir interactions [20,21] and contact problems [22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

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

Xue

Wang

et al. 2022

Fractal Fract

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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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Section: Introductionmentioning

confidence: 99%

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

Xue

Wang

et al. 2022

Fractal Fract

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“…It is worth mentioning that previous investigations have shown that polygonal super elements are quite robust for small and large finite element sizes inside the same mesh [XST18]. This robustness is important if geometric optimization changes the element sizes on the fly.…”

Section: Sbfem Forward Modelmentioning

confidence: 86%

Defect reconstruction in a 2D semi-analytical waveguide model via derivative-based optimization

Bulling,

Jurgelucks,

Prager

et al. 2021

Preprint

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This paper considers the reconstruction of a defect in a two-dimensional waveguide using a derivativebased optimization approach. The propagation of the waves is simulated by the Scaled Boundary Finite Element Method (SBFEM) that builds on a semi-analytical approach. The simulated data is then fitted to a given set of data describing the reflection of a defect to be reconstructed. For this purpose, we apply an iteratively regularized Gauss-Newton method in combination with algorithmic differentiation to provide the required derivative information accurately and efficiently. We present numerical results for three different kinds of defects, namely a crack, a delamination, and a corrosion. These examples show that the parameterization of the defect can be reconstructed efficiently and robustly in the presence of noise.

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“…This method allows the construction and coupling of star-convex polygonal elements consisting of an arbitrary number of edges, where the type and order of interpolation along each edge can be chosen independently. The SBFEM has been applied successfully to quadtree/octree decompositions [61][62][63][64], as well as polytopal meshes [65,66]. For linear static problems, the SBFEM achieves high order convergence while only requiring nodes on the element edges.…”

Section: Introductionmentioning

confidence: 99%

High order transition elements: The xy-element concept—Part I: Statics

Duczek

Saputra

Gravenkamp

2020

Computer Methods in Applied Mechanics and Engineering

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Advanced transition elements are of utmost importance in many applications of the finite element method (FEM) where a local mesh refinement is required. Considering problems that exhibit singularities in the solution, an adaptive hp-refinement procedure must be applied. Even today, this is a very demanding task especially if only quadrilateral/hexahedral elements are deployed and consequently the hanging nodes problem is encountered. These element types, are, however, favored in computational mechanics due to the improved accuracy compared to triangular/tetrahedral elements. Therefore, we propose a compatible transition element -xNy-element -which provides the capability of coupling different element types. The adjacent elements can exhibit different element sizes, shape function types, and polynomial orders. Thus, it is possible to combine independently refined h-and p-meshes. The approach is based on the transfinite mapping concept and constitutes an extension/generalization of the pNh-element concept. By means of several numerical examples, the convergence behavior is investigated in detail, and the asymptotic rates of convergence are determined numerically. Overall, it is found that the proposed approach provides very promising results for local mesh refinement procedures.

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A scaled boundary finite element based node-to-node scheme for 2D frictional contact problems

Cited by 51 publications

References 43 publications

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

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

Defect reconstruction in a 2D semi-analytical waveguide model via derivative-based optimization

High order transition elements: The xy-element concept—Part I: Statics

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