# Contact mechanics using boundary elements

Analysis of 3-D Frictional Contact Mechanics Problems by a Boundary Element Method

Integrating such singular fields is not easy. For simple element geometries e. For more general elements, it is possible to design purely numerical schemes that adapt to the singularity, but at great computational cost. Of course, when source point and target element where the integration is done are far-apart, the local gradient surrounding the point need not be quantified exactly and it becomes possible to integrate easily due to the smooth decay of the fundamental solution. It is this feature that is typically employed in schemes designed to accelerate boundary element problem calculations.

However, for many problems boundary element methods are significantly less efficient than volume-discretisation methods finite element method , finite difference method , finite volume method. A good example of application of the boundary element method is efficient calculation of natural frequencies of liquid sloshing in tanks. Boundary element formulations typically give rise to fully populated matrices. This means that the storage requirements and computational time will tend to grow according to the square of the problem size. By contrast, finite element matrices are typically banded elements are only locally connected and the storage requirements for the system matrices typically grow quite linearly with the problem size.

### A new boundary element approach for contact problems with friction

Method of solving linear partial differential equations. There are several boundary element approaches for crack problems. One such approach is to formulate the conditions on the cracks in terms of hypersingular boundary integral equations, see Ang Therefore, some studies Appendix A.

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For affects the normal and tangential contact compliance. Same effect details on the derivation and implementation see the work of could be appreciated on the second example, considering the Buroni et al. Mathematical non-degenerate case p1 s p2 s p3 the material anisotropy. Steady-state 3D rolling-contact using boundary elements. A mixed formulation for frictional contact problems 2 2 prone to Newton like solution methods. Methods Appl. Alart, P.

investinsider.com/3852-best-cell-locate.php Pure Appl. Aliabadi, M. The Boundary Element Method.

### Contact mechanics using boundary elements

Mech July, The simulated results may pave the way for increasing the efficiency of mining and drilling by improving the design of tools and indentation equipments. Mathematical Theory in Periodic Plane Elasticity. The size and pattern of the elements on the two matching patches should also be close to each other as much as possible to reduce the error. The integral equation may be regarded as an exact solution of the governing partial differential equation. The boundary element method applied to two-dimensonal contact problems with friction. Learn about new offers and get more deals by joining our newsletter.

In: Applications in Solids and Structures, vol. Gas Turbines Power , e Solids Struct. Brebbia, C. Multiple pole residue approach for 3D BEM analysis 3 of mathematical degenerate and non-degenerate materials.

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Two-dimensional boundary element contact mechanics analysis of angled crack Where possible, the BEM results are compared with those available in the. Contact mechanics using boundary elements. Front Cover. K. W. Man. Computational Mechanics Publications, - Technology & Engineering - pages.

Numer, Meth. Contact Problem in the Classical Theory of Elasticity. Mechanics of Elastic Contact. Sliding punches with or without friction along the surface o of an anisotropic elastic half-plane. Mathematical Programming and augmented lagrangian methods for frictional contact problems. In: Curnier, A. Presses Polytechniques et Uni- where the primes are used to denote the derivatives of the func- versitaires Romandes, Lausanne, pp.

Klarbring, A. Mathematical programimg in contact problems. In: tions with respect to the argument p. Computational Mechanics Publications. Laursen, T. Computational Contact and Impact Mechanics. Springer, A. Lee, V. Appendix B. A boundary element formulation for wear modeling on 3D contact and rolling-contact problems. The normal contact operator or normal projection function: J.

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An augmented Lagrangian method for fretting problems. A Solid. Swadener, J. Indentation of elastically anisotropic half-spaces by cones and parabolae of revolution. Anisotropic Elasticity.

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Oxford University Press, Oxford. Crack initiation will take place if the stress intensity factor K reaches its critical value K c. There is a common feature amongst the fracture criteria in that they all try to predict the initiation and direction of crack initial extension under mixed mode I-II loading.

From the viewpoint of practical application, the three fundamental fracture criteria i.

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Therefore, in this modeling, we use this criterion. In this paper, the program TDDQCR 1 is used for the numerical solution of plane infinite problems using the quadratic higher order elements. At first simple problems such as center slant cracks in an infinite plane is solved numerically. The results of TDDQCR are compared with the results of analytical solution to confirm the accuracy and precision of using higher order elements, particularly quadratic elements.

## Quasistatic Electro-Elastic Contact Modeling Using the Boundary Element Method

Slant crack in an infinite plane is shown in Figure 4. The analytical solutions for calculating stress intensity factors, for the infinite body problems are summarized in the Equations 1 and 2. The results of Table 1 are drawn and shown in Figures 5 and 6. Figure 4. Slant crack in an infinite plane under tension. Figure 5. Figure 6. The number of elements of crack length are 32 and 2 special crack tip elements are used. The ratio of crack tip length to crack length is considered as. Table 1. The analytical and numerical values of Mode I and II stress intensity factors.

The computed numerical results are ccompared with analytical results and given in Table 1. Figures 5 and 6 are also drawn based on the results presented in Table 1. Figures 5 and 6 demonstrate the accuracy and effectiveness of the proposed method. The numerical results presented in Table 1 and Figures 5 and 6 demonstrate that this computer code TDDQCR may be effectively used to investigate the crack propagation mechanism of slant edge cracks which may be produced during the indentation process of a blunt rock indenter. For simulating the crack propagation process due to indentation of a blunt rock indenter while acting on the surface of a rock mass, one may assume a square elastic plate, with certain dimensions under plane strain condition containing a semi-circular loaded area with two symmetrical slant edge cracks each of length b as shown in Figure 7.

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This plate contains two equal sized cracks on both of the sides of indenter. And the critical value of stress intensity factor rock fracture toughness is taken as.

The ratio of tip crack length to crack length is considered. For investigating the effect of different angles on the value of stress intensity factors, each free surfaces boundary are divided into 20 elements, 10 elements is considered along the crack and blunt indenter is divided to 10 elements. One special crack tip is used. Figure 7. Assumed elastic plate with symmetrical slant crack.

Figure 8. Normalized stress intensity factors with different angles of crack consequent from Table 2. Table 2. The value of normalized stress intensity factors with different angles of crack. As well as Figure 8 shows the value of. Mechanism of crack propagation under blunt indenter, assuming plane-strain and quasi-static loading condition, has been numerically analyzed by applying the displacement discontinuity method DDM with high-order quadratic elements and based on the linear elastic fracture mechanics LEFM principles.

A simple example i. Ratio of crack length to radius blunt.