On the solvability of closest point projection procedures in contact analysis: Analysis and solution strategy for surfaces of arbitrary geometry

Konyukhov, Alexander; Schweizerhof, Karl

doi:10.1016/j.cma.2008.02.009

Cited by 60 publications

(49 citation statements)

References 23 publications

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“…Alternatively, a closest point projection is used in some cases, which, however, may not be uniquely defined everywhere; see e.g. [37] for a discussion on the solvability of closest point projections. Analogously to the kinematic quantities above, the slave side contact traction is split into a normal and tangential component:…”

Section: Problem Definition Of Finite Deformation Frictional Contactmentioning

confidence: 99%

Isogeometric dual mortar methods for computational contact mechanics

Seitz

Farah

Kremheller

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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In recent years, isogeometric analysis (IGA) has received great attention in many fields of computational mechanics research. Especially for computational contact mechanics, an exact and smooth surface representation is highly desirable. As a consequence, many well-known finite e lement m ethods a nd a lgorithms f or c ontact m echanics h ave b een t ransferred t o I GA. I n t he present contribution, the so-called dual mortar method is investigated for both contact mechanics and classical domain decomposition using NURBS basis functions. In contrast to standard mortar methods, the use of dual basis functions for the Lagrange multiplier based on the mathematical concept of biorthogonality enables an easy elimination of the additional Lagrange multiplier degrees of freedom from the global system. This condensed system is smaller in size, and no longer of saddle point type but positive definite. A very simple and commonly used element-wise construction of the dual basis functions is directly transferred to the IGA case. The resulting Lagrange multiplier interpolation satisfies discrete inf-sup stability and biorthogonality, however, the reproduction order is limited to one. In the domain decomposition case, this results in a limitation of the spatial convergence order to O(h 3 /2 ) in the energy norm, whereas for unilateral contact, due to the lower regularity of the solution, optimal convergence rates are still met. Numerical examples are presented that illustrate these theoretical considerations on convergence rates and compare the newly developed isogeometric dual mortar contact formulation with its standard mortar counterpart as well as classical finite elements based on first and second order Lagrange polynomials.

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Section: Problem Definition Of Finite Deformation Frictional Contactmentioning

confidence: 99%

Isogeometric dual mortar methods for computational contact mechanics

Seitz

Farah

Kremheller

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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“…Since the finite element method requires only continuity of the discretization (Γ c ∈ C 0 ) so the contacting surface may be not smooth (Γ c ∈ C 1 ). Each master segment has its "projection" zone ( Figure 6), each point in this zone has at least one projection onto the master surface [7,8]. But often in the junction zone of master segments (at common edges and nodes) the intersections of "projection" zones does not fill the surrounding space entirely but with some gaps of form of prisms and pyramids in 3D or of form of sectors in 2D.…”

Section: Contact Detectionmentioning

confidence: 98%

“…For the concave surface AND should be replaced by OR in (13). More elaborated approaches (see, for example, [7]) take into account node-tonode and node-to-edge contacts in case of blind spot detection, average normals can be established at edges and vertices. But for most of the contact problems, consideration of only node-to-segment discretization provides the correct results.…”

Section: Contact Detectionmentioning

confidence: 99%

A Local Contact Detection Technique for Very Large Contact and Self-Contact Problems: Sequential and Parallel Implementations

Yastrebov¹,

Cailletaud²,

Feyel³

2011

Trends in Computational Contact Mechanics

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The local contact detection step can be very time consuming for large contact problems reaching the order of time required for their resolution. At the same time, even the most time consuming technique all-to-all does not guarantee the correct establishment of contact elements needed for further contact problem resolution. Nowadays the limits on mesh size in the Finite Element Analysis are largely extended by powerful parallelization methods and affordable parallel computers. In the light of such changes an improvement of existing contact detection techniques is necessary. The aim of our contribution is to elaborate a very general, simple and fast method for sequential and parallel detection for contact problems with known a priori and unknown master-slave discretizations. In the proposed method the strong connections between the FE mesh, the maximal detection distance and the optimal dimension of detection cells are established. Two approaches to parallel treatment of contact problems are developed and compared: SDMR/MDMR -Single/Multiple Detection, Multiple Resolution. Both approaches have been successfully applied to very large contact problems with more than 2 million nodes in contact.

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“…2 Problems related to C 0 only surfaces in contact mechanics non-mortar ω (1) mortar ω (2) n (2) Uniqueness of projection As discussed and shown in [2] there are several difficulties for solvability and uniqueness of the closest point projection. One of those issues is shown in figure 2a.…”

Section: Discontinuous Mortar Side Normal Vectors (Figure 1a)mentioning

confidence: 99%

“…This issue can be solved by averaging. The problem on boundaries corners and others in [2] discussed problems remain.…”

Section: Discontinuous Mortar Side Normal Vectors (Figure 1a)mentioning

confidence: 99%

Structural contact problems for large deformations ‐ Comparison of steady and non steady normal field

Hammer

2011

Proc Appl Math and Mech

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We will present a comparison between two formulations of the normal vector field for contact algorithms based on the mortar method. First the non steady normal field is discussed. The non steadiness is a result of the C 0 continuity of the boundary discretization. This is the common result if one discretize the domain with classical finite element methods. Second we will present results for a special normal field distribution. We average the nodal normal vector of two ascending edges and interpolate this nodal normal throughout the edges. We have implemented both methods and present comparisons based on numerical experiments. .Discontinuous mortar side normal vectors ( Figure 1a) The proposed mortar side normal was presented in [1] and also in other publications. As the normal vector is normal to its adjacent edge on the mortar side it is obvious that the direction of the normal vector jumps on start and end nodes of a mortar edge.Continuously averaged non-mortar side normal vectors (Figure 1b 2 Problems related to C 0 only surfaces in contact mechanics Oscillation of projection For the nearest point projection we have to determine the corresponding edge for a given projection point. This edge might change during the Newton-Raphson procedure from one iteration to the next. This situation is shown in figure 2b. If the "best" projection edge changes back again in the next iteration the projection starts to oscillate and no convergence can be reached. This problem is not influenced by averaging.

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On the solvability of closest point projection procedures in contact analysis: Analysis and solution strategy for surfaces of arbitrary geometry

Cited by 60 publications

References 23 publications

Isogeometric dual mortar methods for computational contact mechanics

Isogeometric dual mortar methods for computational contact mechanics

A Local Contact Detection Technique for Very Large Contact and Self-Contact Problems: Sequential and Parallel Implementations

Structural contact problems for large deformations ‐ Comparison of steady and non steady normal field

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