Abstract
AbstractDevelopment of the numerical contact algorithms for finite element method usually concerns convergence, mesh dependency, etc. Verification of the numerical contact algorithm usually includes only a few cases due to a limited number of available analytic solutions (e.g., the Hertz solution for cylindrical surfaces). The solution of the generalized Euler–Eytelwein, or the belt friction problem is a stand alone task, recently formulated for a rope laying in sliding equilibrium on an arbitrary surface, opens up to a new set of benchmark problems for the verification of rope/beam to surface/solid contact algorithms. Not only a pulling forces ratio , but also the position of a curve on a arbitrary rigid surface withstanding the motion in dragging direction should be verified. Particular situations possessing a closed form solution for ropes and rigid surfaces are analyzed. The verification study is performed employing the specially developed Solid‐Beam finite element with both linear and ‐continuous approximations together with the Curve‐to‐Solid Beam (CTSB) contact algorithm and exemplary employing commercial finite element software. A crucial problem of "contact locking" in contact elements showing stiff behavior despite the good convergence is identified. This problem is resolved within the developed CTSB contact element.
Highlights
In many applications concerning the development of computational contact mechanics algorithms the researchers are dealing with a limited set of verification examples possessing analytical solutions
These conditions are forming an effective benchmark test for verification of the rope/beam to surface contact algorithm because only in the region near the great circle defined by Equation (34) equilibrium is possible, otherwise the rope/beam starts to slide in the dragging direction
The main goal of the current contribution—the analysis of the 3D generalized Euler–Eytelwein problem as a set of benchmark problems, which can be used for the verification of different Curve-To-Surface contact algorithms
Summary
In many applications concerning the development of computational contact mechanics algorithms the researchers are dealing with a limited set of verification examples possessing analytical solutions. The Hertz problem, including friction becomes even more specific especially for rolling applications, see References 1,6 These solutions are widely used for verification and corresponding to two- or three-dimensional numerical models resp. A standalone problem for objects of different nature is the frictional contact between a rope and a cylinder initially formulated by Leonhard Euler as the 2D problem and published in "Remarks on the effect of friction on equilibrium".7 This problem after popularization by Eytelwein in his text book[8] nowadays is known as the Euler–Eytelwein problem or the belt friction problem as well as the Euler formula for rope friction. This set is formulated as frictional contact between a rigid surface of various geometry and a rope with particular geometry laying on this surface in equilibrium
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