arXiv subjects

Hendrik Andresen

Publications and source records attributed to Hendrik Andresen.

6 recordsLinked to original sources

arXiv2021

Representation of incomplete contact problems by half-planes

Methods for finding the optimal choices of the applied remote loads -- the applied normal force, moment, shear force and remote bulk stresses -- needed to solve frictional contact problems in partial-slip using half-plane theory are derived by using data from contacts analysed by the finite element method. While the normal and shear forces and moment are readily found from equilibrium considerations, in order to determine the bulk stresses we must exploit details of the traction ratio and the direct strain within the contact, both of which are readily extracted from simulations. These contact loads enable the formulation of an equivalent half-plane problem for the contact, which can be used to determine much more precise estimates of the slip-zone sizes than are obtainable from direct use of frictional finite element analysis, as aggregated data from the finite element output is employed, and the half-plane analysis will add precision in terms of satisfaction of the laws of frictional slip and stick.

physics.class-ph↗

arXiv2021

Explicit and asymptotic solutions for frictional incomplete half-plane contacts subject to general oscillatory loading in the steady-state

This contribution presents an asymptotic formulation for the stick-slip behaviour of incomplete contacts under oscillatory variation of normal load, moment, shear load and differential bulk tension. The asymptotic description allows us not only to approximate the size of the slip zones during the steady-state of a cyclic problem without knowledge of the geometry or contact law, but provides a solution when all known analytical solutions for incomplete contacts reach their limitations, that is, in the presence of a varying moment and a differential bulk tension large enough to reverse the direction of slip at one end of the contact. An insightful comparison between the mathematically explicit analytical solution and the asymptotic approach is drawn using the example geometry of a shallow wedge.

cond-mat.soft↗

arXiv2019

A review of partial slip solutions for contacts represented by half-planes including bulk tension and moments

Solution procedures for establishing the regimes of stick and slip for frictional contacts capable of idealisation within the framework of half-plane elasticity and subject to complex loading regimes are reviewed, starting with the well known fundamental problems and going on to more complicated ones. These include problems where the normal load, shear force, applied moment and differential remote tensions all vary with time. Transient and steady state solutions are discussed.

physics.class-ph↗

arXiv2019

The steady state partial slip problem for half plane contacts subject to a constant normal load using glide dislocations

A new solution for general half-plane contact problems subject to a constant normal load together with alternating shear loads and tension in the steady state is presented. The method uses a formulation where a displacement correction is made to the fully stuck contact solution. There will be two outer regions of slip and a central permanent stick zone, which is explicitly established. Thereby, the maximum extent of the slip zones is effectively specified. Cases of small and large tension are studied, that is when the direction of slip is the same or opposing at the ends of the contact, respectively.

cond-mat.soft↗

arXiv2019

Frictional half-plane contact problems subject to alternating normal and shear loads and tension in the steady state

The problem of a general, symmetric contact, between elastically similar bodies, and capable of idealisation using half-plane theory, is studied in the presence of interfacial friction. It is subject to a constant set of loads - normal force, shear force and bulk tension parallel with the interface - together with an oscillatory set of the same quantities, and is in the steady state. Partial slip conditions are expected to ensue for a range of these quantities, and the permanent stick zone is explicitly established, thereby effectively specifying the maximum extent of the slip zones. Exact and approximate, easy to apply recipes are obtained.

cond-mat.soft↗

arXiv2019

Closed-form solutions for tilted three-part piecewise-quadratic half-plane contacts

A general half-plane contact problem in which the geometry is specified in a piecewise-quadratic sense over three segments is solved in closed form. This includes the effects of a moment applied sufficient to introduce separation of one segment and the application of a shearing force sufficient or insufficient to cause sliding. Extending existing solutions to asymmetrical problems is necessary in order to broaden our understanding of the behaviour of dovetail roots of gas turbine fan blades. In previous studies symmetrical contacts have often been used to represent a dovetail flank contact. In the asymmetrical case, the contact pressure may be considerably higher at one of the contact edges compared to the corresponding symmetrical case. Exploiting the generality provided with the solution presented in this study, several simpler indenter problems are investigated making use of an algebraic manipulator. The Mathematica code is made available for download.

physics.class-ph↗