scholarly journals Conditions of cracking of a stringer

2005 ◽  
Vol 2005 (3) ◽  
pp. 377-389 ◽  
Author(s):  
D. I. Bardzokas ◽  
G. I. Sfyris
Keyword(s):  
Contact Problem ◽  
Brittle Failure ◽  
Integral Transformation ◽  
Infinite Plate ◽  
Fourier Integral ◽  
Contact Stresses ◽  
Accurate Solution ◽  
Theory And Practice ◽  
External Loading ◽  
Distributed Forces

In the limits of brittle failure of materials, we investigate the problem of possible cracking of an infinite stringer on the boundary of an elastic half-infinite plate. The plate is exposed to tensioning by uniformly distributed forces, and also to contact stresses due to application of forces on the stringer. The accurate solution of a contact problem of interaction of an infinitely continuous stringer is constructed. With the help of this solution, we formulate the condition of cracking of a stringer and the necessary restrictions for external loading, which provide the contacts of a broken stringer with a plate without propagation of a crack inside the stringer. The problem considered here is of interest for theory and practice. We firstly formulate the modified problem of E. Melan and with the help of Fourier integral transformation, we construct its acoustic solution and then formulate the condition of cracking of an infinite stringer. After that, reveal the necessary restrictions on external loadings, which provide the contact of the failed stringer with a plate without propagation of the crack inside the plate.

scholarly journals Consideration of wear in plane contact of rectangular punch and elastic half-plane

2019 ◽  
pp. 138-141
Author(s):  
V. M. Onyshkevych ◽  
G. T. Sulym
Keyword(s):  
Half Plane ◽  
Integral Transformation ◽  
Initial Approximation ◽  
Vertical Displacement ◽  
Fourier Integral ◽  
Mean Value ◽  
Theory Of Elasticity ◽  
Contact Stresses ◽  
Dual Integral Equations ◽  
Plane Contact

The plane contact problem on wear of elastic half-plane by a rigid punch has been considered. The punch moves with constant velocity. Arising thermal effects are neglected because the problem is investigated in stationary statement. In this case the crumpling of the nonhomogeneities of the surfaces and abrasion of half-plane take place. Out of the punch the surface of half-plane is free of load. The solution for problem of theory of elasticity is constructed by means of Fourier integral transformation. Contact stresses are found in Fourier series which coefficients satisfy the dual integral equations. It leads to the system of nonlinear algebraical equations for unknown coefficients by a method of collocations. This system is reduced to linear system in the partial most interesting cases for computing of maximum and minimum wear. The iterative scheme is considered for investigation of other nonlinear cases, for initial approximation the mean value of boundary cases is used. The evolutions of contact stresses, wear and abrasion in the time are given. For both last cases increase or invariable of vertical displacement correspondently is obtained. In the boundary cases coincidence of results with known is obtained.

scholarly journals Exact Solutions of Brinkman Type Fluid Between Side Walls Over an Infinite Plate

2018 ◽  
Author(s):  
Saeed Islam ◽  
Muhammad Asif ◽  
Samiul Haq
Keyword(s):  
Integral Transformation ◽  
Infinite Plate ◽  
Fourier Integral ◽  
Bottom Plate ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Special Cases ◽  
Depth Analysis ◽  
Side Walls ◽  
Oscillating Shear Stress

In this paper Brinkman type fluid over an infinite plate between side walls is being investigated. The flow is generated by oscillating shear stress of the bottom plate and the solutions are obtained by using Fourier integral transformation. The obtained results are presented in steady and transient states for both sin and cos shear stresses. The general solutions are reduced to some special cases corresponding, namely to the Brinkman type fluid over an infinite plate and flow of a Newtonian viscous fluid. Graphical illustrations are carried out to have in depth analysis of the involved physical parameters

scholarly journals The Indentation Rolling Resistance in Belt Conveyors: A Model for the Viscoelastic Friction

Lubricants ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 58 ◽  
Author(s):  
Nicola Menga ◽  
Francesco Bottiglione ◽  
Giuseppe Carbone
Keyword(s):  
Contact Problem ◽  
Finite Thickness ◽  
Numerical Procedure ◽  
Contact Problems ◽  
Accurate Solution ◽  
Rolling Contact ◽  
Viscoelastic Layer ◽  
Force Coefficient ◽  
Belt Conveyors ◽  
Energy Dissipated

In this paper, we study the steady-state rolling contact of a linear viscoelastic layer of finite thickness and a rigid indenter made of a periodic array of equally spaced rigid cylinders. The viscoelastic contact model is derived by means of Green’s function approach, which allows solving the contact problem with the sliding velocity as a control parameter. The contact problem is solved by means of an accurate numerical procedure developed for general two-dimensional contact geometries. The effect of geometrical quantities (layer thickness, cylinders radii, and cylinders spacing), material properties (viscoelastic moduli, relaxation time) and operative conditions (load, velocity) are all investigated. Physical quantities typical of contact problems (contact areas, deformed profiles, etc.) are calculated and discussed. Special emphasis is dedicated to the viscoelastic friction force coefficient and to the energy dissipated per unit time. The discussion is focused on the role played by the deformation localized at the contact spots and the one in the bulk of the thin layer, due to layer bending. The model is proposed as an accurate solution for engineering applications such as belt conveyors, in which the energy dissipated on the rolling contact of idle rollers can, in some cases, be by far the most important contribution to their energy consumption.

scholarly journals RELATIVE PORE VOLUME UNDER INDENTATION OF POROUS MATERIALS

2021 ◽  
Vol 83 (4) ◽  
pp. 462-470
Author(s):  
V.B. Zelentsov ◽  
A.D. Zagrebneva ◽  
P.A. Lapina ◽  
S.M. Aizikovich ◽  
Wang Yun-Che
Keyword(s):  
Porous Material ◽  
Contact Problem ◽  
Porous Layer ◽  
Pore Volume ◽  
Lower Boundary ◽  
Contact Stresses ◽  
Plane Contact ◽  
Plane Contact Problem ◽  
Static Contact ◽  
Rigidity Modulus

Investigation of the function of the relative volume of pores under the load action is carried out on the base of the solution of the static contact problem of the indentation of a layer made of a material with voids or unfilled pores. A rigid strip indenter with a flat base is pressed into a porous layer that is adhered to a non-deformable base along the lower boundary. The formulated 3D problem of the indentation of a porous layer is reduced to solving the plane contact problem of the indentation of a porous strip. The plane contact problem is reduced to solving an integral equation for unknown contact stresses, the solution of which is constructed by the method of successive approximations in the form of an asymptotic expansion in the dimensionless parameter of the problem. The obtained contact stresses and the force acting on the indenter made it possible to study the influence of the nonclassical moduli of the layer porous material (the connectivity modulus and pore rigidity modulus) on the main contact characteristics and on the distribution of the function of the relative pore volume. The connectivity modulus increase leads to an increase in the compliance of the layer porous material, the pore rigidity modulus increase leads to an increase in the rigidity of the layer porous material. The maximum value of the distribution function of the relative pore volume in the porous material of the layer is achieved under the indenter base centre, regardless of the change in the porous material non-classical moduli.

scholarly journals Modelling and solution of contact problem for infinite plate and cross-shaped embedment

2016 ◽  
pp. 61-65
Author(s):  
Oleksandr Kozin ◽  
◽  
Olga Papkovskaya ◽  
Maria Kozina ◽  
◽  
...  
Keyword(s):  
Contact Problem ◽  
Infinite Plate

On the Influence of Interlayer Nonuniformity on Contact Characteristics during the Interaction of a Pipe and a Rigid Cylindrical Insert

2021 ◽  
Vol 887 ◽  
pp. 706-710
Author(s):  
Kirill E. Kazakov
Keyword(s):  
Integral Equation ◽  
Analytical Solution ◽  
Contact Problem ◽  
Analytical Methods ◽  
Integral Operators ◽  
Contact Stresses ◽  
Coating Properties ◽  
Discontinuous Functions ◽  
Different Types ◽  
Separate Factor

Contact problem for viscoelastic aging pipe with a longitudinally nonuniform thin elastic internal coating and a rigid cylindrical insert is considered in the paper. The basic integral equation with integral operators of different types (mixed integral equation) is given. It's analytical solution for contact stresses in insert area is presented. The solution is constructed in such a way that the function describing the inner coating nonuniformity is distinguished by a separate factor. This fact allows one to perform accurate calculations even in cases where the coating properties are described by rapidly changing and even discontinuous functions. Other known analytical methods do not allow one achieving such a results.

scholarly journals Nonsteady frictional heating on a sliding contact

2018 ◽  
Vol 226 ◽  
pp. 03030
Author(s):  
Vladimir B. Zelentsov ◽  
Boris I. Mitrin
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Contact Problem ◽  
Half Plane ◽  
Frictional Heating ◽  
Contact Stresses ◽  
Sliding Contact ◽  
Singular Equation ◽  
Static Contact ◽  
Class Of Functions

We consider quasi-static contact problem on frictional heating on a sliding contact of a rotating rigid cylinder and a half-plane. The cylinder is pressed towards the half-plane material. The problem is reduced to solution of a singular integral equation with respect to contact stresses. Solution of the singular equation is looked for in a class of functions limited on the edge, with two additional conditions to determine timedependent boundaries of the contact area. Temperature at the contact and inside the half-plane is determined in terms of contact stresses.

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