Multiply Loaded Rigid Punch on a Stressed Orthotopic Half-Plane via a Thin Elastic Layer

1992 ◽  
Vol 59 (2S) ◽  
pp. S115-S122 ◽  
Author(s):  
Hans L. Bjarnehed
Keyword(s):  
Half Plane ◽  
Elastic Layer ◽  
Singular Integral Equations ◽  
Free Edge ◽  
Shear Stresses ◽  
Rigid Punch ◽  
Fem Model ◽  
Frictionless Contact ◽  
Thin Elastic Layer ◽  
Elastic Cushion

A uniaxially stressed orthotropic half-plane indented on the free edge by a multiply loaded rigid punch via a thin elastic layer is considered. The layer is formulated as a generalized Winkler cushion including also shear stresses and strains. Governing singular integral equations are stated for the unknown interface stresses between the cushion and the half-plane. Two kinds of friction conditions between the cushion and half-plane are treated, viz. completely adhesive and frictionless contact. An analytical solution for contact with a rigid cushion and a numerical solution with an elastic cushion are presented. Also, a comparison with a corresponding FEM model is performed. For frictionless contact, some analytical results concerning optimum design of the elastic cushion are given.

Multiply Loaded Timoshenko Beam on a Stressed Orthotropic Half-Plane via a Thin Elastic Layer

1993 ◽  
Vol 60 (2) ◽  
pp. 541-547 ◽  
Author(s):  
H. Bjarnehed
Keyword(s):  
Half Plane ◽  
Timoshenko Beam ◽  
Elastic Layer ◽  
Beam Theory ◽  
Singular Integral Equations ◽  
Uniaxial Stress ◽  
Shear Stresses ◽  
Fe Model ◽  
Tangential Load ◽  
Thin Elastic Layer

The problem of bonded contact between a uniform finite Timoshenko beam and an orthotropic half-plane via a thin elastic layer is considered in this paper. The beam is loaded by distributions of normal and tangential forces, and a uniaxial stress load is applied to the half-plane. The Timoshenko beam theory is extended in such a way that the tangential load is included when the shear contribution to the beam central line deflection is calculated. The layer is formulated as a generalized Winkler cushion including also shear stresses and strains. Governing singular integral equations are stated and numerically solved for the unknown interface stresses. A comparison with a corresponding FE-model is also performed.

Frictionless contact of a rigid punch indenting an elastic layer having piezoelectric properties

2016 ◽  
Vol 228 (2) ◽  
pp. 367-384 ◽  
Author(s):  
Rajesh Patra ◽  
S. P. Barik ◽  
P. K. Chaudhuri
Keyword(s):  
Elastic Layer ◽  
Piezoelectric Properties ◽  
Rigid Punch ◽  
Frictionless Contact

Adhesion of a Rigid Punch to a Thin Elastic Layer

1995 ◽  
Vol 48 (1-4) ◽  
pp. 75-84 ◽  
Author(s):  
J. F. Ganghoffer ◽  
A. N. Gent
Keyword(s):  
Elastic Layer ◽  
Rigid Punch ◽  
Thin Elastic Layer

Reduction of Free-Edge Stress Concentration

1985 ◽  
Vol 52 (4) ◽  
pp. 801-805 ◽  
Author(s):  
P. R. Heyliger ◽  
J. N. Reddy
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Finite Element Model ◽  
Three Dimensional ◽  
Element Model ◽  
Free Edge ◽  
Shear Stresses ◽  
Normal Stresses ◽  
Interlaminar Shear ◽  
Three Dimensional Elasticity

A quasi-three dimensional elasticity formulation and associated finite element model for the stress analysis of symmetric laminates with free-edge cap reinforcement are described. Numerical results are presented to show the effect of the reinforcement on the reduction of free-edge stresses. It is observed that the interlaminar normal stresses are reduced considerably more than the interlaminar shear stresses due to the free-edge reinforcement.

The Frictionless Contact Problem for an Elastic Layer Under Gravity

1975 ◽  
Vol 42 (1) ◽  
pp. 136-140 ◽  
Author(s):  
M. B. Civelek ◽  
F. Erdogan
Keyword(s):  
Elastic Layer ◽  
Mixed Boundary ◽  
Contact Problems ◽  
Simple Problem ◽  
Frictionless Contact ◽  
Continuous Contact ◽  
Crack Problems ◽  
Contact Stress Distribution ◽  
Length Of Separation ◽  
Clamping Pressure

The paper presents a technique for solving the plane frictionless contact problems in the presence of gravity and/or uniform clamping pressure. The technique is described by applying it to a simple problem of lifting of an elastic layer lying on a horizontal, rigid, frictionless subspace by means of a concentrated vertical load. First, the problem of continuous contact is considered and the critical value of the load corresponding to the initiation of interface separation is determined. Then the mixed boundary-value problem of discontinuous contact is formulated in terms of a singular integral equation by closely following a technique developed for crack problems. The numerical results include the contact stress distribution and the length of separation region. One of the main conclusions of the study is that neither the separation length nor the contact stresses are dependent on the elastic constants of the layer.

Partial slip contact analysis for a monoclinic half plane

2020 ◽  
pp. 108128652096283
Author(s):  
İ Çömez ◽  
Y Alinia ◽  
MA Güler ◽  
S El-Borgi
Keyword(s):  
Integral Equations ◽  
Half Plane ◽  
Singular Integral ◽  
Integral Transform ◽  
Mixed Boundary ◽  
Normal Load ◽  
Fibrous Composite ◽  
Singular Integral Equations ◽  
Contact Stresses ◽  
Partial Slip

In this paper, the nonlinear partial slip contact problem between a monoclinic half plane and a rigid punch of an arbitrary profile subjected to a normal load is considered. Applying Fourier integral transform and the appropriate boundary conditions, the mixed-boundary value problem is reduced to a set of two coupled singular integral equations, with the unknowns being the contact stresses under the punch in addition to the stick zone size. The Gauss–Chebyshev discretization method is used to convert the singular integral equations into a set of nonlinear algebraic equations, which are solved with a suitable iterative algorithm to yield the lengths of the stick zone in addition to the contact pressures. Following a validation section, an extensive parametric study is performed to illustrate the effects of material anisotropy on the contact stresses and length of the stick zone for typical monoclinic fibrous composite materials.

Frictionless Contact on Elastic Half Plane with Influence of Surface and Couple Stresses

2020 ◽  
Vol 897 ◽  
pp. 73-77
Author(s):  
Toan Minh Le ◽  
Tinh Quoc Bui ◽  
Jintara Lawongkerd ◽  
Suchart Limkatanyu ◽  
Jaroon Rungamornrat
Keyword(s):  
Contact Pressure ◽  
Half Plane ◽  
Numerical Study ◽  
Surface Elasticity ◽  
Fundamental Solutions ◽  
Internal Length ◽  
Frictionless Contact ◽  
Couple Stresses ◽  
Linear Elastic ◽  
Contact Width

In this paper, a frictionless contact of a rigid flat-ended indentor on a linear elastic half plane is investigated by taking the influence of surface and couple stresses into account. The surface elasticity and couple stress theories are utilized to form a mathematical model. The Green’s function method together with the equilibrium condition of the indentor is employed to formulate the key equations governing the contact pressure. A collocation technique and a set of available fundamental solutions of a half plane under the surface loading are adopted to determine the unknown contact pressure. Results from a numerical study reveal that the presence of both surface and couple stresses significantly alters the distribution of the contact pressure from that predicted by the classical linear elasticity, and the size-dependent characteristics of predicted solutions are obviously observed when the contact width is comparable to the internal length scales of the surface and bulk materials.

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