Strain-stress behavior of elastic layer in local loading

2020 ◽  
pp. 56-68
Author(s):  
Aleksey N. Sofinsky
Keyword(s):  
Elastic Layer ◽  
Bessel Functions ◽  
Displacement Vector ◽  
Theory Of Elasticity ◽  
Singular Problem ◽  
Local Loading ◽  
Concentrated Force ◽  
Strain Behavior ◽  
Convergence Of Series ◽  
Strain Stress

The paper studies the problem of a local loading of an elastic layer in 3D perspective. The solution of the boundary value problem subject to a concentrated force is constructed as a combination of two components. The first component is a classical solution of A. Lyav theory of elasticity, the second one is a solution proposed by I.М. Rapoport. The second component is distinctive in that it describes a point edge effect rapidly damping while moving off from the point of force application. This solution is built in a series form, namely, proper decompositions of the auxiliary nonself-adjoint differential operator. The convergence of series is ensured by a rapid growth of eigenvalues. Dying-away to zero at infinity is caused by the exponential law of Macdonald functions damping. The solution of the concentrated force action is used as a kernel to determine displacement vector components, tensors of deformations and strains in the problem of arbitrary local loading of an elastic layer. Eventually, analytical solution of the singular problem makes it possible to reasonably determine the strain-stress state in a local loading zone. Key words: strength, stress-strain behavior, theory of elasticity, differential equations, series, Bessel functions.

Bounds on the Maximum Contact Stress of an Indented Elastic Layer

1971 ◽  
Vol 38 (3) ◽  
pp. 608-614 ◽  
Author(s):  
Y. C. Pao ◽  
Ting-Shu Wu ◽  
Y. P. Chiu
Keyword(s):  
Half Space ◽  
Contact Stress ◽  
Elastic Layer ◽  
Theory Of Elasticity ◽  
Contact Conditions ◽  
Practical Applications ◽  
Method Of Solution ◽  
Elastic Layers ◽  
Maximum Contact ◽  
Contact Stress Distribution

This paper is concerned with the plane-strain problem of an elastic layer supported on a half-space foundation and indented by a cylinder. A study is presented of the effect of the contact condition at the layer-foundation interface on the contact stresses of the indented layer. For the general problem of elastic indenter or elastic foundation, the integral equations governing the contact stress distribution of the indented layer derived on the basis of two-dimensional theory of elasticity are given and a numerical method of solution is formulated. The limiting contact conditions at the layer-foundation interface are then investigated by considering two extreme cases, one with the indented layer in frictionless contact with the half space and the other with the indented layer rigidly adhered to the half space. Graphs of the bounds on the maximum normal stress occurring in indented elastic layers for the cases of rigid cylindrical indenter and rigid half-space foundation are obtained for possible practical applications. Some results of the elastic indenter problem are also presented and discussed.

Studying the Effect of some Factors on the Stress-Strain Behavior of the Rostov Region Limestones in the Course of their Production and Use

2021 ◽  
Vol 1022 ◽  
pp. 80-86
Author(s):  
Mikhail G. Kholodnyak ◽  
Sergey A. Stelmakh ◽  
Evgeniy M. Shcherban ◽  
Mukhuma P. Nazhuev
Keyword(s):  
Construction Material ◽  
Experimental Studies ◽  
Raw Material ◽  
Material Base ◽  
Strain Behavior ◽  
Current State ◽  
Rostov Region ◽  
Literary Sources ◽  
Crushed Granite ◽  
Strain Stress

The paper considers the current state of the mineral raw material base and the construction material market of the Rostov Region. The effect of various factors on the strain-stress behavior of local limestones has been investigated. The scientific and technical literary sources devoted to the processes of rock failure under various loads have been analyzed. The experimental studies have shown that the tested samples of limestone with a high content of cuboidal grains have characteristics comparable to those of the crushed granite stone. It has been concluded that the use of the Rostov Region limestones in the construction industry is competitive and feasible, provided the proper implementation of the engineering measures proposed in their production.

Stress Concentrations in Three-Dimensional Electrostriction

1967 ◽  
Vol 34 (2) ◽  
pp. 431-436 ◽  
Author(s):  
T. E. Smith
Keyword(s):  
Displacement Vector ◽  
Spherical Inclusion ◽  
Crack Problem ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Uniform Electric Field ◽  
Inclusion Problem ◽  
Stress Concentrations ◽  
Displacement Potential ◽  
Penny Shaped Crack

Using the techniques employed in developing a Papkovich-Neuber representation for the displacement vector in classical elasticity, a particular integral of the kinematical equations of equilibrium for the uncoupled theory of electrostriction is developed. The particular integral is utilized in conjunction with the displacement potential function approach to problems of the theory of elasticity to obtain closed-form solutions of several stress concentration problems for elastic dielectrics. Under a prescribed uniform electric field at infinity, the problems of an infinite elastic dielectric having first a spherical cavity and then a rigid spherical inclusion are solved. The rigid spheroidal inclusion problem and the penny-shaped crack problem are also solved for the case where the prescribed field is parallel to their axes of revolution.

The Elastic Plane With a Circular Insert, Loaded by a Tangentially Directed Force

1962 ◽  
Vol 29 (2) ◽  
pp. 362-368 ◽  
Author(s):  
M. Hete´nyi ◽  
J. Dundurs
Keyword(s):  
Closed Form ◽  
Elastic Properties ◽  
Classical Theory ◽  
Theory Of Elasticity ◽  
Elastic Plane ◽  
Elementary Functions ◽  
Explicit Formulas ◽  
Concentrated Force

The problem treated is that of a plate of unlimited extent containing a circular insert and subjected to a concentrated force in the plane of the plate and in a direction tangential to the circle. The elastic properties of the insert are different from those of the plate, and a perfect bond is assumed between the two materials. The solution is exact within the classical theory of elasticity, and is in a closed form in terms of elementary functions. Explicit formulas are given for the components of stress in Cartesian co-ordinates, and also in polar co-ordinates at the circumference of the insert.

Layer-adapted methods for a singularly perturbed singular problem

2011 ◽  
Vol 11 (2) ◽  
pp. 192-205
Author(s):  
Christian Grossmann ◽  
Lars Ludwig ◽  
Hans-Görg Roos
Keyword(s):  
Boundary Layer ◽  
Finite Elements ◽  
Boundary Value Problem ◽  
Bessel Functions ◽  
Basis Functions ◽  
Singularly Perturbed ◽  
Singular Problem ◽  
Dimensional Problem ◽  
Modified Bessel Functions ◽  
One Dimensional

Abstract In the present paper we analyze linear finite elements on a layer adapted mesh for a boundary value problem characterized by the overlapping of a boundary layer with a singularity. Moreover, we compare this approach numerically with the use of adapted basis functions, in our case modified Bessel functions. It turns out that as well adapted meshes as adapted basis functions are suitable where for our one-dimensional problem adapted bases work slightly better.

A family of hyper-Bessel functions and convergent series in them

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Jordanka Paneva-Konovska
Keyword(s):  
Power Series ◽  
Bessel Function ◽  
Classical Theory ◽  
Bessel Functions ◽  
Differential Operators ◽  
Arbitrary Order ◽  
Convergent Series ◽  
Multi Index ◽  
Fatou Theorem ◽  
Convergence Of Series

AbstractThe Delerue hyper-Bessel functions that appeared as a multi-index generalizations of the Bessel function of the first type, are closely related to the hyper-Bessel differential operators of arbitrary order, introduced by Dimovski. In this work we consider an enumerable family of hyper-Bessel functions and study the convergence of series in such a kind of functions. The obtained results are analogues to the ones in the classical theory of the widely used power series, like Cauchy-Hadamard, Abel and Fatou theorem.

The Stress State in Inhomogeneous Elastic Beam at Combined Strength

2014 ◽  
Vol 501-504 ◽  
pp. 645-648 ◽  
Author(s):  
Vladimir I. Andreev ◽  
Elena V. Barmenkova ◽  
Alena V. Matveeva
Keyword(s):  
Inverse Problem ◽  
Stress State ◽  
Modulus Of Elasticity ◽  
Elastic Beam ◽  
Bending Moment ◽  
Optimization Method ◽  
Theory Of Elasticity ◽  
Simultaneous Action ◽  
Concentrated Force ◽  
Inhomogeneous Bodies

In paper describes a method of optimization the stress state of an elastic beam, subjected to the simultaneous action of the central application of concentrated force and bending moment. Optimization method based on solving the inverse problem of the theory of elasticity of inhomogeneous bodies, the essence of which is to determine the law of changing the modulus of elasticity on the beams height for which stress state will be given.

scholarly journals Contact Problem for an Elastic Layer on an Elastic Half Plane Loaded by Means of Three Rigid Flat Punches

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
T. S. Ozsahin ◽  
O. Taskıner
Keyword(s):  
Contact Problem ◽  
Half Plane ◽  
Elastic Layer ◽  
Integral Transformation ◽  
Vertical Displacement ◽  
Theory Of Elasticity ◽  
Load Factor ◽  
Initial Separation ◽  
Compressive Loads ◽  
Contact Stress Distribution

The frictionless contact problem for an elastic layer resting on an elastic half plane is considered. The problem is solved by using the theory of elasticity and integral transformation technique. The compressive loadsPandQ(per unit thickness in direction) are applied to the layer through three rigid flat punches. The elastic layer is also subjected to uniform vertical body force due to effect of gravity. The contact along the interface between elastic layer and half plane is continuous, if the value of the load factor,λ, is less than a critical value, . In this case, initial separation loads, and initial separation points, are determined. Also the required distance between the punches to avoid any separation between the punches and the elastic layer is studied and the limit distance between punches that ends interaction of punches is investigated for various dimensionless quantities. However, if tensile tractions are not allowed on the interface, for the layer separates from the interface along a certain finite region. Numerical results for distance determining the separation area, vertical displacement in the separation zone, contact stress distribution along the interface between elastic layer and half plane are given for this discontinuous contact case.

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