TRANSFER OF LOADS FROM A FINITE NUMBER OF ELASTIC OVERLAYS WITH FINITE LENGTHS TO AN ELASTIC STRIP THROUGH ADHESIVE SHEAR LAYERS

2019 ◽  
Vol 53 (2 (249)) ◽  
pp. 109-118
Author(s):  
A.V. Kerobyan
Keyword(s):  
Finite Number ◽  
Integral Equations ◽  
Characteristic Parameter ◽  
Shear Layers ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Fredholm Integral Equations ◽  
Shear Stresses ◽  
Infinite Strip ◽  
Small Constant

This article deals with the problem of an elastic infinite strip, which is strengthened along its free boundary by a finite number of finite overlays with different elastic characteristics and small constant thicknesses. The interaction between the strip and the overlays is mediated by adhesive shear layers. The overlays are deformed under the action of horizontal forces. The problem of determination of unknown stresses acting between the strip and overlays are reduced to a system of Fredholm integral equations of the second kind for a finite number of unknown functions defined on different finite intervals. It is shown that in the certain domain of variation of the characteristic parameter of the problem this system of integral equations in Banach space may be solved by the method of successive approximations. Particular cases are discussed and the character and behaviour of unknown shear stresses are investigated.

ON A PROBLEM FOR AN ELASTIC INFINITE SHEET STRENGTHENED BY TWO PARALLEL STRINGERS WITH FINITE LENGTHS THROUGH ADHESIVE SHEAR LAYERS

2020 ◽  
Vol 54 (3 (253)) ◽  
pp. 153-164
Author(s):  
Aghasi V. Kerobyan
Keyword(s):  
Banach Space ◽  
Integral Equations ◽  
Shear Layers ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Fredholm Integral Equations ◽  
Shear Stresses ◽  
Characteristic Parameters ◽  
System Of Integral Equations ◽  
Adhesive Layers

The article considers the problem for an elastic infinite sheet (plate), which is strengthened on two parallel finite parts of its upper surface by two parallel finite stringers with different elastic properties. The parallel stringers are located asymmetrically with respect to the horizontal axis of the sheet and deform under the action of horizontal forces. The interaction between the infinite sheet and stringers takes place through thin elastic adhesive layers. The problem of determining unknown shear stresses acting between the infinite sheet and stringers is reduced to a system of Fredholm integral equations of second kind with respect to unknown functions, which are specified on two parallel finite intervals. It is shown that in the certain domain of the change of the characteristic parameters of the problem this system of integral equations in Banach space can be solved by the method of successive approximations. Particular cases are considered, the character and behaviour of unknown shear stresses are investigated.

scholarly journals METHODS FOR SOLVING FREDHOLM INTEGRAL EQUATIONS

2020 ◽  
Vol 69 (1) ◽  
pp. 174-178
Author(s):  
R.S. Ysmagul ◽  
◽  
А.Е. Nurgeldina ◽  
Keyword(s):  
Quantum Mechanics ◽  
Initial Data ◽  
Differential Equations ◽  
Integral Equations ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Fredholm Integral Equations ◽  
Future State ◽  
Continuous Sequence ◽  
The Moment

The article deals with integral equations that are widely used in various sections of physics (theory of waves on the surface of liquids, quantum mechanics, problems of spectroscopy, crystallography, acoustics, analysis and diagnostics of plasma, etc.), Geophysics (problems of gravimetry, kinematic problems of seismics), mechanics (vibrations of structures), etc. When the physics introduced aftereffect, it is not enough ordinary differential equations or partial differential equations, otherwise the initial data would determine the future state. To take into account the continuous sequence of previous States, we need to use integral and integro-differential equations, where the sign of the integral appears functions of parameters that characterize the system, which depend on time for some period preceding the moment under consideration. In this article we have considered the solution of Fredholm integral equations of the second kind by the method of successive approximations and the method of iterated nuclei.

On the Stresses in a Semi-Infinite Strip Subjected to a Concentrated Load

1965 ◽  
Vol 32 (2) ◽  
pp. 456-458 ◽  
Author(s):  
Chih-Bing Ling
Keyword(s):  
Exact Solution ◽  
Integral Equations ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Infinite Strip ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Method Of Images ◽  
Concentrated Load

This Note presents an exact solution for the stresses in a semi-infinite strip subjected to a symmetrically placed concentrated load. The solution is constructed by method of images. The resulting system of equations, which consists partly of integral equations and partly of algebraic equations, is solved by method of successive approximations. Convergence of the method is proved.

scholarly journals Fuzzy Volterra integral equations with in-finite delay

2009 ◽  
Vol 40 (1) ◽  
pp. 19-29 ◽  
Author(s):  
P. Prakash ◽  
V. Kalaiselvi
Keyword(s):  
Integral Equations ◽  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Volterra Integral Equations ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Uniqueness Of Solutions ◽  
Finite Delay

In this paper, we study the existence and uniqueness of solutions for a class of fuzzy Volterra integral equations with infinite delay by using the method of successive approximations.

HIGH-FREQUENCY BACKSCATTERING FROM AN ABSORBING INFINITE STRIP WITH ARBITRARY FACE IMPEDANCES

1967 ◽  
Vol 45 (7) ◽  
pp. 2409-2430 ◽  
Author(s):  
John J. Bowman
Keyword(s):  
High Frequency ◽  
Thin Layers ◽  
Impedance Boundary Condition ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Infinite Strip ◽  
Impedance Boundary ◽  
Diffraction Effects ◽  
Electromagnetic Backscattering ◽  
Approximate Expressions

Approximate expressions are derived for the high-frequency electromagnetic backscattering from an absorbing infinite strip on which an impedance boundary condition is imposed. Each face of the strip is assumed to possess an arbitrary constant surface impedance not necessarily equal to that of the other face. The problem is treated by a method of successive approximations based on known half-plane solutions; secondary (and in some cases, tertiary) diffraction effects are thereby included. Particularly important is the special case of a perfectly-conducting strip coated on one side with thin layers of highly refractive absorbing materials. Some experimental results of backscattering from an absorber-coated rectangular plate are presented and discussed in the light of the theoretical model.

scholarly journals New error estimation based on midpoint iterative method for solving nonlinear fuzzy fredholm integral equations

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1773-1782 ◽  
Author(s):  
Vahid Mahaleh ◽  
Reza Ezzati
Keyword(s):  
Iterative Method ◽  
Integral Equations ◽  
Error Estimation ◽  
Quadrature Formula ◽  
Numerical Stability ◽  
Suggested Method ◽  
Successive Approximations ◽  
Fredholm Integral Equations ◽  
Numerical Examples

In this paper, first, we apply the successive approximations method in terms of midpoint quadrature formula to solve nonlinear fuzzy Fredholm integral equations of the second kind (NFFIE-2). Considering some assumptions, we acquire a new error estimation. Moreover, we prove the convergence of the proposed method. Then, we study the numerical stability of the proposed method with respect to the first iteration choice. Eventually, to demonstrate the accuracy of the suggested method, we present two numerical examples.

scholarly journals Methods of calculating the deflection of an orthotropic inhomogeneous plate on an elastic basis

2019 ◽  
pp. 106-109
Author(s):  
M. V. Lavrenyuk
Keyword(s):  
Iterative Process ◽  
Poisson Ratio ◽  
Elastic Equilibrium ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Shear Stresses ◽  
Orthotropic Plates ◽  
Winkler Model ◽  
The Difference ◽  
Elastic Basis

The problem of elastic equilibrium of an orthotropic nonhomogeneous rectangular plate on an elastic basis (one-parameter Winkler model) is considered, hingedly fixed from all sides. We use the Navier method for finding the deflection function at each step of the iterative process and perturbation methods and successive approximations as iterative methods for solving the problem. The suitability of the method of successive approximations and the method of perturbations for the numerical solution of the problem of determining the stress-strain state of such a plate, the limits of the applicability of these methods, their accuracy and convergence of the iterative process in solving the deformation problems of heterogeneous orthotropic plates have been analyzed. The dependence of the deflection on the mechanical and geometric parameters of the plate and the base is established. It was found that the Poisson ratio practically does not affect the stress state of the plate (when the Poisson ratio is changed two times, the difference between the intensities of the shear stresses does not exceed 10%), it is possible to consider it as a constant using the methods of successive approximations and disturbances. It is also established that the method of successive approximations and the method of perturbations has a limit on the nature of inhomogeneity, the convergence essentially depends on the nature of the heterogeneity.

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