• Structural Engineering and Mechanics
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• 제48권2호
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• pp.241-255
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• 2013

The receding contact problem for two elastic layers whose elastic constants and heights are different supported by two elastic quarter planes is considered. The lower layer is supported by two elastic quarter planes and the upper elastic layer is subjected to symmetrical distributed load whose heights are 2a on its top surface. It is assumed that the contact between all surfaces is frictionless and the effect of gravity force is neglected. The problem is formulated and solved by using Theory of Elasticity and Integral Transform Technique. The problem is reduced to a system of singular integral equations in which contact pressures are the unknown functions by using integral transform technique and boundary conditions of the problem. Stresses and displacements are expressed depending on the contact pressures using Fourier and Mellin formula technique. The singular integral equation is solved numerically by using Gauss-Jacobi integration formulation. Numerical results are obtained for various dimensionless quantities for the contact pressures and the contact areas are presented in graphics and tables.

• Structural Engineering and Mechanics
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• 제21권2호
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• pp.205-220
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• 2005

This paper presents the possibilities of adapting artificial neural networks (ANNs) to predict the dimensionless parameters related to the maximum contact pressures of an elasticity problem. The plane symmetric double receding contact problem for a rigid stamp and two elastic strips having different elastic constants and heights is considered. The external load is applied to the upper elastic strip by means of a rigid stamp and the lower elastic strip is bonded to a rigid support. The problem is solved under the assumptions that the contact between two elastic strips also between the rigid stamp and the upper elastic strip are frictionless, the effect of gravity force is neglected and only compressive normal tractions can be transmitted through the interfaces. A three layered ANN with backpropagation (BP) algorithm is utilized for prediction of the dimensionless parameters related to the maximum contact pressures. Training and testing patterns are formed by using the theory of elasticity with integral transformation technique. ANN predictions and theoretical solutions are compared and seen that ANN predictions are quite close to the theoretical solutions. It is demonstrated that ANNs is a suitable numerical tool and if properly used, can reduce time consumed.

• Journal of applied mathematics & informatics
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• 제12권1_2호
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• pp.183-198
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• 2003

We highlight the alternative presentation of the Cauchy-Riemann conditions for the analyticity of a complex variable function and consider plane equilibrium problem for an elastic transversely isotropic layer, in finite deformation. We state the fundamental problems and consider traction boundary value problem, as an example of fundamental problem-one. A simple solution of“Lame's problem”for an infinite layer is obtained. The profile of the deformed contour is given; and this depends on the order of the term used in the power series specification for the complex potential and on the material constants of the medium.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1996년도 봄 학술발표회 논문집
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• pp.182-189
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• 1996

The focus of this study is on the problem of the design of structure of undetermined topology. This problem has been regarded as being the most challenging of structural optimization problems, because of the difficulty of allowing topology to change. Conventional approaches break down when element sizes approach to zero, due to stiffness matrix singularity. In this study, a novel nonlinear Programming formulation of the topology Problem is developed and examined. Its main feature is the ability to account for topology variation through zero element sizes. Stiffness matrix singularity is avoided by embedding the equilibrium equations as equality constraints in the optimization problem. Although the formulation is general, two dimensional plane elasticity examples are presented. The design problem is to find minimum weight of a plane structure of fixed geometry but variable topology, subject to constraints on stress and displacement. Variables are thicknesses of finite elements, and are permitted to assume zero sizes. The examples demonstrate that the formulation is effective for finding at least a locally minimal weight.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1997년도 추계학술대회 논문집
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• pp.241-244
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• 1997

This paper proposes Electronic Speckle Pattern Interferometry(ESPI) for the quantitative buckling analysis of square tube, which is unable to be measured with previous methods. The quantitative buckling analysis in elasticity is important part to study strain-stress analysis of thick-plated tube and fatigue analysis. However, it is unsolved problem with theory and previous experimental method. The merits of ESPI, Whole-filed measurement and high accurate 3D-displacement measurement make it possible to determinate the buckling analysis in elasticity quantitatively.

• Computers and Concrete
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• 제25권6호
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• pp.551-563
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• 2020

This paper investigates the artificial neural network (ANN) to predict the dimensionless parameters for the maximum contact pressures and contact areas of a contact problem. Firstly, the problem is formulated and solved theoretically by using Theory of Elasticity and Integral Transform Technique. Secondly, the contact problem has been extended based on the ANN. The multilayer perceptron (MLP) with three-layer was used to calculate the contact distances. External load, distance between the two quarter planes, layer heights and material properties were created by giving examples of different values were used at the training and test stages of ANN. Program code was rewritten in C++. Different types of network structures were used in the training process. The accuracy of the trained neural networks for the case was tested using 173 new data which were generated via theoretical solutions so as to determine the best network model. As a result, minimum deviation value (difference between theoretical and C++ ANN results) of was obtained for the network model. Theoretical results were compared with artificial neural network results and well agreements between them were achieved.

• Structural Engineering and Mechanics
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• 제54권4호
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• pp.607-622
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• 2015

This paper presents a comparative study of analytical method and finite element method (FEM) for analysis of a continuous contact problem. The problem consists of two elastic layers loaded by means of a rigid circular punch and resting on semi-infinite plane. It is assumed that all surfaces are frictionless and only compressive normal tractions can be transmitted through the contact areas. Firstly, analytical solution of the problem is obtained by using theory of elasticity and integral transform techniques. Then, finite element model of the problem is constituted using ANSYS software and the two dimensional analysis of the problem is carried out. The contact stresses under rigid circular punch, the contact areas, normal stresses along the axis of symmetry are obtained for both solutions. The results show that contact stresses and the normal stresses obtained from finite element method (FEM) provide boundary conditions of the problem as well as analytical results. Also, the contact areas obtained from finite element method are very close to results obtained from analytical method; disagree by 0.03-1.61%. Finally, it can be said that there is a good agreement between two methods.

• Structural Engineering and Mechanics
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• 제22권1호
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• pp.1-16
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• 2006

This paper presents a virtual boundary element-equivalent collocation method (VBEM) for the plane magnetoelectroelastic solids, which is based on the fundamental solutions of the plane magnetoelectroelastic solids and the basic idea of the virtual boundary element method for elasticity. Besides all the advantages of the conventional boundary element method (BEM) over domain discretization methods, this method avoids the computation of singular integral on the boundary by introducing the virtual boundary. In the end, several numerical examples are performed to demonstrate the performance of this method, and the results show that they agree well with the exact solutions. So the method is one of the efficient numerical methods used to analyze megnatoelectroelastic solids.

• Structural Engineering and Mechanics
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• 제23권1호
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• pp.63-74
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• 2006

In this paper, the scattering of harmonic elastic anti-plane shear waves by two collinear cracks in functionally graded materials is investigated by means of nonlocal theory. The traditional concepts of the non-local theory are extended to solve the fracture problem of functionally graded materials. To overcome the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress field near the crack tips. To make the analysis tractable, it is assumed that the shear modulus and the material density vary exponentially with coordinate vertical to the crack. By use of the Fourier transform, the problem can be solved with the help of a pair of triple integral equations, in which the unknown variable is the displacement on the crack surfaces. To solve the triple integral equations, the displacement on the crack surfaces is expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularities are present at crack tips.

• Structural Engineering and Mechanics
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• 제82권3호
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• pp.401-416
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• 2022

The aim of this study is to examine the frictionless double receding contact problem for two functionally graded (FG) layers pressed with a uniformly distributed load and resting on a homogeneous half plane (HP) using analytical and numerical methods. The FG layers are made of a non-homogeneous material with an isotropic stress-strain law with exponentially varying properties. It is assumed that the contact at the FG layers and FG layer-HP interface is frictionless. The body force of the FG layers and homogeneous HP are ignored in the study. Firstly, an analytical solution for the contact problem has been realized using the theory of elasticity and the Fourier integral transform techniques. Then, the problem modeled and two-dimensional analysis was carried out by using the ANSYS package program based on FEM. Numerical results for contact lengths and contact pressures between FG layers and FG layer-HP were provided for various dimensionless quantities including material inhomogeneity, distributed load width, the shear module ratio, and the heights of the FG layers for both methods. The results obtained using FEM were compared with the results found using the analytical formulation. It was found that the results obtained from analytical formulation were in perfect agreement with the FEM study.