• Structural Engineering and Mechanics
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• v.26 no.5
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• pp.591-615
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• 2007

An improvement is introduced to solve the plane problems of linear elasticity by reciprocal theorem for orthotropic materials. This method gives an integral equation with complex kernels which will be solved numerically. An artificial boundary is defined to eliminate the singularities and also an algorithm is introduced to calculate multi-valued complex functions which belonged to the kernels of the integral equation. The chosen sample problem is a plate, having a circular or elliptical hole, stretched by the forces parallel to one of the principal directions of the material. Results are compatible with the solutions given by Lekhnitskii for an infinite plane. Five different orthotropic materials are considered. Stress distributions have been calculated inside and on the boundary. There is no boundary layer effect. For comparison, some sample problems are also solved by finite element method and to check the accuracy of the presented method, two sample problems are also solved for infinite plate.

• Structural Engineering and Mechanics
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• v.51 no.6
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• pp.923-937
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• 2014

The rational finite element method is different from the standard finite element method, which is constructed using basic solutions of the governing differential equations as interpolation functions in the elements. Therefore, it is superior to the isoparametric approach because of its obvious physical meaning and accuracy; it has successfully been applied to the isotropic elasticity problem. In this paper, the formulation of rational finite elements for plane orthotropic elasticity problems is deduced. This method is formulated directly in the physical domain with full consideration of the requirements of the patch test. Based on the number of element nodes and the interpolation functions, different approaches are applied with complete polynomial interpolation functions. Then, two special stiffness matrixes of elements with four and five nodes are deduced as a representative application. In addition, some typical numerical examples are considered to evaluate the performance of the elements. The numerical results demonstrate that the present method has a high level of accuracy and is an effective technique for solving plane orthotropic elasticity problems.

• Structural Engineering and Mechanics
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• v.31 no.6
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• pp.625-638
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• 2009

Applications of membrane mechanisms are widely found in nano-devices and nano-sensor technologies nowadays. An alternative approach for large deflection analysis of the orthotropic, elliptic membranes - subject to gravitational, uniform pressures often found in nano-sensors - is described in this paper. The material properties of membranes are assumed to be orthogonally isotropic and linearly elastic, while the principal directions of elasticity are parallel to the coordinate axes. Formulating the potential energy functional of the orthotropic, elliptic membranes involves the strain energy that is attributed to inplane stress resultant and the potential energy due to applied pressures. In the solution method, Rayleigh-Ritz method can be used successfully to minimize the resulting total potential energy generated. The set of equilibrium equations was solved subsequently by Newton-Raphson. The unparalleled model formulation capable of analyzing the large deflections of both circular and elliptic membranes is verified by making numerical comparisons with existing results of circular membranes as well as finite element solutions. The results are found in excellent agreements at all cases. Then, the parametric investigations are given to delineate the impacts of the aspect ratios and orthotropic elasticity on large static tensions and deformations of the orthotropic, elliptic membranes.

• Journal of the Society of Disaster Information
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• v.10 no.1
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• pp.1-14
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• 2014

This paper presents the three-dimensional stress analysis of orthotropic thick plates using the three-dimensional spline strip method based on the theory of elasticity. The orthotropic plates are made of Aragonite crystal and sitka spruce. To demonstrate the convergence and accuracy of the present method, several examples are solved, and results are compared with those obtained by other exact and numerical methods based on the theory of elasticity. Good convergence and accuracy are obtained. The effects of thickness/width ratio, aspect ratio and boundary conditions on normal stress distributions of Aragonite crystal plates and sitka spruce plates are investigated. Moreover, the difference of weak orthotropic and strong orthotropic properties given to the characteristics of stress distributions are also shown.

• Structural Engineering and Mechanics
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• v.14 no.6
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• pp.661-677
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• 2002

The subject of this investigation is to study the buckling of cross-ply laminated orthotropic cylindrical thin shells with variable elasticity moduli and densities in the thickness direction, under external pressure, which is a power function of time. The dynamic stability and compatibility equations are obtained first. These equations are subsequently reduced to a system of time dependent differential equations with variable coefficients by using Galerkin's method. Finally, the critical dynamic and static loads, the corresponding wave numbers, the dynamic factors, critical time and critical impulse are found analytically by applying a modified form of the Ritz type variational method. The dynamic behavior of cross-ply laminated cylindrical shells is investigated with: a) lamina that present variations in the elasticity moduli and densities, b) different numbers and ordering of layers, and c) external pressures which vary with different powers of time. It is concluded that all these factors contribute to appreciable effects on the critical parameters of the problem in question.

• Structural Engineering and Mechanics
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• v.64 no.1
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• pp.23-31
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• 2017

In the study, dynamic behavior of laminated orthotropic beams on elastic foundation is investigated. Consistent model presented here combines the finite element solution of the system with SAP2000 software and the calculation of soil parameters with MATLAB software using Modified Vlasov Model type elastic foundation. For this purpose, a computing tool is coded in MATLAB which employs Open Application Programming Interface (OAPI) feature of SAP2000 to provide two-way data flow during execution. Firstly, an example is taken from the literature to demonstrate the accuracy of the consistent FEM-Vlasov Model. Subsequently, the effects of boundary conditions, subsoil depth, elasticity modulus of subsoil, slenderness ratio, velocity of moving load and lamination scheme on the behavior of laminated orthotropic beams on elastic foundation are investigated on a new numerical example. It can be concluded that it is really convenient to use OAPI feature of SAP2000 to model this complex behavior of laminated orthotropic beams on elastic foundation under moving load.

• Smart Structures and Systems
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• v.13 no.1
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• pp.25-39
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• 2014

The axisymmetric dynamic instability of polar orthotropic sandwich annular plate combined with electrorheological (ER) fluid core layer and constraining layer are studied in this paper. And, the ER core layer and constraining layer are used to improve the stability of the annular plate system. The boundaries of instability regions for the polar orthotropic sandwich annular plate system are obtained by discrete layer annular finite element and the harmonic balance method. The rheological property of an electrorheological material, such as viscosity, plasticity, and elasticity can be controlled by applying different electric field strength. Thus, the damping characteristics of the sandwich system are more effective when the electric field is applied on the sandwich structure. Additionally, variations of the instability regions for the polar orthotropic sandwich annular plate with different applying electric field strength, thickness of ER layer and some designed parameters are investigated and discussed in this study.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.9
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• pp.1051-1061
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• 2011

The influences of density variation on stress and displacement fields at a propagating Mode-III crack tip in orthotropic functionally graded materials (OFGMs) are studied. The crack propagates dynamically at a right angle to the gradient of physical properties. Three kinds of elasticity and density gradients are analyzed in this study. They are as follows: (1) the density varies without elasticity variation, (2) the directions of the density and elasticity gradients are opposite to each other, and (3) same. For these cases, the stress and displacement fields at the crack tip are developed and the dynamic stress intensity factors for propagating cracks are also studied. When the crack speed is low, the influence of density variation on the stresses and displacement is low. However, when the crack speed is high, this influence is very high.

• Structural Engineering and Mechanics
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• v.13 no.3
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• pp.329-343
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• 2002

In this research, the dynamic stability of an orthotropic elastic conical shell, with elasticity moduli and density varying in the thickness direction, subject to a uniform external pressure which is a power function of time, has been studied. After giving the fundamental relations, the dynamic stability and compatibility equations of a nonhomogeneous elastic orthotropic conical shell, subject to a uniform external pressure, have been derived. Applying Galerkin's method, these equations have been transformed to a pair of time dependent differential equations with variable coefficients. These differential equations are solved using the method given by Sachenkov and Baktieva (1978). Thus, general formulas have been obtained for the dynamic and static critical external pressures and the pertinent wave numbers, critical time, critical pressure impulse and dynamic factor. Finally, carrying out some computations, the effects of the nonhomogeneity, the loading speed, the variation of the semi-vertex angle and the power of time in the external pressure expression on the critical parameters have been studied.

• Geomechanics and Engineering
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• v.25 no.4
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• pp.331-339
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• 2021

In this work, an analytical solution is provided for the dynamical response of an orthotropic non-homogeneous elastic material. The present study has engineering applications in the fields of geophysical physics, structural elements, plasma physics, and the corresponding measurement techniques of magneto-elasticity. The analytical performances for the elastodynamic equations has been solved regarding displacements. The influences of the rotation, the magnetic field, the non-homogeneity based radial displacement and the corresponding stresses in an orthotropic material are investigated. The variations of the stresses, the displacement, and the perturbation magnetic field have been illustrated. The comparisons is performed using the previous solutions in the magnetic field absence, the non-homogeneity and the rotation.