• Coupled systems mechanics
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• v.9 no.3
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• pp.289-309
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• 2020

The paper studies the fluid flow profile contained between the orthotropic plate and rigid wall under the action of the moving load on the plate and main attention is focused on the fluid velocity profile in the load moving direction. It is assumed that the plate material is orthotropic one and the fluid is viscous and barotropic compressible. The plane-strain state in the plate and the plane flow of the fluid is considered. The motion of the plate is described by utilizing the exact equations of elastodynamics for anisotropic bodies, however, the flow of the fluid by utilizing the linearized Navier-Stokes equations. For the solution of the corresponding boundary value problem, the moving coordinate system associated with the moving load is introduced, after which the exponential Fourier transformation is employed with respect to the coordinate which indicates the distance of the material points from the moving load. The exact analytical expressions for the Fourier transforms of the sought values are obtained, the originals of which are determined numerically. Presented numerical results and their analyses are focused on the question of how the moving load acting on the face plane of the plate which is not in the contact with the fluid can cause the fluid flow and what type profile has this flow along the thickness direction of the strip filled by the fluid and, finally, how this profile changes ahead and behind with the distance of the moving load.

• Smart Structures and Systems
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• v.21 no.1
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• pp.15-25
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• 2018

This work presents the buckling investigation of embedded orthotropic nanoplates such as graphene by employing a new refined plate theory and nonlocal small-scale effects. The elastic foundation is modeled as two-parameter Pasternak foundation. The proposed two-variable refined plate theory takes account of transverse shear influences and parabolic variation of the transverse shear strains within the thickness of the plate by introducing undetermined integral terms, hence it is unnecessary to use shear correction factors. Nonlocal governing equations for the single layered graphene sheet are obtained from the principle of virtual displacements. The proposed theory is compared with other plate theories. Analytical solutions for buckling loads are obtained for single-layered graphene sheets with isotropic and orthotropic properties. The results presented in this study may provide useful guidance for design of orthotropic graphene based nanodevices that make use of the buckling properties of orthotropic nanoplates.

• Structural Engineering and Mechanics
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• v.86 no.4
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• pp.535-546
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• 2023

In the present paper, multiple interface cracks between a functionally graded orthotropic coating and an orthotropic half-plane substrate under concentrated loading are considered by means of the distribution dislocation technique (DDT). With the use of integration of Fourier transform the problem is reduced to a system of Cauchy-type singular integral equations which are solved numerically to compute the dislocation density on the surfaces of the cracks. The distribution dislocation is a powerful method to calculate accurate solutions to plane crack problems, especially this method is very good to find SIFs for multiple unequal cracks located at the interface. Hence this technique allows considering any number of interface cracks. The primary objective of this paper is to investigate the effects of the interaction of multiple interface cracks, load location, material orthotropy, nonhomogeneity parameters and geometry parameters on the modes I and II SIFs. Numerical results show that modes I/II SIFs decrease with increasing the nonhomogeneity parameter and the highest magnitude of SIF occurs where distances between the load location and crack tips are minimal.

• Steel and Composite Structures
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• v.33 no.4
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• pp.509-523
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• 2019

In the present work, the buckling analysis of micro sandwich plate with an isotropic/orthotropic cores and piezoelectric/polymeric nanocomposite face sheets is studied. In this research, two cases for core of micro sandwich plate is considered that involve five isotropic Devineycell materials (H30, H45, H60, H100 and H200) and an orthotropic material also two cases for facesheets of micro sandwich plate is illustrated that include piezoelectric layers reinforced by carbon and boron-nitride nanotubes and polymeric matrix reinforced by carbon nanotubes under temperature-dependent and hydro material properties on the elastic foundations. The first order shear deformation theory (FSDT) is adopted to model micro sandwich plate and to apply size dependent effects from modified strain gradient theory. The governing equations are derived using the minimum total potential energy principle and then solved by analytical method. Also, the effects of different parameters such as size dependent, side ratio, volume fraction, various material properties for cores and facesheets and temperature and humidity changes on the dimensionless critical buckling load are investigated. It is shown from the results that the dimensionless critical buckling load for boron nitride nanotube is lower than that of for carbon nanotube. It is illustrated that the dimensionless critical buckling load for Devineycell H200 is highest and lowest for H30. Also, the obtained results for micro sandwich plate with piezoelectric facesheets reinforced by carbon nanotubes (case b) is higher than other states (cases a and c).The results of this research can be used in aircraft, automotive, shipbuilding industries and biomedicine.

• Structural Engineering and Mechanics
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• v.24 no.1
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• pp.31-50
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• 2006

This paper deals with the mechanical behaviour of the thin-walled cylindrical air-spring shell (CAS) made of rubber-textile cord composite (RCC) subjected to different types of loading. An orthotropic hyperelastic constitutive model is presented which can be applied to numerical simulation for the response of biological soft tissue and of the nonlinear anisotropic hyperelastic material of the CAS used in vibroisolation of driver's seat. The parameters of strain energy function of the constitutive model are fitted to the experimental results by the nonlinear least squares method. The deformation of the inflated CAS is calculated by solving the system of five first-order ordinary differential equations with the material constitutive law and proper boundary conditions. Nonlinear hyperelastic constitutive equations of orthotropic composite material are incorporated into the finite strain analysis by finite element method (FEM). The results for the deformation analysis of the inflated CAS made of RCC are given. Numerical results of principal stretches and deformed profiles of the inflated CAS obtained by numerical deformation analysis are compared with experimental ones.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2001.05a
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• pp.135-140
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• 2001

A post-tensioned reinforced concrete slab bridge is analyzed by specially orthotropic laminate theory. Symmetrically reinforced slab with tension and compression steel is considered for convenience of analysis. Each longitudinal and transverse steel layer is regarded as a lamina, and material constants of each lamina is calculated by the use of the rule of mixture. This bridge is under uniformly distributed vertical loads, and axial loads and end moments due to post-tensioning. In this paper, finite difference method is used for numerical analysis of this bridge. Theory and analysis method of specially orthotropic laminate plates used in this paper can be used for design of new bridges, and maintenance and repair of old bridges.

• Journal of the Korean Society of Industry Convergence
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• v.9 no.1
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• pp.37-44
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• 2006

Stress and displacement fields of a Mode III crack propagating along the normal to gradient in an orthotropic functionally gradient materials (OFGM), which has (1) an exponential variation of shear modulus and density, and (2) linear variation of shear modulus with a constant density, are derived. The equations of motion in OFGM are developed and solution to the displacement and stress fields for a propagating crack at constant speed though an asymptotic analysis. The first three terms in expansion of stress and displacement are derived to explicitly bring out the influence of nonhomogeneity. When the FGM constant ${\zeta}$ is zero or $r{\rightarrow}0$, the fields for OFGM are almost same as the those for homogeneous orthotropic material. Using the stress components, the effects of nonhomogeneity on stress components are discussed.

• Structural Engineering and Mechanics
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• v.54 no.1
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• pp.135-148
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• 2015

The present investigation is concerned with a study effect of magnetic field and non-homogenous on the elastic stresses in rotating orthotropic infinite circular cylinder. A certain boundary conditions closed form stress fields solutions are obtained for rotating orthotropic cylinder under initial magnetic field with constant thickness for three cases: (1) Solid cylinder, (2) Cylinder with a circular hole at the center, (3) Cylinder mounted on a circular rigid shaft. Analytical expressions for the components of the displacement and stress fields in different cases are obtained. The effect of rotation and magnetic field and non-homogeneity on the displacement and stress fields are studied. Numerical results are illustrated graphically for each case. The effects of rotating and magnetic field and non-homogeneity are discussed.

• Structural Engineering and Mechanics
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• v.7 no.1
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• pp.53-67
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• 1999

The natural frequencies and modes of free vibration of specially orthotropic elliptic and circular plates are analysed using the Rayleigh-Ritz method. The assumed functions used are two-dimensional boundary characteristic orthogonal polynomials which are generated using the Gram-Schmidt orthogonalization procedure. The first five natural frequencies are reported here for various values of aspect ratio of the ellipse. Results are given for various boundary conditions at the edges i.e., the boundary may be any of clamped, simply-supported or fret. Numerical results are presented here for several orthotropic material properties. For rectilinear orthotropic circular plates, a few results are available in the existing literature, which are compared with the present results and are found to be in good agreement.

• Structural Engineering and Mechanics
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• v.4 no.5
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• pp.541-552
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• 1996

This paper is concerned with the structural optimization problem of maximizing the compressive buckling load of orthotropic rectangular plates for a given volume of material. The optimality condition is first derived via variational calculus. It states that the thickness distribution is proportional to the strain energy density contrary to popular claims of constant strain energy density at the optimum. An engineers physical meaning of the optimality condition would be to make the average strain energy density with respect to the depth a constant. A double cosine thickness varying plate and a double sine thickness varying plate are then fine tuned in a one parameter optimization using the Rayleigh-Ritz method of analysis. Results for simply supported square plates indicate an increase of 89% in capacity for an orthotropic plate having 100% of its fibers in $0^{\circ}$ direction.