• Geomechanics and Engineering
• /
• v.18 no.1
• /
• pp.85-96
• /
• 2019

A free vibration analysis and wave propagation of triclinic and orthotropic plate has been presented in this work using an efficient quasi 3D shear deformation theory. The novelty of this paper is to introducing this theory to minimize the number of unknowns which is three; instead four in other researches, to studying bulk waves in anisotropic plates, other than it can model plates with great thickness ratio, also. Another advantage of this theory is to permits us to show the effect of both bending and shear components and this is carried out by dividing the transverse displacement into the bending and shear parts. Hamilton's equations are a very potent formulation of the equations of analytic mechanics; it is used for the development of wave propagation equations in the anisotropic plates. The analytical dispersion relationship of this type of plate is obtained by solving an eigenvalue problem. The accuracy of the present model is verified by confronting our results with those available in open literature for anisotropic plates. Moreover Numerical examples are given to show the effects of wave number and thickness on free vibration and wave propagation in anisotropic plates.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.11 no.1
• /
• pp.69-78
• /
• 1991

This paper concentrates on the analysis of deflection of the reinforced concrete flexural members under monotonic loading. Concrete is treated as an orthotropic nonlinear material. The concept of equivalent strain and crack strain are used to establish independent stress-strain relationships in the directions of orthotropy. Steel is modeled as an elstoplastic material, and von Mises failure criterion is applied. The finite element computer program for the nonlinear analysis of the deflection of RC flexural members under monotonic loading is developed. The accuracy and reliability of the numerical procedure is demonstrated by the FEM analysis and experiments of the under reinforced concrete beams over the entire loading range up to failure.

• Interaction and multiscale mechanics
• /
• v.1 no.2
• /
• pp.279-301
• /
• 2008

This paper develops a 3D homogenization based continuum damage mechanics (HCDM) model for fiber reinforced composites undergoing micromechanical damage under monotonic and cyclic loading. Micromechanical damage in a representative volume element (RVE) of the material occurs by fiber-matrix interfacial debonding, which is incorporated in the model through a hysteretic bilinear cohesive zone model. The proposed model expresses a damage evolution surface in the strain space in the principal damage coordinate system or PDCS. PDCS enables the model to account for the effect of non-proportional load history. The loading/unloading criterion during cyclic loading is based on the scalar product of the strain increment and the normal to the damage surface in strain space. The material constitutive law involves a fourth order orthotropic tensor with stiffness characterized as a macroscopic internal variable. Three dimensional damage in composites is accounted for through functional forms of the fourth order damage tensor in terms of components of macroscopic strain and elastic stiffness tensors. The HCDM model parameters are calibrated from homogenization of micromechanical solutions of the RVE for a few representative strain histories. The proposed model is validated by comparing results of the HCDM model with pure micromechanical analysis results followed by homogenization. Finally, the potential of HCDM model as a design tool is demonstrated through macro-micro analysis of monotonic and cyclic damage progression in composite structures.

• Composites Research
• /
• v.16 no.4
• /
• pp.1-9
• /
• 2003

2 ply laminated composite is regarded to simulate the interply behavior of the belt layer of the tire. It was cone with 3 dimensional FE(Finite Element) analysis to determine interply shear stress and strain. Widthwise, the shear strain was measured by the pin method. These results are compared with those of CLT(classical lamination theory) in center region and those of Kassapoglou's and Kelsey's theory in edge region. In the FE analysis. rubber is assumed as linear elastic material. and rubber/cord laminate as the orthotropic material composed of cord and rubber In the FE result, interlaminar shear stress causing the interlaminar delamination has the largest value in the edge region of the inner rubber layer. Numerical results obtained coincides with CLT well in the center region, and agrees with other theoretical result little in the edge region.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.24 no.2 s.173
• /
• pp.496-505
• /
• 2000

A semi-infinite parallel crack propagated with constant velocity in two bonded anisotropic strip under anti-plane clamped displacement is analyzed. Using Fourier integral transform a Wiener-Hopf equation is derived. By solving this equation the asymptotic stress and displacement fields near the crack tip are determined, where the results give the more general expression applicable to the extent of the anisotropic material having one plane of elastic symmetry for the parallel crack. The dynamic stress intensity factor and energy release rate are also obtained as a closed form, which are the results applicable to the problem both of dynamic and static crack under the same geometry as this study. The stress intensity factor approaches zero at the critical crack velocity which is less than the shear wave velocity, but in typical case of isotropic or orthotropic material agrees with the velocity of shear wave. Also a circular shear stress around crack tip is considered, from which the stress is shown to be approximately symmetric about the horizontal axis. Referring to the maximum stress criteria, it could be shown that a brenched crack is formed by crack growth as crack velocity increases.

• International Journal of Concrete Structures and Materials
• /
• v.6 no.4
• /
• pp.247-250
• /
• 2012

Composites are somewhat more difficult to model than an isotropic material such as iron or steel due to the fact that each layer may have different orthotropic material properties. In finite element literature the asphalt mixes are represented by using rectangular meshes, not the actual picture of their cross-sections. Asphalt aggregate size and distribution in the asphalt concrete sample, aggregate shape, and fractured surface effects are ignored. In this research, the actual image of the sample including all these effects were directly considered in the finite element. The samples, were cut into cross-sections and were scanned. The image-processing toolbox of Labview was utilized in obtaining the rectangular gray images of the scanned images. In the rectangular sample the aggregates were white and the asphalt binders were black. The grayscale images were converted by LABVIEW into the format required by ANSYS as an input file, with the same dimensions. The nodes at the bottom of the model were constrained in both x and y directions. Left and right edges were symmetry and top was free. Certain amount of pressure was applied along the top surface to simulate the tire pressure.

• Wind and Structures
• /
• v.29 no.6
• /
• pp.371-387
• /
• 2019

In the present paper, a simple refined nth-higher-order shear deformation theory is applied for the free vibration analysis of laminated composite plates. The proposed displacement field is based on a novel kinematic in which include the undetermined integral terms and contains only four unknowns, as against five or more in case of other higher-order theories. The present theory accounts for adequate distribution of the transverse shear strains through the plate thickness and satisfies the shear stress-free boundary conditions on the top and bottom surfaces of the plate, therefore, it does not require problem dependent shear correction factor. The governing equations of motion are derived from Hamilton's principle and solved via Navier-type to obtain closed form solutions. The numerical results of non-dimensional natural frequencies obtained by using the present theory are presented and compared with those of other theories available in the literature to verify the validity of present solutions. It can be concluded that the present refined theory is accurate and efficient in predicting the natural frequencies of isotropic, orthotropic and laminated composite plates.

• Steel and Composite Structures
• /
• v.24 no.4
• /
• pp.499-512
• /
• 2017

This paper deals with nonlinear dynamic stability of embedded piezoelectric nano-composite separators conveying pulsating fluid. For presenting a realistic model, the material properties of structure are assumed viscoelastic based on Kelvin-Voigt model. The separator is reinforced with single-walled carbon nanotubes (SWCNTs) which the equivalent material properties are obtained by mixture rule. The separator is surrounded by elastic medium modeled by nonlinear orthotropic visco Pasternak foundation. The separator is subjected to 3D electric and 2D magnetic fields. For mathematical modeling of structure, three theories of classical shell theory (CST), first order shear deformation theory (FSDT) and sinusoidal shear deformation theory (SSDT) are applied. The differential quadrature method (DQM) in conjunction with Bolotin method is employed for calculating the dynamic instability region (DIR). The detailed parametric study is conducted, focusing on the combined effects of the external voltage, magnetic field, visco-Pasternak foundation, structural damping and volume percent of SWCNTs on the dynamic instability of structure. The numerical results are validated with other published works as well as comparing results obtained by three theories. Numerical results indicate that the magnetic and electric fields as well as SWCNTs as reinforcer are very important in dynamic instability analysis of structure.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2002.04a
• /
• pp.319-326
• /
• 2002

A p-version finite element model based on degenerate shell element is proposed for the analysis of orthotropic laminated plates. In the nonlinear formulation of the model, the total Lagrangian formulation is adopted with large deflection and moderate rotation being accounted for in the sense of von Karman hypothesis. The material model Is based on the Huber-Mises yield criterion and Prandtl-Reuss flow rule in accordance with the theory of strain hardening yield function, which is generalized for anisotropic materials by introducing the parameters of anisotropy. The model is also based on extension of equivalent-single layer laminate theory(ESL theory) with shear deformation, leading to continuous shear strain at the interface of two layers. The Integrals of Legendre Polynomials we used for shape functions with p-level varying from 1 to 10. Gauss-Lobatto numerical quadrature is used to calculate the stresses at the nodal points instead of Gauss points. The validity of the proposed p-version finite element model is demonstrated through several comparative points of view in terms of ultimate load, convergence characteristics, nonlinear effect, and shape of plastic zone

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.25 no.6
• /
• pp.949-958
• /
• 2001

A semi-infinite interfacial crack propagated with constant velocity in two bonded anisotropic strips under out-of-plane clamped displacements is analyzed. Using Fourier integral transform the problem is formulated and the Wiener-Hopf equation is derived. By solving this equation the asymptotic stress and displacement fields near the crack tip are obtained, where the results get more general expressions applicable not only to isotropic/orthotropic materials but also to the extent of the anisotropic material having one plane of elastic symmetry for the interfacial crack. The dynamic stress intensity factor is obtained as a closed form, which is decreased as the velocity of crack propagation increases. The critical velocity where the stress intensity factor comes to zero is obtained, which agrees with the lower value between the critical values of parallel crack merged in the material 1 and 2 adjacent to the interface. Using the near tip fields of stresses and displacements, the dynamic energy release rate is also obtained as a form of the stress intensiy factor.