• Title/Summary/Keyword: Shear Deformation

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Flexure of cross-ply laminated plates using equivalent single layer trigonometric shear deformation theory

  • Sayyad, Atteshamuddin S.;Ghugal, Yuwaraj M.
    • Structural Engineering and Mechanics
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    • v.51 no.5
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    • pp.867-891
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    • 2014
  • An equivalent single layer trigonometric shear deformation theory taking into account transverse shear deformation effect as well as transverse normal strain effect is presented for static flexure of cross-ply laminated composite and sandwich plates. The inplane displacement field uses sinusoidal function in terms of thickness coordinate to include the transverse shear deformation effect. The cosine function in thickness coordinate is used in transverse displacement to include the effect of transverse normal strain. The kinematics of the present theory is much richer than those of the other higher order shear deformation theories, because if the trigonometric term (involving thickness coordinate z) is expanded in power series, the kinematics of higher order theories (which are usually obtained by power series in thickness coordinate z) are implicitly taken into account to good deal of extent. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. The closed-form solutions of simply supported cross-ply laminated composite and sandwich plates have been obtained. The results of present theory are compared with those of the classical plate theory (CPT), first order shear deformation theory (FSDT), higher order shear deformation theory (HSDT) of Reddy and exact three dimensional elasticity theory wherever applicable. The results predicted by present theory are in good agreement with those of higher order shear deformation theory and the elasticity theory.

An analytical solution for free vibration of functionally graded beam using a simple first-order shear deformation theory

  • Larbi, Latifa Ould;Hadji, Lazreg;Meziane, Mohamed Ait Amar;Adda Bedia, E.A.
    • Wind and Structures
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    • v.27 no.4
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    • pp.247-254
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    • 2018
  • In this paper, a simple first-order shear deformation theory is presented for dynamic behavior of functionally graded beams. Unlike the existing first-order shear deformation theory, the present one contains only three unknowns and has strong similarities with the classical beam theory in many aspects such as equations of motion, boundary conditions, and stress resultant expressions. Equations of motion and boundary conditions are derived from Hamilton's principle. Analytical solutions of simply supported FG beam are obtained and the results are compared with Euler-Bernoulli beam and the other shear deformation beam theory results. Comparison studies show that this new first-order shear deformation theory can achieve the same accuracy of the existing first-order shear deformation theory.

Dynamic instability region analysis of sandwich piezoelectric nano-beam with FG-CNTRCs face-sheets based on various high-order shear deformation and nonlocal strain gradient theory

  • Arefi, Mohammad;Pourjamshidian, Mahmoud;Arani, Ali Ghorbanpour
    • Steel and Composite Structures
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    • v.32 no.2
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    • pp.157-171
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    • 2019
  • In this research, the dynamic instability region (DIR) of the sandwich nano-beams are investigated based on nonlocal strain gradient elasticity theory (NSGET) and various higher order shear deformation beam theories (HSDBTs). The sandwich piezoelectric nano-beam is including a homogenous core and face-sheets reinforced with functionally graded (FG) carbon nanotubes (CNTs). In present study, three patterns of CNTs are employed in order to reinforce the top and bottom face-sheets of the beam. In addition, different higher-order shear deformation beam theories such as trigonometric shear deformation beam theory (TSDBT), exponential shear deformation beam theory (ESDBT), hyperbolic shear deformation beam theory (HSDBT), and Aydogdu shear deformation beam theory (ASDBT) are considered to extract the governing equations for different boundary conditions. The beam is subjected to thermal and electrical loads while is resting on Visco-Pasternak foundation. Hamilton principle is used to derive the governing equations of motion based on various shear deformation theories. In order to analysis of the dynamic instability behaviors, the linear governing equations of motion are solved using differential quadrature method (DQM). After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as various shear deformation theories, nonlocal parameter, strain gradient parameter, the volume fraction of the CNTs, various distributions of the CNTs, different boundary conditions, dimensionless geometric parameters, Visco-Pasternak foundation parameters, applied voltage and temperature change on the dynamic instability characteristics of sandwich piezoelectric nano-beam.

A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates

  • Houari, Mohammed Sid Ahmed;Tounsi, Abdelouahed;Bessaim, Aicha;Mahmoud, S.R.
    • Steel and Composite Structures
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    • v.22 no.2
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    • pp.257-276
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    • 2016
  • In this paper, a new simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded (FG) plates is developed. The significant feature of this formulation is that, in addition to including a sinusoidal variation of transverse shear strains through the thickness of the plate, it deals with only three unknowns as the classical plate theory (CPT), instead of five as in the well-known first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The accuracy of the present solutions is verified by comparing the obtained results with those predicted by classical theory, first-order shear deformation theory, and higher-order shear deformation theory. Verification studies show that the proposed theory is not only accurate and simple in solving the bending and free vibration behaviours of FG plates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns.

Theoretical Analysis of Anisotropic Laminated Shells with Shear Deformation (전단변형을 고려한 이방성 적층셜의 이론해석)

  • Kwun, Ik-No;Kwun, Taek-Jin
    • Journal of Korean Association for Spatial Structures
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    • v.1 no.2
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    • pp.85-92
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    • 2001
  • The structural behaviors of anisotropic laminated shells are quite different from that of isotropic shells, Also, the classical theory of shells based on neglecting transverse shear deformation is invalid for laminated shells. Thus, to obtain the more exact behavior of laminated shells, effects of shear deformation should be considered in the analysis. As the length of x-axis or y-axis is increase, the effects of transverse shear deformation are decrease because the stiffness for the axis according to the increasing of length is large gradually. In this paper, the governing equations for anisotropic laminated shallow shell including the effects of shear deformation are derived. And then, by using Navier's solutions for shallow shells having simple supported boundary, extensive numerical studies for anisotropic laminated shallow shells were made to investigate the effects of shear deformation for 3 typical shells. Also, static analysis is carried out for cross-ply laminated shells considering the effects of various geometrical parameters, e,g., the shallowness ratio, the thickness ratio and the ratio of a(length of x-axis)-to-b(length of y-axis). The results are compared with existed one and show good agreement.

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A Simple Modification of the First-order Shear Deformation Theory for the Analysis of Composite Laminated Structures (복합적층구조해석을 위한 1차전단변형이론의 간단한 수정방안)

  • Chun, Kyoung-Sik;Ji, Hyo-Seon
    • Journal of Korean Society of Steel Construction
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    • v.23 no.4
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    • pp.475-481
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    • 2011
  • In this study, a simplified method of improving not only transverse shear stress but also shear strain based on the first-order shear deformation theory was developed. Unlike many established methods, such as the higher-order shear deformation and layerwise theories, this method can easily apply to finite elements as only $C^0$ continuity is necessary and the formulation of equations is very simple. The basic concept in this method, however, must be corrected:the distribution of the transverse shear stresses and shear strains through the thickness from the formulation based on the higher-order shear deformation theory. Therefore, the shear correction factors are no longer required, based on the first-order shear deformation theory. Numerical analyses were conducted to verify the validity of the proposed formulations. The solutions based on the simplified method were in very good agreement with the results considering the higher-order shear deformation theory.

Modelling of shear deformation and bond slip in reinforced concrete joints

  • Biddah, Ashraf;Ghobarah, A.
    • Structural Engineering and Mechanics
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    • v.7 no.4
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    • pp.413-432
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    • 1999
  • A macro-element model is developed to account for shear deformation and bond slip of reinforcement bars in the beam-column joint region of reinforced concrete structures. The joint region is idealized by two springs in series, one representing shear deformation and the other representing bond slip. The softened truss model theory is adopted to establish the shear force-shear deformation relationship and to determine the shear capacity of the joint. A detailed model for the bond slip of the reinforcing bars at the beam-column interface is presented. The proposed macro-element model of the joint is validated using available experimental data on beam-column connections representing exterior joints in ductile and nonductile frames.

Effects of shear deformation on the effective length of tapered columns with I-section for steel portal frames

  • Li, Guo-Qiang;Li, Jin-Jun
    • Structural Engineering and Mechanics
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    • v.10 no.5
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    • pp.479-489
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    • 2000
  • Based on the stiffness equation of the tapered beam element involving the effects of axial force and shear deformation, numerical investigations are carried out on elastic instability for web-linearly tapered columns with I-section of steel portal frames. Effects of shear deformation on the effective length of the tapered columns with I-section are studied. An efficient approach for determining the effective length of the tapered portal frame columns considering effects of shear deformation is proposed.

Finite Element Analysis of Functionally Graded Plates using Inverse Hyperbolic Shear Deformation Theory

  • Kulkarni, Kamlesh;Singh, Bhrigu Nath;Maiti, Dipak Kumar
    • International Journal of Aerospace System Engineering
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    • v.3 no.1
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    • pp.1-4
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    • 2016
  • Functionally graded materials (FGMs) are becoming very popular in various industries due to their effectiveness of the utilization of their constituent elements. However, the modelling of these materials is difficult due to the complex nature of variation of material properties across the thickness. Many shear deformation theories have been developed and employed for the analysis of such functionally graded plates (FGPs). A recently developed inverse hyperbolic shear deformation theory has been successfully employed by Grover et al. [1] for the analysis of laminated composites and sandwich plates. The objective of the study is to obtain finite element solution for the structural analysis of functionally graded plates using inverse hyperbolic shear deformation theory. Finite element analysis facilitates the analysis of complex problems such as functionally graded plates with different boundary conditions and different loadings.

Effect of shear deformation on the critical buckling of multi-step bars

  • Li, Q.S.
    • Structural Engineering and Mechanics
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    • v.15 no.1
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    • pp.71-81
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    • 2003
  • The governing differential equation for buckling of a one-step bar with the effect of shear deformation is established and its exact solution is obtained. Then, the exact solution is used to derive the eigenvalue equation of a multi-step bar. The new exact approach combining the transfer matrix method and the closed form solution of one step bar is presented. The proposed methods is convenient for solving the entire and partial buckling of one-step and multi-step bars with various end conditions, with or without shear deformation effect, subjected to concentrated axial loads. A numerical example is given explaining the proposed procedure and investigating the effect of shear deformation on the critical buckling force of a multi-step bar.