• Title, Summary, Keyword: deformation theory

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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.

A refined theory with stretching effect for the flexure analysis of laminated composite plates

  • Draiche, Kada;Tounsi, Abdelouahed;Mahmoud, S.R.
    • Geomechanics and Engineering
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    • v.11 no.5
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    • pp.671-690
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    • 2016
  • This work presents a static flexure analysis of laminated composite plates by utilizing a higher order shear deformation theory in which the stretching effect is incorporated. The axial displacement field utilizes sinusoidal function in terms of thickness coordinate to consider the transverse shear deformation influence. The cosine function in thickness coordinate is employed in transverse displacement to introduce the influence of transverse normal strain. The highlight of the present method is that, in addition to incorporating the thickness stretching effect (${\varepsilon}_z{\neq}0$), the displacement field is constructed with only 5 unknowns, as against 6 or more in other higher order shear and normal deformation theory. Governing equations of the present theory are determined by employing the principle of virtual work. The closed-form solutions of simply supported cross-ply and angle-ply laminated composite plates have been obtained using Navier solution. The numerical results of present method are compared with those of the classical plate theory (CPT), first order shear deformation theory (FSDT), higher order shear deformation theory (HSDT) of Reddy, higher order shear and normal deformation theory (HSNDT) 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. It can be concluded that the proposed method is accurate and simple in solving the static bending response of laminated composite plates.

A Study of Plastic Deformation Mechanisms in $Fe_3$Al Intermetallics Alloys by Inelastic Deformation Theory (비탄성 변형이론을 이용한 $Fe_3$Al 금속간화합물의 소성변형 기구 고찰)

  • 정호철
    • Proceedings of the Korean Society for Technology of Plasticity Conference
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    • pp.180-183
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    • 1999
  • It is well known that Fe3Al intermetallic compound shows an anomalous peak of the yield strength at about 50$0^{\circ}C$ and then decrease at higher temperatures The dislocation structure was examined by transmission electron microscopy and high temperatures. The dislocation structure was examined by transmission electron microscopy and high temperature mechanical properties were examined by tensile and load relaxation tests. The flow stress curves obtained from load relaxation tests were then analyzed in terms of internal variable deformation theory. it was found that the flow curves consisted of three micro-deformation mechanisms -i. e inelastic deformation mode plastic deformation mode and dislocation creep deformation mode depending on both dislocation structure and deformation temperature. The flow curves could be well described by the constitutive equations of these three micro-deformation mechanisms based on the internal variable deformation theory.

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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.

A Four-Variable First-Order Shear Deformation Theory Considering the Variation of In-plane Rotation of Functionally Graded Plates

  • Park, Minwo;Choi, Dong-Ho
    • International journal of steel structures
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    • v.18 no.4
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    • pp.1265-1283
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    • 2018
  • This paper presents a four-variable first-order shear deformation theory considering in-plane rotation of functionally graded plates. In recent studies, a simple first-order shear deformation theory was developed and extended to functionally graded plates. It has only four variables, separating the deflection into bending and shear parts, while the conventional first-order shear deformation theory has five variables. However, this simple first-order shear deformation theory only provides good predictions for simply supported plates since it does not consider in-plane rotation varying through the thickness of the plates. The present theory also has four variables, but considers the variation of in-plane rotation such that it is able to correctly predict the responses of the plates with any boundary conditions. Analytical solutions are obtained for rectangular plates with various boundary conditions. Comparative studies demonstrate the effects of in-plane rotation and the accuracy of the present theory in predicting the responses of functionally graded plates.

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.

Cylindrical bending of multilayered composite laminates and sandwiches

  • Sayyad, Atteshamuddin S.;Ghugal, Yuwaraj M.
    • Advances in aircraft and spacecraft science
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    • v.3 no.2
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    • pp.113-148
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    • 2016
  • In a whole variety of higher order plate theories existing in the literature no consideration is given to the transverse normal strain / deformation effects on flexural response when these higher order theories are applied to shear flexible composite plates in view of minimizing the number of unknown variables. The objective of this study is to carry out cylindrical bending of simply supported laminated composite and sandwich plates using sinusoidal shear and normal deformation plate theory. The most important feature of the present theory is that it includes the effects of transverse normal strain/deformation. The displacement field of the presented theory is built upon classical plate theory and uses sine and cosine functions in terms of thickness coordinate to include the effects of shear deformation and transverse normal strain. The theory accounts for realistic variation of the transverse shear stress through the thickness and satisfies the shear stress free conditions at the top and bottom surfaces of the plate without using the problem dependent shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of minimum potential energy. The accuracy of the proposed theory is examined for several configurations of laminates under various static loadings. Some problems are presented for the first time in this paper which can become the base for future research. For the comparison purpose, the numerical results are also generated by using higher order shear deformation theory of Reddy, first-order shear deformation plate theory of Mindlin and classical plate theory. The numerical results show that the present theory provides displacements and stresses very accurately as compared to those obtained by using other theories.

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.

Comparison of Indentation Characteristics According to Deformation and Incremental Plasticity Theory (변형 및 증분소성이론에 따른 압입특성 비교)

  • Lee, Jin-Haeng;Lee, Hyung-Yil
    • Proceedings of the KSME Conference
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    • pp.177-184
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    • 2000
  • In this work, some inaccuracies and limitation of prior indentation theory, which is based on the deformation theory of plasticity and experimental observations, are first investigated. Then effects of major material properties on the configuration of indentation load-deflection curve are examined via incremental plasticity theory based finite element analyses. It is confirmed that subindenter deformation and stress-strain distribution from the deformation theory of plasticity are quite dissimilar to those from incremental theory of plasticity. We finally suggest the optimal data acquisition location, where the strain gradient is the least and the effect of friction is negligible. This data acquisition point increases the strain range by a factor of five.

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Buckling Analysis of Laminated Composite Plate and Shell Structures considering a Higher-Order Shear Deformation (고차전단변형을 고려한 복합적층판 및 쉘구조의 좌굴해석)

  • Lee, Won Hong;Yoon, Seok Ho;Han, Seong Cheon
    • Journal of Korean Society of Steel Construction
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    • v.9 no.1
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    • pp.3-11
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    • 1997
  • Laminated composite shells exhibit properties comsiderably different from those of the single-layer shell. Thus, to obtain the more accurate solutions to laminated composite shells ptoblems, effects of shear strain should be condidered in analysis of them. A higher-order shear deformation theory requires no shear correction coefficients. This theory is used to determine the buckling loads of elastic shells. The theory accounts for parabolic distribution of the transverse shear through the thickness of the shell and rotary inertia. Exact solutions of simply-supported shells are obtained and the results are compared with the exact solutions of the first-order shear deformation theory, and the classical theory. The present theory predicts the buckling loads more accurately when compared to the first -order and classical theory.

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