An efficient higher order zigzag theory for composite and sandwich beams subjected to thermal loading

Kapuria, S.; Dumir, P.C.; Ahmed, A.

doi:10.1016/j.ijsolstr.2003.08.014

Cited by 93 publications

(59 citation statements)

References 30 publications

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“…A family of models, called zig-zag models, was first employed in [di Sciuva 1986], then in [Bhaskar and Varadan 1989;Lee et al 1992;Cho and Parmerter 1993]. More recently, it was modified and improved in [Gaudenzi et al 1995;Averill and Yip 1996;Aitharaju and Averill 1999;di Sciuva and Icardi 2001;Kapuria et al 2003;Gherlone and di Sciuva 2007] with different-order kinematics assumptions, taking into account transverse normal strain.…”

Section: (Mixed)mentioning

confidence: 99%

A refined sine-based finite element with transverse normal deformation for the analysis of laminated beams under thermomechanical loads

Vidal¹,

Polit²

2009

JOMMS

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In the framework of a sine model family, two new three-node beam finite elements including the transverse normal effect are designed for the analysis of laminated beams. They are based on a sine distribution with layer refinement and a second-order expansion for the deflection. The transverse shear strain is obtained using a cosine function, avoiding the use of shear correction factors. This kinematics accounts for the interlaminar continuity conditions on the interfaces between layers, and the boundary conditions on the upper and lower surfaces of the beam. A conforming FE approach is carried out using Lagrange and Hermite interpolations. It is important to notice that the number of unknowns is independent of the number of layers.Both mechanical and thermomechanical tests for thin and thick beams are presented in order to evaluate the capability of these new finite elements to give accurate results with respect to elasticity or finite element reference solutions. Both convergence velocity and accuracy are discussed and this new finite element yields very satisfactory results at a low computational cost. In particular, the transverse stress computed from the constitutive relation is well estimated with regards to classical equivalent single layer models. This work focuses on the necessity to take into account the transverse normal stress, especially for thick beam and coupled analysis.

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Section: (Mixed)mentioning

confidence: 99%

A refined sine-based finite element with transverse normal deformation for the analysis of laminated beams under thermomechanical loads

Vidal¹,

Polit²

2009

JOMMS

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“…FU et al [6] presented three solving methods to deal with the governing equations for symmetric laminated composite beams subjected to uniform temperature rise, based on the first-order shear deformation beam theory. KAPURIA et al [7] presented a new efficient higher zigzag theory for thermal stress analysis of laminated beams under thermal loads. WU and ZHAO [8] proposed an enhanced Reddy's theory for laminated composite beams.…”

Section: Introductionmentioning

confidence: 99%

Elasticity solution of laminated beams subjected to thermo-loads

Qian

Zhou

Liu

et al. 2015

J. Cent. South Univ.

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According to the two-dimensional (2-D) thermo-elasticity theory, the exact elasticity solution of the simply supported laminated beams subjected to thermo-loads was studied. An analytical method was presented to obtain the temperature, displacement and stress fields in the beam. Firstly, the general solutions of temperature, displacements and stresses for a single-layered simply supported beam were obtained by solving the 2-D heat conduction equation and the 2-D elasticity equations, respectively. Then, based on the continuity of temperature, heat flux, displacements and stresses on the interface of two adjacent layers, the formulae of temperature, displacements and stresses between the lowest layer and the top layer of the beam were derived out in a recurrent manner. Finally, the unknown coefficients in the solutions were determined by the use of the upper surface and lower surface conditions of the beam. The distributions of temperature, displacement and stress in the beam were obtained by substituting these coefficients back to the recurrence formulae and the solutions. The excellent convergence of the present method has been demonstrated and the results obtained by the present method agree well with those from the finite element method. The effects of surface temperatures, thickness, layer number and material properties of the plate on the temperature distribution were discussed in detail. Numerical results reveal that the displacements and stresses monotonically increase with the increase of surface temperatures. In particular, the horizontal stresses are discontinuous at the interface.

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“…Furthermore, the higher-order zig-zag theories [15,16] involving transverse normal strain were proposed to predict the deformation and stresses of thick piezoelectric composites under mechanical, thermal and electric loads. By considering the thermal expansion effects in the transverse direction of laminated composite plates, the third-order zig-zag theories [17,18] were proposed for analysis of laminated composites and sandwiches under thermal loads. Furthermore, Kapuria and his colleagues [19][20][21] developed the coupled zig-zag models to analyze the static and the dynamic behaviors of piezoelectric laminated plates.…”

Section: Introductionmentioning

confidence: 99%

A C0-type zig–zag theory and finite element for laminated composite and sandwich plates with general configurations

Ren

Wanji

2011

Arch Appl Mech

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In order to conveniently develop C 0 continuous element for the accurate analysis of laminated composite and sandwich plates with general configurations, this paper develops a C 0 -type zig-zag theory in which the interlaminar continuity of transverse shear stresses is a priori satisfied and the number of unknowns is independent of the number of layers. The present theory is applicable not only to the cross-ply but also to the angle-ply laminated composite and sandwich plates. On the premise of retaining the merit of previous zig-zag theories, the derivatives of transverse displacement have been taken out from the displacement fields. Therefore, based on the proposed zig-zag theory, it is very easy to construct the C 0 continuous element. To assess the performance of the proposed model, the classical quadratic six-node triangular element with seven degrees of freedom at each node is presented for the static analysis of laminated composite and sandwich plates.The typical examples are taken into account to assess the performance of finite element based on the proposed zig-zag theory by comparing the present results with the three-dimensional elasticity solutions. Numerical results show that the present model can produce the more accurate deformations and stresses compared with the previous zig-zag theories.

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An efficient higher order zigzag theory for composite and sandwich beams subjected to thermal loading

Cited by 93 publications

References 30 publications

A refined sine-based finite element with transverse normal deformation for the analysis of laminated beams under thermomechanical loads

A refined sine-based finite element with transverse normal deformation for the analysis of laminated beams under thermomechanical loads

Elasticity solution of laminated beams subjected to thermo-loads

A C0-type zig–zag theory and finite element for laminated composite and sandwich plates with general configurations

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