Accurate determination of transverse normal stresses in sandwich panels subjected to thermomechanical loadings

Noor, Ahmed K.; Malik, M.

doi:10.1016/s0045-7825(99)00025-0

Cited by 18 publications

(11 citation statements)

References 15 publications

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“…In this framework, other approaches are proposed to evaluate transverse shear or normal stresses accurately. Some authors use a hybrid mixed finite element formulation [Han and Hoa 1993] or an iterative predictor-corrector computational procedure [Noor and Malik 1999]. The transverse normal stress is calculated from the integration of the equilibrium equation, avoiding the discontinuity that arises from the use of the constitutive law.…”

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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“…The second re-analysis method is based on the computational model introduced by Noor and Malik in [7,19], where the nonlinear through the thickness distributions of displacement components are successively enhanced based on the Rayleigh-Ritz approximation. The method in the present paper is modified version of [7,19], to enable integration with an assumed strain degenerated solid finite element model based on the FSDT for practical usefulness.…”

Section: Re-analysis With Nonlinear Displacement Correction Coefficientmentioning

confidence: 99%

“…The method in the present paper is modified version of [7,19], to enable integration with an assumed strain degenerated solid finite element model based on the FSDT for practical usefulness.…”

Section: Re-analysis With Nonlinear Displacement Correction Coefficientmentioning

confidence: 99%

“…To overcome the restraint of the initial analysis, it is natural to supplement re-analysis or iterative steps which utilizes results of the post-processing method. Recently a predictor-corrector procedure [19] utilized successive re-analysis using the Rayleigh-Ritz method to sequentially correct the through the thickness distribution of displacements. Also, re-analysis procedure utilizing post-processing results to update the force vector in the re-analaysis phase was introduced [20].…”

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confidence: 99%

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Comparative study of finite element based response evaluation methods for laminated plates

Park

Lee

Kim

2003

Computational Mechanics

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In this paper, four methods for the through the thickness response evaluation of laminated composite and sandwich plates are comparatively evaluated in terms of their characteristics and numerical accuracy. The laminated composite and sandwich plates are subjected to thermo-mechanical loading. The four methods include two post-processor-type methods and two re-analysis-type methods. The post-processor-type methods based on the three-dimensional stress equilibrium equations and the three-dimensional thermo-elasticity equations. And the re-analysis methods are based on the incorporation of the nonlinear through the thickness displacements recovered using post-processing technique in the re-analysis phase. The accuracy of the proposed methods for the evaluation of the through the thickness responses of the laminated plates are assessed via numerical examples of various configurations of laminated plates. Also, applicability and computational efficiencies of the methods are discussed.Keywords Laminated plates, Finite elements, Stress recovery IntroductionNumerous computational approaches for studying the through-the-thickness behavior of laminated composite and sandwich plates have been proposed. These range from those based on three-dimensional continuum mechanics to two-dimensional approaches based on classical laminated plate theory (CLPT) or first order shear deformation theory (FSDT). Description of the various computational approaches can be found in several survey papers [1][2][3][4][5][6][7].Recently those based on simplified kinematic models combined with post-processing methods have been extensively investigated due to their computational efficiencies. These include those based on the through the thickness integration of the three dimensional stress equilibrium equations [8][9][10][11][12][13][14] and those based on obtaining transverse shear stresses directly from transverse shear force, reducing the required order of derivatives of interpolation functions in the stress equilibrium type postprocessing methods for the evaluation of transverse normal stress [15][16][17]. The proposed approaches could enhance the accuracy of the through the thickness responses considerably. However, even for the most advanced post-processing techniques, the final accuracy of the results are bounded by the limitation of the initial finite element results which are based on a simplified kinematic model. Although researches have shown that for mechanical loading, accurate evaluations of transverse stresses can be achieved even for relatively thick laminated composites, problems still reside for sandwich structures with soft core materials. This is more true especially for the transverse normal stress in thermally loaded laminates (see [18] which describes the cause of inaccuracies). To overcome the restraint of the initial analysis, it is natural to supplement re-analysis or iterative steps which utilizes results of the post-processing method. Recently a predictor-corrector procedure [19] utilized successive re-analysis using th...

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“…To overcome the restraint of the initial analysis, it is natural to supplement re-analysis steps which utilizes results of the post-processing method. Recently, a predictorcorrector procedures (Noor and Malik, 1999), utilized successive re-analysis using the Rayleigh-Ritz method to correct the through-the-thickness distribution of displacements. The results of the predictor-corrector approach show considerable improvement in accuracy for laminated composites and sandwiches.…”

Section: Introductionmentioning

confidence: 99%

Re-analysis procedure for laminated plates using FSDT finite element model

Park

Kim

2002

Computational Mechanics

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A new method is proposed for effective analysis of laminated plates incorporating accurate through-thethickness distribution of displacements, strains and stresses in the finite element formulation. It is a two-step analysis procedure. In the first step, displacements are obtained using a post-processing procedure based on the three-dimensional stress equilibrium equations and the thermoelasticity equations, from the results of FSDT finite element analysis. In the second step, the higher-order through-the-thickness distribution of displacements are reflected on the subsequent finite element analysis. The effectiveness of the present approach for the analysis of laminated plates is shown by numerical examples. IntroductionNumerous approaches have been proposed for studying the through-the-thickness behavior of laminated composite and sandwich plates. These approaches include those using (1) finite element analysis based on three-dimensional continuum mechanics, (2) finite element analysis based on quasi-three-dimensional models or higher-order twodimensional models and (3) finite element analysis based on two-dimensional or shell models based on classical laminate plate theory (CLPT) or first order shear deformation theory (FSDT) combined with post-processing procedures. Description of the various computational approaches can be found in several survey papers (Kapania, Three-dimensional or quasi-three-dimensional finite element analysis can become computationally expensive for problems with complicated geometry, especially for laminates with large number of layers.Finite element analysis based on two-dimensional finite element models or shell models based on first order shear deformation theory has limited accuracy as the thickness increases or for sandwich plates. Particularly, accurate evaluation of transverse stresses cannot be expected. Twodimensional finite element analysis used in conjunction with post-processing procedures based on the integration of the three-dimensional stress equilibrium equations or predictor-corrector procedures based on the threedimensional stress equilibrium equations and the threedimensional thermoelasticity equations have been proposed (Engblom and Ochoa, 1985;Chaudhuri, 1986;Noor et al., , 1994 Kim, 1999, 2000). Also proposed are the methods based on obtaining transverse shear stresses directly from transverse shear forces, reducing the required order of derivatives of interpolation functions in the stress equilibrium type post-processing methods for the evaluation of transverse normal stress (Rolfes and Rohwer, 1997; Rolfes et al., 1998a, b). The proposed approaches could enhance the accuracy of the through-the-thickness responses considerably. However, even for the most advanced post-processing techniques, the final accuracy of the results are bounded by the limitation of the initial finite element results which are based on a simplified model. This is more true especially for the transverse normal stress in thermally loaded laminates. To overcome the restraint of the initial an...

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Accurate determination of transverse normal stresses in sandwich panels subjected to thermomechanical loadings

Cited by 18 publications

References 15 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

Comparative study of finite element based response evaluation methods for laminated plates

Re-analysis procedure for laminated plates using FSDT finite element model

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