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

Abstract

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...