Buckling of Composite Laminates Using Higher Order Deformation Theory

2004 ◽  
Author(s):  
N. G. R. Iyengar ◽  
Arindam Chakraborty
Keyword(s):  
Transverse Shear ◽  
Composite Laminates ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Shear Loading ◽  
Side Ratio ◽  
Order Deformation ◽  
Shear Effects ◽  
Transverse Shear Effects

Response of composite laminates under in-plane compressive or shear loadings is of interest to the analyst and designers. Since they are thin, they are prone to instability under in-plane loads. Transverse shear effects are important even for thin laminates since elastic modulus and shear modulus are independent properties. For very thick laminates neglecting transverse shear effects leads to completely erroneous results. A number of different theories have been suggested by different investigators to account for transverse shear effects. In this investigation, an attempt has been made to take into account transverse shear effects for the stability analysis of moderately thick/very thick composite laminates under in-plane compressive and shear loading using a “SIMPLE HIGHER ORDER SHEAR DEFORMATION THEORY” based on four unknown displacements instead of five which is commonly used for most of the other higher order theories. A C1 continuous shear flexible finite element based on the proposed HSDT is developed using the Hermite cubic rectangular element. The analytical results obtained have been compared with the available results in literature. Effect of various parameters like aspect ratio, thickness to side ratio, fiber orientation and material properties have been studied in detail.

Free-Vibration of Rotating Composite Beams Incorporating Higher-Order Transverse Shear Effects

2001 ◽  
Author(s):  
N. K. Chandiramani ◽  
L. I. Librescu ◽  
C. D. Shete
Keyword(s):  
Free Vibration ◽  
Transverse Shear ◽  
Present Model ◽  
Structural Model ◽  
Laminated Composite ◽  
Higher Order ◽  
Rotating Blade ◽  
Box Beam ◽  
Shear Effects ◽  
Transverse Shear Effects

Abstract The free vibration behavior of a rotating blade modeled as a laminated composite hollow (single celled) box beam is studied. The geometrically nonlinear structural model developed herein incorporates a number of non-classical effects such as anisotropy, heterogeneity, transverse shear flexibility, and warping inhibition. The centrifugal and Coriolis force field effects are also included. The main focus here being the refinement of the existing model, the traction-free boundary conditions are satisfied here in contrast to the existing model. The resulting linearized equations and numerical results based on them are presented. Results obtained for the present higher-order shearable model are compared with those of the existing first-order shearable and the non-shearable models. Tailoring studies using the present model reveal an enhancement of eigenfrequency characteristics.

scholarly journals An exponential-trigonometric higher order shear deformation theory (HSDT) for bending, free vibration, and buckling analysis of functionally graded materials (FGMs) plates

2020 ◽  
Vol 29 ◽  
pp. 096369351987573 ◽  
Author(s):  
Yamna Belkhodja ◽  
Djamel Ouinas ◽  
Fatima Zohra Zaoui ◽  
Hamida Fekirini
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Functionally Graded Materials ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Graded Materials

Two assumptions have been made based on by this proposed theory, which come from recently developed exponential–trigonometric shape function for transverse shear deformation effect and a simple higher order shear deformation theory for plate, based on a constraint between two rotational displacements of axis parallel to the plate midplane, about the axes x, y Cartesian coordinates system, which caused fewer unknown number. For the application of this method, a displacement field extended as only bending membrane for transverse displacement is used, a governing equations of motion as a result are determined according to Hamilton’s principle, and simplified using Navier analytical solutions, as well as the transverse shear stresses effect that satisfied the stress-free boundary conditions on the simply supported plate free faces as a parabolic variation along the thickness are taken into account. A functionally graded materials plates are chosen for the parametric study, where the plates are functionally graded continuously in materials through the plate thickness as a function of power law or exponential form. The aim of this study is to analyze the bending, free vibration as well as the buckling mechanical behaviors, where the results are more focused on the investigation of different parameters such as the volume fraction index, geometric ratios, frequency modes, in-plane compressive load parameters and material properties effects on the deflection, stresses, natural frequencies, and critical buckling load, which are validated in terms of accuracy and efficiency with other plate theories results found in the literature.

scholarly journals Buckling Analysis of Functionally Graded Material Plates Using Higher Order Shear Deformation Theory

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
B. Sidda Reddy ◽  
J. Suresh Kumar ◽  
C. Eswara Reddy ◽  
K. Vijaya Kumar Reddy
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Functionally Graded Plates ◽  
Transverse Shear Stresses

The prime aim of the present study is to present analytical formulations and solutions for the buckling analysis of simply supported functionally graded plates (FGPs) using higher order shear deformation theory (HSDT) without enforcing zero transverse shear stresses on the top and bottom surfaces of the plate. It does not require shear correction factors and transverse shear stresses vary parabolically across the thickness. Material properties of the plate are assumed to vary in the thickness direction according to a power law distribution in terms of the volume fractions of the constituents. The equations of motion and boundary conditions are derived using the principle of virtual work. Solutions are obtained for FGPs in closed-form using Navier’s technique. Comparison studies are performed to verify the validity of the present results from which it can be concluded that the proposed theory is accurate and efficient in predicting the buckling behavior of functionally graded plates. The effect of side-to-thickness ratio, aspect ratio, modulus ratio, the volume fraction exponent, and the loading conditions on the critical buckling load of FGPs is also investigated and discussed.

Finite element bending analysis of symmetric and non-symmetric functionally graded sandwich beams using a novel parabolic shear deformation theory

2021 ◽  
pp. 146442072110050
Author(s):  
Mohamed-Ouejdi Belarbi ◽  
Abdelhak Khechai ◽  
Aicha Bessaim ◽  
Mohammed-Sid-Ahmed Houari ◽  
Aman Garg ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Beam Element ◽  
Functionally Graded ◽  
Sandwich Beams

In this paper, the bending behavior of functionally graded single-layered, symmetric and non-symmetric sandwich beams is investigated according to a new higher order shear deformation theory. Based on this theory, a novel parabolic shear deformation function is developed and applied to investigate the bending response of sandwich beams with homogeneous hardcore and softcore. The present theory provides an accurate parabolic distribution of transverse shear stress across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the functionally graded sandwich beam without using any shear correction factors. The governing equations derived herein are solved by employing the finite element method using a two-node beam element, developed for this purpose. The material properties of functionally graded sandwich beams are graded through the thickness according to the power-law distribution. The predictive capability of the proposed finite element model is demonstrated through illustrative examples. Four types of beam support, i.e. simply-simply, clamped-free, clamped–clamped, and clamped-simply, are used to study how the beam deflection and both axial and transverse shear stresses are affected by the variation of volume fraction index and beam length-to-height ratio. Results of the numerical analysis have been reported and compared with those available in the open literature to evaluate the accuracy and robustness of the proposed finite element model. The comparisons with other higher order shear deformation theories verify that the proposed beam element is accurate, presents fast rate of convergence to the reference results and it is also valid for both thin and thick functionally graded sandwich beams. Further, some new results are reported in the current study, which will serve as a benchmark for future research.

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