A new developed shear deformation plate (original) (raw)
Related papers
A new shear deformation theory for laminated composite plates
2009
In the present study, a new higher order shear deformable laminated composite plate theory is proposed. It is constructed from 3-D elasticity bending solutions by using an inverse method. Present theory exactly satisfies stress boundary conditions on the top and the bottom of the plate. It was observed that this theory gives most accurate results with respect to 3-D elasticity solutions for bending and stress analysis when compared with existing five degree of freedom shear deformation theories [Reddy JN. A simple higher-order theory for laminated composite plates. J Appl Mech 1984;51:745-52; Touratier M. An efficient standard plate theory. Int J Eng Sci 1991;29(8):901-16; Karama M, Afaq KS, Mistou S. Mechanical behaviour of laminated composite beam by new multi-layered laminated composite structures model with transverse shear stress continuity. Int J Solids Struct 2003;40:1525-46]. All shear deformation theories predict the vibration and buckling results with reasonable accuracy, generally within %2 for investigated problems. Previous exponential shear deformation theory of can be found as a special case.
Analysis of laminated composite plates based on different shear deformation plate theories
Structural Engineering and Mechanics, 2020
A finite strip formulation was developed for buckling and free vibration analysis of laminated composite plates based on different shear deformation plate theories. The different shear deformation theories such as Zigzag higher order, Refined Plate Theory (RPT) and other higher order plate theories by variation of transverse shear strains through plate thickness in the parabolic form, sine and exponential were adopted here. The two loaded opposite edges of the plate were assumed to be simply supported and remaining edges were assumed to have arbitrary boundary conditions. The polynomial shape functions are applied to assess the in-plane and out-of-plane deflection and rotation of the normal cross-section of plates in the transverse direction. The finite strip procedure based on the virtual work principle was applied to derive the stiffness, geometric and mass matrices. Numerical results were obtained based on various shear deformation plate theories to verify the proposed formulatio...
A rectangular non-conforming element based on Reddy's higher-order shear deformation plate theory is developed. Although the plate theory is quite attractive but it could not be exploited as expected in finite-element analysis. This is due to the difficulties associated with satisfaction of inter-elemental continuity requirement and satisfy zero shear stress boundary conditions of the plate theory. In this paper, the proposed element is developed where Reddy's plate theory is successfully implemented. It has four nodes and each node contains 7 degrees of freedom. The performance of the element is tested with different numerical examples, which show its precision and range of applicability.
Applied Composite Materials, 2010
This paper extends the applicability of a modified higher order shear deformation theory to accurately determine the in-plane and transverse shear stress distributions in an orthotropic laminated composite plate subjected to different boundary conditions. A simpler, two-dimensional, shear deformable, plate theory accompanied with an appropriate set of through-thickness variations, is used to accurately predict transverse shear stresses. A finite element code was developed based on a higher order shear deformation theory to study the effects of boundary conditions on the behavior of thin-to-thick anisotropic laminated composite plates. The code was verified against three dimensional elasticity results. The study also compared the stresses and deformation results of higher order theory with those obtained using commercial software such as LUSAS, ANSYS and ALGOR. The commercial software are heavily used by designers to design various components/products made of composites. Various combinations of fixed, clamped and simply supported boundary conditions were used to verify a large class of anticipated applications. Results obtained from software are in good agreement for some cases and significantly differ for others. It was found that LUSAS and ANSYS yield better results for transverse deflection and in-plane stresses. But for transverse shear stresses, it is highly dependent on boundary conditions.
Composite Structures, 2011
A new higher order shear deformation theory for elastic composite/sandwich plates and shells is developed. The new displacement field depends on a parameter ''m'', whose value is determined so as to give results closest to the 3D elasticity bending solutions. The present theory accounts for an approximately parabolic distribution of the transverse shear strains through the shell thickness and tangential stress-free boundary conditions on the shell boundary surface. The governing equations and boundary conditions are derived by employing the principle of virtual work. These equations are solved using Navier-type, closed form solutions. Static and dynamic results are presented for cylindrical and spherical shells and plates for simply supported boundary conditions. Shells and plates are subjected to bi-sinusoidal, distributed and point loads. Results are provided for thick to thin as well as shallow and deep shells. The accuracy of the present code is verified by comparing it with various available results in the literature.
Archives of Mechanics, 2019
A single layer shear deformation plate theory with superposed shape functions for laminated composite plates has been proposed. Some of the previously developed, five degrees of freedom shear deformation theories, including parabolic [1], hyperbolic [2], exponential [3] and trigonometric [4] plate theories have been superposed by applying different theories in the different in-plane directions of the composite plate. Statics and dynamics of composite plate problems have been investigated. It was obtained that using different shape functions in the different in-plane directions may decrease the percentage error of stress and deflection. Present hyperbolic-exponential and parabolic-exponential theories predict stiffer properties (give lower bending and stress values, and higher frequency, and buckling loads when compared to the 3-D elasticity). Some improvements were determined for y-z component of the transverse shear stress using hyperbolic-exponential and parabolic-exponential theories for symmetric cross-ply composite plates when compared to available single shape function plate models. Global behaviours (vibration frequency and critical buckling loads) are predicted within %5 accuracy similar to plate theories with single shape functions.
A new shear deformation theory for the static analysis of laminated composite and sandwich plates
International Joirnal of Mechanical Science
In the present work, a new Inverse Trigonometric Zigzag Theory is proposed and implemented for the static analysis of laminated composite and sandwich plates. The theory assumes the higher order displacement field across the plate thickness satisfying the continuity conditions at the layer interfaces. Zero transverse shear stress boundary conditions at the top and bottom surfaces of the plate are also satisfied. An efficient C0 finite element model is developed and employed to investigate the static response of laminated and sandwich plates. Numerical examples covering different features of laminated composite and sandwich plates are pronounced in the present study. The performance of the model is observed by comparing the evaluated results with different published results available in literature which ascertain its precision and range of applicability.
Cylindrical Bending of Laminated Composite Plates Using Refined Shear Deformation Theory
This paper presents a displacement based refined shear deformation theory which includes transverse shear effect for laminated plates. Appropriate reviews of the recent developments in the analysis of plates with an emphasis placed on shear deformation effects are considered. A refined shear deformation theory for flexural analysis of thick laminated composite plates under cylindrical bending, taking into account transverse shear deformation effects, is developed. The parabolic functions are used in displacement field in terms of thickness coordinate to represent the shear deformation effects. The theory obviates the need of shear correction factor. Governing differential equations and boundary conditions are obtained by using the principle of virtual work. In the present work the laminated composite plates under cylindrical bending are considered for the numerical studies to demonstrate the efficiency of the theory.
International Journal of Mechanics and Materials in Design, 2014
In the present study, a sinusoidal shear and normal deformation theory taking into account effects of transverse shear as well as transverse normal is used to develop the analytical solution for the bidirectional bending analysis of isotropic, transversely isotropic, laminated composite and sandwich rectangular plates. The theory accounts for adequate distribution of the transverse shear strains through the plate thickness and traction free boundary conditions on the plate boundary surface, thus a shear correction factor is not required. The displacement field uses sinusoidal function in terms of thickness coordinate to include the effect of transverse shear and the cosine function in terms of thickness coordinate is used in transverse displacement to include the effect of transverse normal. The kinematics of the present theory is much richer than those of the other higher order shear deformation theories, because if the trigonometric term is expanded in power series, the kinematics of higher order theories 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 Navier solution for simply supported laminated composite plates has been developed. Results obtained for displacements and stresses of simply supported rectangular plates are compared with those of other refined theories and exact elasticity solution wherever applicable.