Computational and analytical modelling of composite structures based on exact and higher order theories (original) (raw)
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International Journal of Engineering Science, 1993
improved higher-order theory is developed for the stress analysis of laminated tranversely isotropic plates and shells subject to transverse shear deformation and normal compression. The theory is capable of analyzing the stress-strain behavior of layered plates and shells with an arbitrary number and sequence of layers which may differ significantly in their physical and mechanical properties. New variables which have a clear physical meaning are introduced. Various loading and boundary conditions are considered which enable transverse shear and normal reduction to be fully taken into account, and the complete set of boundary conditions is derived. The closed-form solutions of some multilayered plates and shells are derived. Numerical results are compared with those given in the literature, in order to validate the analysis presented. The features of this theory and the implications of the numerical results are discussed.
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.
A geometrically nonlinear analysis of laminated composite plates using a shear deformation theory
1989
Meccanica.-A geometrically nonlinear analysis of laminated composite plates using a shear deformation theory. Nota di GIACINTO PORCO (*), GIUSEPPE SPADEA (*) e RAFFAELE ZINNO(*), presentata (**) dal Socio E. GIANGRECO. ABSTRACT.-A shear deformation theory is developed to analyse the geometrically nonlinear behaviour of layered composite plates under transverse loads. The theory accounts for the transverse shear (as in the Reissner Mindlin plate theory) and large rotations (in the sense of the von Karman theory) suitable for simulating the behaviour of moderately thick plates. Square and rectangular plates are considered: the numerical results are obtained by a finite element computational procedure and are given for various boundary and loading conditions, a/b ratios, stacking and orientation of layers and material properties (Ei/E 2 ratio, E 1 /G ratio, etc.).
Journal of Mechanical Engineering and Sciences
In the present study, a generalized shell theory is presented and applied for the analysis of laminated composite cylindrical shells. A theoretical unification of the several refined shell theories is presented. The principle of work done is employed to derive five differential equations corresponding to five unknowns involved in the present generalized shell theory. Five differential equations are solved by an analytical procedure suggested by the Navier. The numerical results for simply supported laminated composite cylindrical shells are presented and compared with 3D elasticity solutions. Displacements, stresses and fundamental frequencies are obtained for isotropic, orthotropic, 00/900 and 00/900/00 laminated cylindrical shells. The numerical results are obtained for h/a=0.1, a/b=1 and different values of R/a ratio. Displacements and stresses of laminated cylindrical shells are estimated under sinusoidal transverse load. In the case of free vibration analysis, first five natura...
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.
Theories of Composite Plates and Numerical Methods used on Bending and Buckling of Laminated Plates
A comprehensive literature review on different theories of laminated plates have been reviewed and discussed thoroughly. It has been found that there are two main theories of laminated plates which are known as linear and nonlinear theories. The two theories are depending on the magnitude of deformation resulting from loading the given plates. The difference between the two theories is that the deformations are small in the linear theory, whereas they are finite or large in the nonlinear theory. In comparisons between FEM and different numerical methods it has been found that FEM can be considered of acceptable accuracy, and can also be applied to different complicated geometries and shapes. Keywords: Theories of laminates, linear and nonlinear, numerical methods, finite element method, small and large deformations. Developments in the theories of laminated plates: From the point of view of solid mechanics, the deformation of a plate subjected to transverse and / or in plane loading consists of two components: flexural deformation due to rotation of cross – sections, and shear deformation due to sliding of section or layers. The resulting deformation depends on two parameters: the thickness to length ratio and the ratio of elastic to shear moduli. When the thickness to length ratio is small, the plate is considered thin, and it deforms mainly by flexure or bending; whereas when the thickness to length and the modular ratios are both large, the plate deforms mainly through shear. Due to the high ratio of in – plane modulus to transverse shear modulus, the shear deformation effects are more pronounced in the composite laminates subjected to transverse and / or in plane loads than in the isotropic plates under similar loading conditions. The three – dimensional theories of laminates in which each layer is treated as homogeneous anisotropic medium (see Reddy [ ]) are intractable. Usually, the anisotropy in laminated composite structures causes complicated responses under different loading conditions by creating complex couplings between extensions and bending, and shears deformation modes. Expect for certain cases, it is inconvenient to fully solve a problem in three dimensions due to the complexity, size of computation, and the production of unnecessary data specially for composite structures.
Response of Laminated Composite Cylindrical Shell Using Higher Order Shear Deformation Theory
Journal of Physics: Conference Series, 2019
The present work proposes the response of composite laminated cylindrical shell using higher order shear deformation theory (HSDT). For the finite element formulation a displacement field having five degrees of freedom is considered and a nine noded isoparametric element is used. The finite element model is developed using MATLAB code. The numerical results are obtained for the deflection of cylindrical shell for arbitrary boundary condition, stacking angle and radius to thickness ratio. The results are validated using literature and it shows good agreement
A nonlinear finite element method is adopted for the large displacement dynamic analysis of anisotropic plates under in-plane compressive loads. The analysis is based on the two-dimensional layered approach with higher order shear deformation theory with five, seven, nine, and eleven degrees of freedom per node, nine-node Lagrangian isoparametric quadrilateral elements are used for the discretization of the laminated plates. A complete bond between the layers is assumed (no delamination occurs). A consistent mass matrix is used in the present study. Damping property is considered by using Rayleigh type damping which is linearly related to the mass and the stiffness matrices. Newmark integration method and Harmonic acceleration method are used for solving the dynamic equilibrium equations. The effects of number of layers, damping factor, and number of degree of freedom per node on the large displacement dynamic analysis are considered. From the present study, noticed that the central deflection increase with increasing the degree of freedom per node.
This paper represents the laminated plate growing researc to dynamic loading in their working life and vibration affects working life of the structure predict of the free vibratio displacements of each layer are expressed in terms of Layerwise HSDT the thickness. The displacement field of present theory contains nine unknowns, as in the higher order shear deformation finding the analytical solutions. supported cross been obtained by using Layerwise HSDT. It is sh can provide accurate results. comparing it with various available results in the literature. The results show that the present model performs better than all the exist theories. ABSTRACT This paper represents the aminated plate growing researc to dynamic loading in their working life and vibration affects working life of the structure. Layerwise predict of the free vibratio displacements of each layer are expressed in terms of Layerwise HSDT the thickness. The displacement field of present theory contains nine unknowns, as in the higher order shear deformation finding the analytical solutions. supported cross been obtained by using Layerwise HSDT. It is sh can provide accurate results. comparing it with various available results in the literature. The results show that the present model performs better than all the exist heories. This paper represents the aminated plate. As we know that vibration and composite material are two main growing research topics now a days. Almost all the structural components subjected to dynamic loading in their working life and vibration affects working life of the Layerwise Higher Order Shear Deformation Theory (predict of the free vibratio displacements of each layer are expressed in terms of Layerwise HSDT the thickness. The displacement field of present theory contains nine unknowns, as in the higher order shear deformation finding the analytical solutions. supported cross-ply and anti been obtained by using Layerwise HSDT. It is sh can provide accurate results. comparing it with various available results in the literature. The results show that the present model performs better than all the exist IJMET/index.asp This paper represents the investigation As we know that vibration and composite material are two main h topics now a days. Almost all the structural components subjected to dynamic loading in their working life and vibration affects working life of the Higher Order Shear Deformation Theory (predict of the free vibration characteristics of laminated composite plates. displacements of each layer are expressed in terms of Layerwise HSDT the thickness. The displacement field of present theory contains nine unknowns, as in the higher order shear deformation finding the analytical solutions. Non ply and anti-symmetric angle been obtained by using Layerwise HSDT. It is sh can provide accurate results. The accuracy of the present theory is ascertained by comparing it with various available results in the literature. The results show that the present model performs better than all the exist asp 414 investigation on the response of a As we know that vibration and composite material are two main h topics now a days. Almost all the structural components subjected to dynamic loading in their working life and vibration affects working life of the Higher Order Shear Deformation Theory (n characteristics of laminated composite plates. displacements of each layer are expressed in terms of Layerwise HSDT the thickness. The displacement field of present theory contains nine unknowns, as in the higher order shear deformation theory Navier's solution method is used for Non-dimensional fundamental frequencies of simply symmetric angle-ply laminated composite plates have been obtained by using Layerwise HSDT. It is sh The accuracy of the present theory is ascertained by comparing it with various available results in the literature. The results show that the present model performs better than all the exist the response of a As we know that vibration and composite material are two main h topics now a days. Almost all the structural components subjected to dynamic loading in their working life and vibration affects working life of the Higher Order Shear Deformation Theory (n characteristics of laminated composite plates. displacements of each layer are expressed in terms of Layerwise HSDT the thickness. The displacement field of present theory contains nine unknowns, as in theory Navier's solution method is used for dimensional fundamental frequencies of simply-ply laminated composite plates have been obtained by using Layerwise HSDT. It is shown that the present Layerwise HSDT The accuracy of the present theory is ascertained by comparing it with various available results in the literature. The results show that the present model performs better than all the existing higher order shear deformation the response of a symmetric composite As we know that vibration and composite material are two main h topics now a days. Almost all the structural components subjected to dynamic loading in their working life and vibration affects working life of the Higher Order Shear Deformation Theory (HSDT n characteristics of laminated composite plates. displacements of each layer are expressed in terms of Layerwise HSDT the thickness. The displacement field of present theory contains nine unknowns, as in theory Navier's solution method is used for dimensional fundamental frequencies of simply ply laminated composite plates have own that the present Layerwise HSDT The accuracy of the present theory is ascertained by comparing it with various available results in the literature. The results show that the ing higher order shear deformation symmetric composite As we know that vibration and composite material are two main h topics now a days. Almost all the structural components subjected to dynamic loading in their working life and vibration affects working life of the HSDT) is used to n characteristics of laminated composite plates. displacements of each layer are expressed in terms of Layerwise HSDT functions of the thickness. The displacement field of present theory contains nine unknowns, as in theory Navier's solution method is used for dimensional fundamental frequencies of simply ply laminated composite plates have own that the present Layerwise HSDT The accuracy of the present theory is ascertained by comparing it with various available results in the literature. The results show that the ing higher order shear deformation symmetric composite As we know that vibration and composite material are two main h topics now a days. Almost all the structural components subjected to dynamic loading in their working life and vibration affects working life of the is used to The functions of the thickness. The displacement field of present theory contains nine unknowns, as in theory Navier's solution method is used for dimensional fundamental frequencies of simply ply laminated composite plates have own that the present Layerwise HSDT The accuracy of the present theory is ascertained by comparing it with various available results in the literature. The results show that the ing higher order shear deformation