Analysis of Shear Flexible Layered Isotropic and Composite Shells by ‘EPSA’ (original) (raw)
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Refined shell model for the linear analysis of isotropic and composite elastic structures
European Journal of Mechanics - A/Solids, 2012
A refined finite element shell model has been developed in this work using an eight-nodes element with nine degrees of freedom for each node. This model enhances the classical shell approaches by including the transverse normal strain. The three displacement components are quadratically expanded in the thickness direction, therefore the transverse shear and normal strains effects are included in such a model making it suitable for thin and thick multilayered composite structures. The transverse normal strain is linear in the thickness direction z and the related shell theory is free from Poisson locking. Finite element locking mechanisms (shear and membrane locking) have been opportunely corrected: good convergence rate has been shown for the considered shell problems (with various geometries, thickness ratios and stacking layer sequences). No shear correction factors are requested.
A general fibre-reinforced composite shell element based on a refined shear deformation theory
Computers & Structures, 1992
A refined shell theory has been developed for the analysis of isotropic, orthotropic and anisotropic fibre-reinforced laminated composite and sandwich shells. This theory is based on a higher-order displacement model and the three-dimensional Hooke's laws for shell material, giving rise to a more realistic representation of the cross-sectional deformation. The superparametric shell element with four-noded linear eight/nine-noded quadratic and twelve/sixteen-noded cubic, serendipity/ Lagrangian shape functions can be employed. In addition to the present higher-order shear deformation shell theory (HOST), a first-order shear deformation shell theory (FOST), following Reissner-Mindlin plate's formulation, is developed and the results are compared with the closed-form solutions (CFS). The parametric effects of the finite element mesh, radius-to-arc length ratio, arc length-to-thickness ratio, lamination scheme, Gaussian integration rule, and material anisotropy on the response of the laminated composite shells are investigated. Results are tabulated to provide an easy means for future comparisons by other investigators.
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2001
A rational transverse shear deformation higher-order theory of multilayered anisotropic plates and shallow shells is developed for the solution of statical problems for two possible cases: cross-ply and angle-ply laminates. The theory developed diers from existing ones by three features. Firstly, it is based on the hypotheses which are fully tied to the physical and mechanical characteristics of the anisotropic layers. Secondly, the theory is built on a rational level of diculty, i.e. it does not add complexity in comparison with other known theories developed for more simple laminated structure. Thirdly, the hypotheses take directly into account the in¯uence of external subject to both normal and tangential loads.
Plate and shell analysis using classical plate theory (CPT) has a lack of accuracy in predicting the influence of transverse deformation, because of its assumption that the line normal to the surface remains straight and normal to the midplane before and after deformation. The next revision by constant shear deformation theory or famous as first order shear deformation theory (CSDT/FOSDT) still suffers a disadvantage that has a constant value in the shear term that is called shear locking phenomenon. This matter has been corrected by higher order shear deformation theory (HOSDT) using a refined assumption that the line normal to the surface should be in a parabolic function and not normal to the midplane, but normal to the surfaces so that it fulfills the zero strain in the surface. The analysis of the bending part of laminated composite flat shell element is applied by higher order lamination theory (HOLT) that is adopted from HOSDT. This model is accurate for thicknesses variation and complex materials. HOLT model is implemented into finite element procedure to find deflection, stresses and internal forces. It can be concluded that the displacement and stresses in HOLT model are higher than FOLT the ones (first order lamination theory) in small ratio of a/h dan its result almost the same value for a/h ratio more than 10. In a square plate case, the displacement gets smaller if the fiber arranged into cross-ply sequence. Interlaminar stresses along the thickness is not distributed continuously, but they have certain modes that depend on the depth of point position, the lamina or layer number, fiber orthotropic angle of each layer and a/h ratio.
A Finite Element Formulation of Multi-Layered Shells for the Analysis of Laminated Composites
This paper presents a multi-layered/multi-director and shear-deformable finite element formulation of shells for the analysis of composite laminates. The displacement field is assumed continuous across the finite element layers through the composite thickness. The rotation field is, however, layer-wise continuous and is assumed discontinuous across these layers. This kinematic hypothesis results in independent shear deformation of the director associated with each individual layer and thus allows the warping of the composite crosssection. The resulting strain field is discontinuous across the different material sets, thereby creating the provision that the inter-laminar transverse stresses computed from the constitutive equations can be continuous. Numerical results are presented to show the performance of the method.
General non-linear finite element analysis of thick plates and shells
International Journal of Solids and Structures, 2006
A non-linear finite element analysis is presented, for the elasto-plastic behavior of thick shells and plates including the effect of large rotations. The shell constitutive equations developed previously by the authors [Voyiadjis, G.Z., Woelke, P., 2004. A refined theory for thick spherical shells. Int. J. Solids Struct. 41, 3747-3769] are adopted here as a base for the formulation. A simple C 0 quadrilateral, doubly curved shell element developed in the authorsÕ previous paper [Woelke, P., Voyiadjis, G.Z., submitted for publication. Shell element based on the refined theory for thick spherical shells] is extended here to account for geometric and material non-linearities. The small strain geometric non-linearities are taken into account by means of the updated Lagrangian method. In the treatment of material non-linearities the authors adopt: (i) a non-layered approach and a plastic node method [Ueda, Y., Yao, T., 1982. The plastic node method of plastic analysis. Comput. Methods Appl. Mech. Eng. 34, 1089-1104], (ii) an IliushinÕs yield function expressed in terms of stress resultants and stress couples [Iliushin, A.A., 1956. PlastichnostÕ. Gostekhizdat, Moscow], modified to investigate the development of plastic deformations across the thickness, as well as the influence of the transverse shear forces on plastic behaviour of plates and shells, (iii) isotropic and kinematic hardening rules with the latter derived on the basis of the Armstrong and Frederick evolution equation of backstress [Armstrong, P.J., Frederick, C.O., 1966. A mathematical representation of the multiaxial Bauschinger effect. (CEGB Report RD/B/N/731). Berkeley Laboratories. R&D Department, California.], and reproducing the Bauschinger effect. By means of a quasi-conforming technique, shear and membrane locking are prevented and the tangent stiffness matrix is given explicitly, i.e., no numerical integration is employed. This makes the current formulation not only mathematically consistent and accurate for a variety of applications, but also computationally extremely efficient and attractive.
Composite Structures, 2018
In this work, a mathematical model of multilayer orthotropic shells with the account of both the 3 rd-order generalized model (the so-called Grigoluk-Kulikov model) and a temperature field is presented. An asymptotically stable modified model is proposed. The reported conservative difference schemes associated with the considered models are developed based on the variationaldifference method. The stability of a symmetric/non-symmetric pack of layers is addressed. In particular, the influence of the number of layers on the shell stability properties is illustrated and discussed.
A Geometrically Nonlinear Shear Deformation Theory for Composite Shells
Journal of Applied Mechanics, 2004
A geometrically nonlinear shear deformation theory has been developed for elastic shells to accommodate a constitutive model suitable for composite shells when modeled as a two-dimensional continuum. A complete set of kinematical and intrinsic equilibrium equations are derived for shells undergoing large displacements and rotations but with small, two-dimensional, generalized strains. The large rotation is represented by the general finite rotation of a frame embedded in the undeformed configuration, of which one axis is along the normal line. The unit vector along the normal line of the undeformed reference surface is not in general normal to the deformed reference surface because of transverse shear. It is shown that the rotation of the frame about the normal line is not zero and that it can be expressed in terms of other global deformation variables. Based on a generalized constitutive model obtained from an asymptotic dimensional reduction from the three-dimensional energy, and ...
Vietnam Journal of Mechanics, 2022
This study investigates the static and free vibration responses of orthotropic laminated composite spherical shells using various refined shear deformation theories. Displacement-based refined shear deformation theories are presented herein for the analysis of laminated composite spherical shells via unified mathematical formulations. Equations of motion associated with the present theory are derived within the framework of Hamilton's principle. Analytical solutions for the static and free vibration problems of laminated spherical shells are obtained using Navier's technique for the simply supported boundary conditions. Few higher order and classical theories are recovered from the present unified formulation; however, many other theories can be recovered from the present unified formulation. The numerical results are obtained for symmetric as well as anti-symmetric laminated shells. The present results are compared with previously published results and 3-D elasticity solution. From the numerical results, it is concluded that the present theories are in good agreement with other higher order theories and 3-D solutions.