Theories and finite elements for multilayered anisotropic, composite plates and shells.
type: Item
instance of: scholarly article
title: Theories and finite elements for multilayered anisotropic, composite plates and shells.
zbMATH Open document ID: 1062.74048
DOI: 10.1007/BF02736649
published in: Archives of Computational Methods in Engineering
publication date: 2002-01-01T00:00:00Z
review text: The paper is a review of available theories and finite elements, FEs, that have been developed for multilayered anisotropic composite plate and shell structures. 325 books and papers have been used by the author. Of all the possible topics, this review covers mainly the aspects related to two-dimensional modeling of layered structures and to finite element implementations. The paper has been divided into three parts. Part I is devoted to the description and development of possible approaches to plate and shell structures. Complicating effects that have been introduced by anisotropic behavior and layered constructions, such as high transverse deformabilty, zig-zag effects and interlaminar continuity, have been discussed. Two-dimensional theories have been dealt with in Part II. Contributions based on axiomatic, asymptotic and continuum based approaches have been overviewed. Classical theories and their refinements are considered. Both cases of equivalent single-layer and layer-wise variables descriptions are discussed. The three possible zig-zag approaches (Lekhnitskii-Ren, Ambartsumian-Whitney-Rath-Das, Reissner-Murakami-Carrera) have been discussed. FE implementations are examined in Part III. The possible developments of finite elements for layered plates and shells are outlined. FEs based on the theories considered in Part II are discussed along with those approaches which consist in a specific application of FE techniques, such as hybrid methods and so-called global/local techniques. The author describes the extension of FEs that were originally developed for isotropic one-layered structures to multilayered plates and shells. Development of available zig-zag FEs has been considered for the three above cases of zig-zag theories. FEs based on other approaches are also discussed. Unfortunately, the paper does not report on numerical results and assessments for the reviewed theories and FEs.
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74K25
Mathematics Subject Classification ID: 74-02
Mathematics Subject Classification ID: 74E30
Mathematics Subject Classification ID: 74E10
zbMATH DE Number: 1799327
zbMATH Keywords: transverse deformability
zbMATH Keywords: zig-zag effects
zbMATH Keywords: interlaminar continuity
zbMATH Keywords: hybrid methods
Wikidata QID: Q113327824
author: Erasmo Carrera
reviewed by: V. L. Leontiev
MaRDI profile type: Publication
cites work: Recent advances in analysis of laminated beams and plates. Part I - Sheareffects and buckling.
cites work: On refined computational models of composite laminates
cites work: Q4493639
cites work: Q5683798
cites work: Q4102832
cites work: Q4003286
cites work: Q4349185
cites work: Three-dimensional solutions of laminated cylinders
cites work: Stress fields in composite laminates
cites work: Exact Elasticity Solution for Laminated Anisotropic Cylindrical Shells
cites work: Benchmark elasticity solution for locally loaded laminated orthotropic cylindrical shells
cites work: Three-dimensional elasticity solutions to some orthotropic plate problems
cites work: Analytical solution of finite-geometry composite panels under transient surface loading
cites work: Q5570190
cites work: Q3848032
cites work: Q5581338
cites work: Q5681642
cites work: Q5589986
cites work: Q3282443
cites work: Q4890340
cites work: On a certain mixed variational theorem and a proposed application
cites work: On a mixed variational theorem and on shear deformable plate theory
cites work: Q5548879
cites work: General two-dimensional theory of laminated cylindrical shells
cites work: Free vibration analysis of laminated plates using a layerwise theory
cites work: Refined geometrically nonlinear theories of anisotropic laminated shells
cites work: Bending and Stretching of Certain Types of Heterogeneous Aeolotropic Elastic Plates
cites work: Q5845521
cites work: Q5808124
cites work: A Simple Higher-Order Theory for Laminated Composite Plates
cites work: Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory
cites work: A High-Order Theory of Plate Deformation—Part 2: Laminated Plates
cites work: Refined theories of elastic anisotropic shells accounting for small strains and moderate rotations
cites work: A refined theory for thick composite plates
cites work: Q3833735
cites work: A shear deformable theory of laminated composite shallow shell-type panels and their response analysis. II: Static response
cites work: An efficient standard plate theory
cites work: A refined theory of laminated shallow shells
cites work: A generalization of shear deformation theories for axisymmetric multilayered shells
cites work: A refined theory for laminated beams. I: A new higher order approach
cites work: Q4355190
cites work: A theory of laminated cylindrical shells consisting of layers of orthotropic laminae
cites work: Rotationally symmetric vibrations of orthotropic layered cylindrical shells
cites work: Free vibrations of thick, layered cylinders having finite length with various boundary conditions
cites work: A refined analysis of composite laminates
cites work: Modelling of thick composites using a layerwise laminate theory
cites work: On a general theory of anisotropic shells
cites work: Vibration of layered shells
cites work: Q3336813
cites work: An Improved Shear-Deformation Theory for Moderately Thick Multilayered Anisotropic Shells and Plates
cites work: Efficient higher order composite plate theory for general lamination configurations
cites work: Zigzag theory for composite laminates
cites work: A rectangular finite element for analysing composite multilayered shallow shells in statics, vibration and buckling
cites work: COMPARATIVE DYNAMIC STUDIES FOR SYMMETRIC CROSS-PLY CIRCULAR CYLINDRICAL SHELLS ON THE BASIS OF A UNIFIED SHEAR DEFORMABLE SHELL THEORY
cites work: A Laminated Beam Theory With Interlayer Slip
cites work: Laminated Composite Plate Theory With Improved In-Plane Responses
cites work: A Composite Plate Theory for Arbitrary Laminate Configurations

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A high-order laminated plate theory with improved in-plane responses

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Anisotropic Beam Theories With Shear Deformation

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Refined shear deformation theory of laminated shells

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: On a Variational Theorem in Elasticity

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Asymptotic Solutions for Orthotropic Nonhomogeneous Shells of Revolution

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Effect of Accuracy Loss in Classical Shell Theory

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Application of the variational-asymptotical method to laminated composite plates

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: An asymptotic theory for dynamic response of anisotropic inhomogeneous and laminated plates

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A three-dimensional analysis of anisotropic inhomogeneous and laminated plates

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: On asymptotically correct linear laminated plate theory

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Derivation of Plate Theory Accounting Asymptotically Correct Shear Deformation

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A refined asymptotic theory for dynamic analysis of doubly curved laminated shells

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Exact theory of stress and strain in rods and shells

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A Theory of Laminated Composite Plates

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Continuum Theory for a Laminated Medium

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A continuum model for curvilinear laminated composites

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Nonlinear analysis of multilayered shells

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Multilayered shells and directed surfaces

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Differential quadrature method for thick symmetric cross-ply laminates with first-order shear flexibility

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Stress fields in general composite laminates

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Predictor-corrector procedures for stress and free vibration analyses of multilayered composite plates and shells

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: The generalized plane strain deformations of thick anisotropic composite laminated plates

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Nonlinear Finite Element Analysis of Sandwich Shells of Revolution

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Finite element analysis of anisotropic plates

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Finite element analysis of laminated composite plates

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Free vibration of antisymmetric, angle-ply laminated plates including transverse shear deformation by the finite element method

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A penalty plate-bending element for the analysis of laminated anisotropic composite plates

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A study on thermal postbuckling behaviour of laminated composite plates using a shear-flexible finite element

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A study of quadrilateral plate bending elements with ‘reduced’ integration

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Mixed finite element methods - reduced and selective integration techniques: a unification of concepts

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: TheC° structural finite elements reformulated

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: The four-node \(C^ 0\) Mindlin plate bending element reformulated. I: Formulation. II: Verification

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: On implementation of a nonlinear four node shell finite element for thin multilayered elastic shells

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A shear deformable plate element with an exact thin limit

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A mixed-enhanced finite-element for the analysis of laminated composite plates

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A refined higher-order C° plate bending element

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Higher-order shear deformable theories for flexure of sandwich plates. Finite element evaluations

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Large amplitude free vibration analysis of cross-ply composite and sandwich laminates with a refined theory and finite elements

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Analysis of laminated composite plates using a higher-order shear deformation theory

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A higher-order plate theory with ideal finite element suitability

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A three-node Mindlin plate element with improved transverse shear

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A priori identification of shear locking and stiffening in triangular Mindlin elements

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A higher-order theory for bending analysis of laminated shells of revolution

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A plate bending element based on a generalized laminate plate theory

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A layer-wise triangle for analysis of laminated composite plates and shells

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: On first- and second-order moderate rotation theories of laminated plates

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A consistent model for first-order moderate rotation plate theory

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A Refined Small Strain and Moderate Rotation Theory of Elastic Anisotropic Shells

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: On a moderate rotation theory of laminated anisotropic shells. I: Theory

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: On a moderate rotation theory of laminated anisotropic shells. II: Finite-element analysis

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Static, free vibration and thermal analysis of composite plates and shells using a flat triangular shell element

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Allgemeine Schalentheorie beliebiger Werkstoffe und Verformungen

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Lagrangian description and incremental formulation in the nonlinear theory of thin shells

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Nonlinear analysis of isotropic, orthotropic and laminated plates and shells

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A nonlinear composite shell element with continuous interlaminar shear stresses

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Refined shear-deformation models for composite laminates with finite rotations

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Finite-rotation theories for composite laminates

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Nonlinear shell formulations for complete three-dimensional constitutive laws including composites and laminates

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A refined mixed shear flexible finite element for the nonlinear analysis of laminated plates

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: MITC finite elements for laminated composite plates

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Vibration and buckling of laminated plates

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A general quadrilateral multilayered plate element with continuous interlaminar stresses

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A third‐order triangular multilayered plate finite element with continuous interlaminar stresses

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: AC0 EIGHT-NODE MEMBRANE-SHEAR-BENDING ELEMENT FOR GEOMETRICALLY NON-LINEAR (STATIC AND DYNAMIC) ANALYSIS OF LAMINATES

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Shear flexible curved spline beam element for static analysis

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: AC1 finite element including transverse shear and torsion warping for rectangular sandwich beams

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: High-order triangular sandwich plate finite element for linear and nonlinear analyses.

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Finite element for composite plate bending based on efficient higher order theory

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Stability analysis of a rotating multi-layer annular plate with a stationary frictional follower load

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Analysis of a rotating multi-layer annular plate modeled via layerwise zig-zag theory: Free vibration and transient analysis

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Thick beam theory and finite element model with zig-zag sublaminate approximations

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Partial hybrid stress element for the analysis of thick laminated composite plates

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: C0 REISSNER-MINDLIN MULTILAYERED PLATE ELEMENTS INCLUDING ZIG-ZAG AND INTERLAMINAR STRESS CONTINUITY

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: An investigation of non-linear dynamics of multilayered plates accounting for C0z requirements

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Q4493863

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Classical and advanced multilayered plate elements based upon PVD and RMVT. Part 1: Derivation of finite element matrices

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Classical and advanced multilayered plate elements based upon PVD and RMVT. Part 2: Numerical implementations

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A geometric and material nonlinear plate and shell element

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Large deformation analysis of laminated shells by ftnife element method

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Analysis of laminated composite shells using a degenerated 3-D element

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A solid-shell transition element for geometrically non-linear analysis of laminated composite structures

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Continuum-based stiffened composite shell element for geometrically nonlinear analysis

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A multi‐director formulation for elastic—viscoelastic layered shells

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: On a stress resultant geometrically exact shell model. I: Formulation and optimal parametrization

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: On a stress resultant geometrically exact shell model. II: The linear theory; computational aspects

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: On a stress resultant geometrically exact shell model. III: Computational aspects of the nonlinear theory

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Linear and geometrically nonlinear bending of isotropic and multilayered composite plates by the natural mode method

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: An efficient and locking-free flat anisotropic plate and shell triangular element

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A practicable and locking-free laminated shallow shell triangular element of varying and adaptable curvature

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Three-dimensional asymptotic finite element method for anisotropic inhomogeneous and laminated plates

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Hierarchic models for laminated composites

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Hierarchic plate and shell models based onp-extension

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Piecewise hierarchical p-version axisymmetric shell element for laminated composites

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Global‐local finite element

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Global-local laminate variational model

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A hybrid-stress finite-element formulation for thick multilayer laminates

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Hybrid-stress eight-node elements for thin and thick multilayer laminated plates

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: A three-dimensional hybrid stress isoparametric element for the analysis of laminated composite plates

Theories and finite elements for multilayered anisotropic, composite plates and shells. (cites work)
cites work: Hybrid stress formulation for higher-order theory of laminated shell analysis

Theories and finite elements for multilayered anisotropic, composite plates and shells. (full work available at URL)
full work available at URL: https://doi.org/10.1007/bf02736649

Theories and finite elements for multilayered anisotropic, composite plates and shells. (OpenAlex ID)
OpenAlex ID: W2032779577