Nonlinear analysis of multilayered shells

Epstein, Marcelo; Glöckner, P.G.

doi:10.1016/0020-7683(77)90078-6

Cited by 67 publications

(7 citation statements)

References 11 publications

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“…Multilayer shell kinematics have been ÿrst introduced in connection with composite laminates in order to predict interlaminar e ects more accurately [50][51][52][53][54][55]. This concept has been shown later [54; 56; 57] to be also very e ective to simulate stress concentrations particularly in shells with dissimilar material properties across the thickness.…”

Section: Introductionmentioning

confidence: 99%

Ductile damage analysis of elasto-plastic shells at large inelastic strains

Eckstein

2000

Int. J. Numer. Meth. Engng.

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SUMMARYThe objective of this contribution is to model ductile damage phenomena under consideration of large inelastic strains, to couple the corresponding constitutive law with a multi-layer shell kinematics and to give ÿnally an adequate ÿnite element formulation. An elastic-plastic constitutive law is formulated by using a spatial hyperelasto-plastic formulation based on the multiplicative decomposition of the deformation gradient. To include isotropic ductile damage the continuum damage model of Rousselier is modiÿed so as to consider large strains and additionally extended by various void nucleation and macro-crack criteria. In order to achieve numerical e ciency, elastic strains are supposed to be su ciently small providing a numerical e ective integration based on the backward Euler rule. Finite element formulation is enriched by means of the enhanced strain concept. Thus the well-known deÿciencies due to incompressible deformations and the inclusion of transverse strains are avoided. Several examples are given to demonstrate the performance of the algorithms developed concerning large inelastic strains of shells and ductile damage phenomena.

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Section: Introductionmentioning

confidence: 99%

Ductile damage analysis of elasto-plastic shells at large inelastic strains

Eckstein

2000

Int. J. Numer. Meth. Engng.

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“…Substituting Fourier series (48) in Eqs. (9), (10), (25) and (28), and taking into account (34) and (35) …”

Section: Analytical Solution For Laminated Fg Rectangular Platesmentioning

confidence: 99%

“…The most general form of layer-wise kinematics presented in Carrera's unified formulation [31] is written as is the thickness of the nth layer; x 1 and x 2 are the Cartesian coordinates of the middle surface X; x 3 is the thickness coordinate normal to the middle surface; the index n identifies the belonging of any quantity to the nth layer and runs from 1 to N, where N is the number of layers. Historically, the first order layer-wise models [32][33][34][35] were first. Then, the second order models with R = 2 and third order models with R = 3 were developed [36][37][38].…”

Section: Introductionmentioning

confidence: 99%

A sampling surfaces method and its implementation for 3D thermal stress analysis of functionally graded plates

Куликов

Плотникова

2015

Composite Structures

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“…Multi-layer shell kinematics have been first introduced in connection with composite laminates in order to predict interlaminar effects more accurately (Epstein and Glockner [17], Reddy [18], Noor et al [19], Ba~ar [20], Ba~ar and Ding [21], Braun et al [22]). This concept has been shown later (Wagner and Gruttmann [23], Ba~ar and Ding [21], Ba~ar et al [24]) to be also very effective in dealing with stress concentrations particularly with shells affected by dissimilar material properties.…”

Section: Introductionmentioning

confidence: 99%

Large inelastic strain analysis by multilayer shell elements

Başar

Eckstein

2000

Acta Mechanica

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Summary. The objective of this contribution is to model large inelastic strains of ductile metals, to couple this material model with a multilayer shell kinematics and finally to achieve a finite element formulation applicable in general form to shell analysis. Elasto-plastic constitutive law is formulated by using the multiplicative decomposition of the deformation gradient and Neo-Hookean model for elastic strains assuming an overall isotropic material behavior. These 3D-material model is then enforced directly into a multilayer shell kinematics which provides a very accurate consideration of local effects, particularly stresses across the thickness. Finite element formulation is accomplished by means of the enhanced strain concept, Thus the well known deficiencies due to incompressible deformations and the inclusion of transverse strains are avoided. Several examples are given to demonstrate the performance of the algorithms developed concerning various aspects. Notation Variable definitions

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Nonlinear analysis of multilayered shells

Cited by 67 publications

References 11 publications

Ductile damage analysis of elasto-plastic shells at large inelastic strains

Ductile damage analysis of elasto-plastic shells at large inelastic strains

A sampling surfaces method and its implementation for 3D thermal stress analysis of functionally graded plates

Large inelastic strain analysis by multilayer shell elements

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