Accuracy of refined finite elements for laminated plate analysis

Carrera, Erasmo; Miglioretti, Federico; Petrolo, Marco

doi:10.1016/j.compstruct.2010.11.007

Cited by 109 publications

(19 citation statements)

References 28 publications

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“…Thereby, the next section shows the solution of two different case studies using different plate theories in order to further investigate the potentialities and limitations of the implemented unified formulation. The results are not as detailed as the ones published by Carrera, Miglioretti and Petrolo for the sake of brevity.…”

Section: Resultsmentioning

confidence: 99%

A new finite element for thick laminates and sandwich structures using a generalized and unified plate theory

Caliri

Ferreira

Tita

2016

Numerical Meth Engineering

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The contribution of this work is the implementation of a new elastic solution method for thick laminated composites and sandwich structures based on a generalized unified formulation using finite elements. A quadrilateral four-node element was developed and evaluated using an in-house finite element program. The C-1 continuity requirements are fulfilled for the transversal displacement field variable. This method is tagged as Caliri's generalized formulation. The results employing the proposed solution method yielded coherent results with deviations as low as 0.05% for a static simply supported symmetric laminate and 0.5% for the modal analyses of a soft core sandwich structure. FINITE ELEMENT USING A GENERALIZED UNIFIED PLATE THEORY 291 the variety of theories developed to solve such complex laminated structures. When carefully analyzed, some of these theories can be grouped into the so-called unified or generalized theories.Li and Liu [9] exploited the concept of superposition and proposed a global-local refined multilayered plate theory. Such theory can be classified as an equivalent single layer (ESL) theory because the number of degrees of freedom was made independent of the number of layers through zig-zag refinements. However, despite its generalization, this formulation lacks unification properties. Unified plate/shell theories can group nearly all existing pate/shell theories into one from which they can be derived.In addition, when using unified formulations, theories with different orders of expansions can be directly compared, because no changes (but the index of the order of the thickness expansion) in the theory or solution method are performed to carry out the comparison. Moreover, other typing and precision errors, which may appear because of the use of different implemented solution methods, can be avoided. In addition, it is a powerful formulation to be implemented as a computer program. The works of Carrera, Demasi and Ferreira et al. [10][11][12][13][14][15][16][17][18][19][20][21][22][23] bring an extensive review and evaluation of the topic. Carrera [10,11] proposed a unification method, which generates a kernel matrix from which infinite axiomatic plate/shell theories can be extracted. Demasi improved Carrera's proposal and generalized it by decoupling the order of the displacement fields in each direction [14][15][16][17][18][19][20][21][22].Considering the aforementioned scope, this paper works on a new finite element solution method to solve thick laminates and sandwich elastic plates. The main contribution of this work is the implementation of a new solution approach, using the FEM, in order to solve unified plate formulations. The novelty of the present work is that the finite element solution is not fully C-0, but it now preserves the C-1 continuity requirements of the transverse displacement field. Carrera [10-13] also showed finite element results, along with closed-form solutions, but they are C-0 solutions. Thus, the present method (tagged as Caliri's generalized formulation -CGF)...

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Section: Resultsmentioning

confidence: 99%

A new finite element for thick laminates and sandwich structures using a generalized and unified plate theory

Caliri

Ferreira

Tita

2016

Numerical Meth Engineering

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“…On the other hand, the layer-wise theories are obtained assuming displacement distribution through each layer and imposing suitable continuities at interfaces [13]. Obviously these models could be extremely accurate, but also expensive [14].…”

Section: Introductionmentioning

confidence: 99%

Enhanced modeling approach for multilayer anisotropic plates based on dimension reduction method and Hellinger–Reissner principle

Auricchio

Balduzzi

Khoshgoftar

et al. 2014

Composite Structures

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a b s t r a c tThis paper illustrates an innovative approach to obtain an analytical model for elastic, multilayer, anisotropic, and moderately thick plates. The goals of the proposed approach are (i) provide an accurate stress description, (ii) take into account the effects of material anisotropies and inhomogeneities, and (iii) lead to a plate model that does not need shear correction factors.The first step of the modeling procedure is the weak formulation of the 3D elastic problem. In particular, we choose the Hellinger-Reissner functional expressed in a way that privileges an accurate description of stress field. The second step consists of the reduction of the 3D elastic problem weak formulation to a 2D weak formulation (i.e. the properly called plate-theory) using the dimension reduction method. Finally, the third step allows to obtain the plate-theory strong formulation.We evaluate some analytical solutions of the obtained plate-theory and we compare them with Classical Plate Theory, First order Shear Deformation Theory, and Elasticity Theory solutions with the aim to evaluate the proposed method accuracy. The results highlight the following main advantages: needless of shear correction factors and accurate description of both stress and displacement fields also in complex situations, like multilayer, anisotropic, and moderately thick plates.

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“…In the CUF framework, a novel axiomatic/asymptotic method (AAM) has been recently developed for beams [30,31] and plates [32,33]. AAM allows us to investigate the effectiveness of each generalized displacement variable in detecting the solution for a given problem and different values of typical parameters such as the thickness, the orthotropic ratio and the stacking sequence.…”

Section: Introductionmentioning

confidence: 99%

Results on best theories for metallic and laminated shells including Layer-Wise models

Carrera

Cinefra

Lamberti

et al. 2015

Composite Structures

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Accuracy of refined finite elements for laminated plate analysis

Cited by 109 publications

References 28 publications

A new finite element for thick laminates and sandwich structures using a generalized and unified plate theory

A new finite element for thick laminates and sandwich structures using a generalized and unified plate theory

Enhanced modeling approach for multilayer anisotropic plates based on dimension reduction method and Hellinger–Reissner principle

Results on best theories for metallic and laminated shells including Layer-Wise models

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