Evaluation of mixed theories for laminated plates through the axiomatic/asymptotic method

Petrolo, Marco; Cinefra, Maria; Lamberti, Alessandro; Carrera, Erasmo

doi:10.1016/j.compositesb.2015.02.027

Cited by 23 publications

(7 citation statements)

References 48 publications

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“…This leads to the development of reduced models whose accuracies are equivalent to those of full higher-order models. The AAM has been applied to several problems, including: static and free vibration of beams [38,40], metallic and composite plates [39,41], shells [42,43], LW models [44,45], advanced models based on the Reissner Mixed Variational Theorem [46], and piezoelectric plates [47].…”

Section: Fgmmentioning

confidence: 99%

Best Theory Diagrams for cross-ply composite plates using polynomial, trigonometric and exponential thickness expansions

Yarasca

Mantari

Petrolo³

et al. 2017

Composite Structures

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This paper presents Best Theory Diagrams (BTDs) employing combinations of Maclaurin, trigonometric and exponential terms to build two-dimensional theories for laminated cross-ply plates. The BTD is a curve in which the least number of unknown variables to meet a given accuracy requirement is read. The used refined models are Equivalent Single Layer and are obtained using the Unified Formulation developed by Carrera. The governing equations are derived from the Principle of Virtual Displacement (PVD), and Navier-type closed form solutions have been obtained in the case of simply supported plates loaded by a bisinuisoidal transverse pressure. BTDs have been constructed using the Axiomatic/Asymptotic Method (AAM) and genetic algorithms (GA). The influence of trigonometric and exponential terms in the BTDs has been studied for different layer configurations, length-to-thickness ratios and stresses. It is shown that the addition of trigonometric and exponential expansion terms to Maclaurin ones may improve the accuracy and computational cost of refined plate theories. The combined use of CUF, AAM and GA is a powerful tool to evaluate the accuracy of any structural theory.

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Section: Fgmmentioning

confidence: 99%

Best Theory Diagrams for cross-ply composite plates using polynomial, trigonometric and exponential thickness expansions

Yarasca

Mantari

Petrolo³

et al. 2017

Composite Structures

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“…A bimetallic square plate used in [31] is considered as a second study case. Figure 4 shows BTDs for , whereas Fig.…”

Section: Bimetallic Platementioning

confidence: 99%

“…In order to reduce the computational cost, the Axiomatic/Asymptotic Method (AAM), introduced by Carrera and Petrolo [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], can provide asymptotic-like results starting from a preliminary axiomatic theory by evaluating the effectiveness of each term against a reference solution and retaining those variables whose influence cannot be neglected. The BTD is stemmed from the AAM [21] as a tool to evaluate the best models against given accuracies or computational costs.…”

Section: Introductionmentioning

confidence: 99%

An axiomatic/asymptotic evaluation of best theories for isotropic metallic and functionally graded plates employing non-polynomic functions

Candiotti

Mantari

Yarasca

et al. 2017

Aerospace Science and Technology

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“…Based on a layerwise mixed least‐squares formulation, Moleiro et al presented a finite element model for laminated composite and sandwich structures. Petrolo et al applied the asymptotic/axiomatic method to mixed theories based on the RMVT, where ESL and layerwise schemes were adopted. Based on piecewise descriptions of stress and displacement fields, these layerwise mixed theories provided accurate predictions for the distributions of both stress and displacement fields through the thickness of sandwich structures.…”

Section: Introductionmentioning

confidence: 99%

A new formulation of continuous transverse shear stress field for static and dynamic analysis of sandwich beams with soft core

Ren

Zhao

2019

Numerical Meth Engineering

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Summary This article presents a novel formulation for sandwich beams with soft core based on a layerwise description of continuous transverse shear stress field. The transverse shear stress field is assumed to follow a quadratic distribution in thick face layers and a uniform distribution in soft core. Based on stress‐strain relations, transverse shear strain is obtained, and in‐plane displacement field is determined by taking the integral of the transverse shear stain. By enforcing interlaminar displacement continuity, an explicit displacement field expression containing only displacement variables is formulated. In this formulation, interlaminar continuity conditions of displacement and transverse shear stress are satisfied simultaneously, and transverse shear and crosssectional warping effects in thick face layers are accurately taken account. To show characteristics and advantages of the present model, some classical theoretical models are further developed under different kinematic assumptions. The governing equations are derived using Hamilton principle, and finite element solutions for static and dynamic analysis of sandwich beams are presented. Comparisons with exact solution and other well‐known solutions, well demonstrate high accuracy of the present model for sandwich beams with different features. Besides, numerical discussions further reflect accuracy advantages of the present model in static and dynamic analysis of sandwich beams.

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Evaluation of mixed theories for laminated plates through the axiomatic/asymptotic method

Cited by 23 publications

References 48 publications

Best Theory Diagrams for cross-ply composite plates using polynomial, trigonometric and exponential thickness expansions

Best Theory Diagrams for cross-ply composite plates using polynomial, trigonometric and exponential thickness expansions

An axiomatic/asymptotic evaluation of best theories for isotropic metallic and functionally graded plates employing non-polynomic functions

A new formulation of continuous transverse shear stress field for static and dynamic analysis of sandwich beams with soft core

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