Arbitrarily shaped plates analysis via Line Element-Less Method (LEM)

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Abstract

An innovative procedure is introduced for the analysis of arbitrarily shaped thin plates with various boundary conditions and under generic transverse loading conditions. Framed into Line Element-less Method, a truly meshfree method, this novel approach yields the solution in terms of the deflection function in a straightforward manner, without resorting to any discretization, neither in the domain nor on the boundary. Specifically, expressing the deflection function through a series expansion in terms of harmonic polynomials, it is shown that the proposed method requires only the evaluation of line integrals along the boundary parametric equation. Further, minimization of appropriately introduced novel functionals directly leads to simple systems of linear algebraic equations for the unknown expansion coefficients. Notably, the proposed procedure yields exact solutions, when available, for different plate geometries. Additionally, several numerical applications are presented to show the reliability and simplicity of the approach, and comparisons with pertinent Finite Element method data demonstrate the efficiency and accuracy of the proposed procedure.
Lingua originaleEnglish
pagine (da-a)235-248
Numero di pagine14
RivistaThin-Walled Structures
Volume133
Stato di pubblicazionePublished - 2018

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Linear equations
Polynomials
Boundary conditions
Finite element method
Geometry

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Building and Construction
  • Mechanical Engineering

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@article{d60061296cd3443d990d8a06def31b76,
title = "Arbitrarily shaped plates analysis via Line Element-Less Method (LEM)",
abstract = "An innovative procedure is introduced for the analysis of arbitrarily shaped thin plates with various boundary conditions and under generic transverse loading conditions. Framed into Line Element-less Method, a truly meshfree method, this novel approach yields the solution in terms of the deflection function in a straightforward manner, without resorting to any discretization, neither in the domain nor on the boundary. Specifically, expressing the deflection function through a series expansion in terms of harmonic polynomials, it is shown that the proposed method requires only the evaluation of line integrals along the boundary parametric equation. Further, minimization of appropriately introduced novel functionals directly leads to simple systems of linear algebraic equations for the unknown expansion coefficients. Notably, the proposed procedure yields exact solutions, when available, for different plate geometries. Additionally, several numerical applications are presented to show the reliability and simplicity of the approach, and comparisons with pertinent Finite Element method data demonstrate the efficiency and accuracy of the proposed procedure.",
keywords = "Arbitrary shape, Harmonic polynomials, Kirchoff plate, Line Element-Less Method, Meshfree method",
author = "Antonina Pirrotta and Giuseppe Battaglia and {Di Matteo}, Alberto and Micale, {Giorgio Domenico Maria} and Antonina Pirrotta",
year = "2018",
language = "English",
volume = "133",
pages = "235--248",
journal = "Thin-Walled Structures",
issn = "0263-8231",
publisher = "Elsevier Limited",

}

TY - JOUR

T1 - Arbitrarily shaped plates analysis via Line Element-Less Method (LEM)

AU - Pirrotta, Antonina

AU - Battaglia, Giuseppe

AU - Di Matteo, Alberto

AU - Micale, Giorgio Domenico Maria

AU - Pirrotta, Antonina

PY - 2018

Y1 - 2018

N2 - An innovative procedure is introduced for the analysis of arbitrarily shaped thin plates with various boundary conditions and under generic transverse loading conditions. Framed into Line Element-less Method, a truly meshfree method, this novel approach yields the solution in terms of the deflection function in a straightforward manner, without resorting to any discretization, neither in the domain nor on the boundary. Specifically, expressing the deflection function through a series expansion in terms of harmonic polynomials, it is shown that the proposed method requires only the evaluation of line integrals along the boundary parametric equation. Further, minimization of appropriately introduced novel functionals directly leads to simple systems of linear algebraic equations for the unknown expansion coefficients. Notably, the proposed procedure yields exact solutions, when available, for different plate geometries. Additionally, several numerical applications are presented to show the reliability and simplicity of the approach, and comparisons with pertinent Finite Element method data demonstrate the efficiency and accuracy of the proposed procedure.

AB - An innovative procedure is introduced for the analysis of arbitrarily shaped thin plates with various boundary conditions and under generic transverse loading conditions. Framed into Line Element-less Method, a truly meshfree method, this novel approach yields the solution in terms of the deflection function in a straightforward manner, without resorting to any discretization, neither in the domain nor on the boundary. Specifically, expressing the deflection function through a series expansion in terms of harmonic polynomials, it is shown that the proposed method requires only the evaluation of line integrals along the boundary parametric equation. Further, minimization of appropriately introduced novel functionals directly leads to simple systems of linear algebraic equations for the unknown expansion coefficients. Notably, the proposed procedure yields exact solutions, when available, for different plate geometries. Additionally, several numerical applications are presented to show the reliability and simplicity of the approach, and comparisons with pertinent Finite Element method data demonstrate the efficiency and accuracy of the proposed procedure.

KW - Arbitrary shape

KW - Harmonic polynomials

KW - Kirchoff plate

KW - Line Element-Less Method

KW - Meshfree method

UR - http://hdl.handle.net/10447/356332

M3 - Article

VL - 133

SP - 235

EP - 248

JO - Thin-Walled Structures

JF - Thin-Walled Structures

SN - 0263-8231

ER -