A sampling surfaces method and its application to three-dimensional exact solutions for piezoelectric laminated shells

Куликов, Г. М.; Плотникова, С. В.

doi:10.1016/j.ijsolstr.2013.02.010

Cited by 24 publications

(23 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Next, we accept the third and fourth assumptions of the proposed piezoelectric laminated shell formulation. Let the electric potential and the electric field be distributed through the thickness of the nth layer as follows [3]:…”

Section: Sas Formulation For Electric Fieldmentioning

confidence: 99%

See 1 more Smart Citation

Sampling Surfaces Formulation for Functionally Graded and Laminated Composite Shells

Куликов¹,

Mamontov²,

Плотникова³

et al. 2016

AM&T

Self Cite

View full text Add to dashboard Cite

This paper focuses on a finite element implementation of the sampling surfaces (SaS) method for the three-dimensional (3D) stress analysis of functionally graded (FG) laminated elastic and electroelastic shells. The SaS formulation is based on choosing inside the nth layer n I not equally spaced SaS parallel to the middle surface of the shell in order to introduce the electric potentials and displacements of these surfaces as basic shell variables. Such choice of unknowns permits the presentation of the proposed FG shell formulation in a very compact form. The SaS are located inside each layer at Chebyshev polynomial nodes that improves the convergence of the SaS method significantly. KeywordsFunctionally graded material; laminated piezoelectric shell; sampling surfaces method, exact geometry solid-shell element.

show abstract

Section: Sas Formulation For Electric Fieldmentioning

confidence: 99%

“…The first four approaches were applied efficiently to the 3D analysis of FG piezoelectric structures in many papers [1]. Recently, the SaS approach has been also applied to the 3D modelling of FG piezoelectric plates and shells [2][3][4].…”

Section: Introductionmentioning

confidence: 99%

Sampling Surfaces Formulation for Functionally Graded and Laminated Composite Shells

Куликов¹,

Mamontov²,

Плотникова³

et al. 2016

AM&T

Self Cite

View full text Add to dashboard Cite

show abstract

“…The SaS formulation has been applied recently to the 3D analysis of FG and laminated piezoelectric plates and shells subjected to electric and mechanical loading (Kulikov and Plotnikova, 2013a, 2013b, 2013d, 2014. As SaS O (n)1 , O (n)2 , .…”

Section: Introductionmentioning

confidence: 99%

An analytical approach to three-dimensional coupled thermoelectroelastic analysis of functionally graded piezoelectric plates

Куликов

Плотникова

2016

Journal of Intelligent Material Systems and Structures

View full text Add to dashboard Cite

This article deals with the sampling surfaces method developed recently by the authors and its implementation for the three-dimensional coupled steady-state thermoelectroelastic analysis of functionally graded piezoelectric laminated plates subjected to thermal loading. The sampling surfaces formulation is based on choosing inside the nth layer I n not equally spaced sampling surfaces parallel to the middle surface of the plate in order to introduce temperatures, electric potentials, and displacements of these surfaces as basic plate variables. Such choice of unknowns with the consequent use of Lagrange polynomials of degree I n À 1 in the thickness direction for each layer permits the presentation of the proposed functionally graded piezoelectric plate formulation in a very compact form. The sampling surfaces are located inside each layer at Chebyshev polynomial nodes that allow one to minimize uniformly the error due to the Lagrange interpolation. As a result, the sampling surfaces method can be applied efficiently to analytical solutions for functionally graded piezoelectric laminated plates, which asymptotically approach the three-dimensional exact solutions of thermoelectroelasticity as I n ! '.

show abstract

“…The SaS method has been applied very recently to the exact 3D analysis of elastic, electroelastic, and thermoelastic laminated composite plates and shells in papers [18][19][20][21][22][23]. As SaS denoted by (n)1 , (n)2 , ... , (n)I n , we choose inner surfaces inside the nth layer and interfaces to introduce temperatures Address correspondence to G. M. Kulikov, Department of Applied Mathematics and Mechanics, Tambov State Technical University, Sovetskaya Street 106, Tambov 392000, Russian Federation.…”

Section: Introductionmentioning

confidence: 99%

Exact 3D Thermoelectroelastic Analysis of Piezoelectric Plates through a Sampling Surfaces Method

Куликов

Плотникова

2014

Mechanics of Advanced Materials and Structures

View full text Add to dashboard Cite

The article focuses on the use of the method of sampling surfaces (SaS) to exact three-dimensional (3D) solutions of the steady-state problem of thermoelectroelasticity for piezoelectric laminated plates subjected to thermal loading. The SaS method is based on selecting inside the nth layer I n not equally spaced SaS parallel to the middle surface of the plate in order to choose temperatures, electric potentials, and displacements of these surfaces as basic plate variables. This permits the representation of the proposed thermopiezoelectric plate formulation in a very compact form. The SaS are located inside each layer at Chebyshev polynomial nodes that improves the convergence of the SaS method significantly. As a result, the SaS method can be applied to 3D exact solutions of thermoelectroelasticity for piezoelectric laminated plates with a specified accuracy using the sufficient number of SaS.

show abstract

A sampling surfaces method and its application to three-dimensional exact solutions for piezoelectric laminated shells

Cited by 24 publications

References 29 publications

Sampling Surfaces Formulation for Functionally Graded and Laminated Composite Shells

Sampling Surfaces Formulation for Functionally Graded and Laminated Composite Shells

An analytical approach to three-dimensional coupled thermoelectroelastic analysis of functionally graded piezoelectric plates

Exact 3D Thermoelectroelastic Analysis of Piezoelectric Plates through a Sampling Surfaces Method

Contact Info

Product

Resources

About