Sampling Surfaces Method Research Articles

Sampling Surfaces Formulation for Functionally Graded and Laminated Composite Shells

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.

Sampling surfaces formulation for thermoelastic analysis of laminated functionally graded shells

This paper focuses on implementation of the sampling surfaces (SaS) method for the three-dimensional (3D) thermal stress analysis of steady-state thermoelasticity problems for laminated functionally graded (FG) shells. The SaS formulation is based on choosing inside the nth layer I n not equally spaced SaS parallel to the middle surface of the shell in order to introduce the temperatures and displacements of these surfaces as basic shell variables. Such choice of unknowns permits the presentation of the proposed thermoelastic 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. As a result, the SaS formulation can be applied efficiently to analytical solutions for laminated FG shells, which asymptotically approach the 3D exact solutions of thermoelasticity as the number of SaS I n tends to infinity.

Three-Dimensional Analysis of Metal-Ceramic Shells by the Method of Sampling Surfaces

An efficient method for solving three-dimensional elasticity problems for metal-ceramic composite shells is presented. According to this method, in the shell body, N sampling surfaces (SaS) parallel to its midsurface are chosen in order to introduce the displacement vectors of these surfaces as unknown functions. The SaS pass through the nodes of a Chebyshev polynomial, which improves the convergence of the SaS method significantly. As a result, this method can be applied to the derivation of such analytical solutions for metal-ceramic shells that asymptotically approach the exact three-dimensional solutions of elasticity as the number N of SaS tends to infinity.

Coupled thermoelectroelastic stress analysis of piezoelectric shells

The paper deals with the sampling surfaces (SaS) method proposed by the authors and its implementation for the three-dimensional (3D) coupled steady-state thermoelectroelastic analysis of laminated piezoelectric shells subjected to thermal loading. The SaS formulation is based on choosing inside the nth layer In not equally spaced SaS parallel to the middle surface of the shell in order to introduce the temperatures and displacements of these surfaces as basic shell variables. Such choice of unknowns with the consequent use of Lagrange polynomials of degree In-1 in the thickness direction for each layer permits the presentation of the laminated piezoelectric shell formulation in a very compact form. The SaS are located inside each layer at Chebyshev polynomial nodes that allows one to minimize uniformly the error due to the Lagrange interpolation. As a result, the SaS formulation can be applied efficiently to derivation of the analytical solutions for laminated piezoelectric shells, which asymptotically approach the 3D exact solutions of thermoelectroelasticity as the number of SaS goes to infinity.

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

The paper deals with a recently developed method of sampling surfaces (SaS) and its implementation for the three-dimensional (3D) steady-state problem of thermoelasticity for laminated functionally graded (FG) plates subjected to thermomechanical loading. The SaS method is based on choosing inside the nth layer In not equally spaced SaS parallel to the middle surface of the plate in order to introduce temperatures and displacements of these surfaces as basic plate variables. Such an idea permits the presentation of the thermoelastic laminated FG plate formulation in a very compact form. The SaS are located inside each layer at Chebyshev polynomial nodes that provides a uniform convergence of the SaS method. This means that the SaS method can be applied efficiently to the 3D stress analysis for thermoelastic laminated FG plates with a specified accuracy utilizing the sufficient number of SaS.

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

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 In 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.

Three-dimensional thermal stress analysis of laminated composite plates with general layups by a sampling surfaces method

Abstract A paper focuses on the application of the method of sampling surfaces (SaS) to three-dimensional (3D) steady-state thermoelasticity problems for orthotropic and anisotropic laminated plates subjected to thermal loading. This method is based on selecting inside the n th layer I n not equally spaced SaS parallel to the middle surface of the plate in order to choose temperatures and displacements of these surfaces as basic plate variables. Such an idea permits the presentation of the proposed thermoelastic laminated plate formulation in a very compact form. It is worth noting that the SaS are located inside each layer at Chebyshev polynomial nodes that leads to a uniform convergence of the SaS method. As a result, the SaS method can be applied efficiently to the 3D stress analysis of cross-ply and angle-ply composite plates with a specified accuracy utilizing the sufficient number of SaS.

3D exact thermoelastic analysis of laminated composite shells via sampling surfaces method

This paper focuses on the implementation of the method of sampling surfaces (SaS) for three-dimensional (3D) exact solutions of the steady-state problem of thermoelasticity for laminated composite shells. The SaS method is based on selecting inside the nth layer In not equally spaced SaS parallel to the middle surface of the shell to choose temperatures and displacements of these surfaces as basic shell variables. This permits the presentation of the proposed thermoelastic shell formulation in a very compact form. The SaS are located inside each layer at Chebyshev polynomial nodes improving the convergence of the SaS method significantly. As a result, the SaS method can be applied efficiently to 3D exact solutions of thermoelasticity for laminated composite shells with a specified accuracy by using the sufficient number of SaS.

Heat conduction analysis of laminated shells by a sampling surfaces method

A paper focuses on the use of the method of sampling surfaces (SaS) for the exact three-dimensional (3D) heat conduction analysis of laminated orthotropic and anisotropic shells. This method is based on selecting inside the nth layer In not equally spaced SaS parallel to the middle surface of the shell in order to choose the temperatures of these surfaces as basic variables. Such an idea permits the representation of the proposed thermal laminated 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. As a result, the SaS method can be applied efficiently to exact 3D solutions of the steady-state heat conduction problem for cross-ply and angle-ply composite shells with a specified accuracy using a sufficient number of SaS.

Exact electroelastic analysis of functionally graded piezoelectric shells

A paper focuses on implementation of the sampling surfaces (SaS) method for the three-dimensional (3D) exact solutions for functionally graded (FG) piezoelectric laminated shells. According to this method, we introduce inside the nth layer In not equally spaced SaS parallel to the middle surface of the shell and choose displacements and electric potentials of these surfaces as basic shell variables. Such choice of unknowns yields, first, a very compact form of governing equations of the FG piezoelectric shell formulation and, second, allows the use of strain–displacement equations, which exactly represent rigid-body motions of the shell in any convected curvilinear coordinate system. It is worth noting that the SaS are located inside each layer at Chebyshev polynomial nodes that leads to a uniform convergence of the SaS method. As a result, the SaS method can be applied efficiently to 3D exact solutions of electroelasticity for FG piezoelectric cross-ply and angle-ply shells with a specified accuracy by using a sufficient number of SaS.

Three-Dimensional Exact Analysis of Laminated Piezoelectric Plates and Shells

A paper focuses on the use of the efficient approach to three-dimensional (3D) exact solutions of electroelasticity for laminated piezoelectric plates and shells. This approach is based on the new method of sampling surfaces (SaS). We introduce inside the nth layer Ιn not equally spaced SaS parallel to the middle surface of the shell and choose displacements of these surfaces as basic shell variables. This permits the derivation of 3D exact solutions of electroelasticity for thick and thin laminated piezoelectric anisotropic structures with a specified accuracy using a sufficient number of SaS, which are located at interfaces and Chebyshev polynomial nodes.

A new approach to three-dimensional exact solutions for functionally graded piezoelectric laminated plates

A paper presents the sampling surfaces (SaS) method and its implementation for the three-dimensional (3D) exact analysis of functionally graded (FG) piezoelectric laminated plates. According to this method, we introduce inside the nth layer In not equally spaced SaS parallel to the middle surface of the plate and choose displacement vectors and electric potentials of these surfaces as basic plate variables. Such choice of unknowns with the consequent use of Lagrange polynomials of degree In−1 in the thickness direction for each layer leads to a very compact form of governing equations of the FG piezoelectric plate formulation. This fact gives an opportunity to derive the 3D exact solutions of electroelasticity for thick and thin FG piezoelectric laminated plates with a specified accuracy utilizing a sufficient number of SaS, which are located at interfaces and Chebyshev polynomial nodes.

Three-dimensional exact analysis of piezoelectric laminated plates via a sampling surfaces method

A paper focuses on the use of the efficient approach to three-dimensional (3D) exact solutions of electroelasticity for piezoelectric laminated plates. This approach is based on the new method of sampling surfaces (SaS) developed recently by the authors. We introduce inside the nth layer In not equally spaced SaS parallel to the middle surface of the plate and choose displacements of these surfaces as basic plate variables. Such an idea permits the representation of the proposed piezoelectric plate formulation in a very compact form. This fact gives the opportunity to derive the 3D exact solutions of electroelasticity for thick and thin piezoelectric laminated plates with a specified accuracy utilizing a sufficient number of SaS, which are located at interfaces and Chebyshev polynomial nodes.

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

The application of the sampling surfaces (SaS) method to piezoelectric laminated composite plates is presented in a companion paper (Kulikov, G.M., Plotnikova, S.V., Three-dimensional exact analysis of piezoelectric laminated plates via sampling surfaces method. International Journal of Solids and Structures 50, http://dx.doi.org/10.1016/j.ijsolstr.2013.02.015). In this paper, we extend the SaS method to shells to solve the static problems of three-dimensional (3D) electroelasticity for cylindrical and spherical piezoelectric laminated shells. For this purpose, we introduce inside the nth layer In not equally spaced SaS parallel to the middle surface of the shell and choose displacements of these surfaces as basic kinematic variables. Such choice of displacements permits, first, the presentation of governing equations of the proposed piezoelectric shell formulation in a very compact form and, second, gives an opportunity to utilize the strain–displacement equations, which precisely represent all rigid-body shell motions in any convected curvilinear coordinate system. It is shown that the developed piezoelectric shell formulation can be applied efficiently to finding of 3D exact solutions for piezoelectric cross-ply and angle-ply shells with a specified accuracy using a sufficient number of SaS, which are located at Chebyshev polynomial nodes and layer interfaces as well.

Advanced formulation for laminated composite shells: 3D stress analysis and rigid-body motions

The application of the sampling surfaces (SaS) method to laminated composite plates is presented in a companion paper (Kulikov GM, Plotnikova SV. Exact 3D stress analysis of laminated composite plates by sampling surfaces method. Compos Struct 2012;94:3654–3663). In this paper, we extend the SaS method to shells to solve the 3D elasticity problems for cylindrical and spherical laminated composite shells. For this purpose, we introduce inside the nth layer In not equally spaced SaS parallel to the middle surface of the shell and choose displacements of these surfaces as basic kinematic variables. Such choice of displacements allows the derivation of strain–displacement equations, which are invariant under all rigid-body shell motions in any convected curvilinear coordinate system. This gives in turn the opportunity to find the 3D elasticity solutions for laminated composite shells with a prescribed accuracy utilizing a sufficiently large number of SaS, which are located at Chebyshev polynomial nodes and layer interfaces as well.

On the use of sampling surfaces method for solution of 3D elasticity problems for thick shells

AbstractThis paper presents a simple and effective method of solving the 3D elasticity problems for thick shells. It is based on the new concept of sampling surfaces (S‐surfaces) inside the shell body. According to this concept, we introduce N not equally located S‐surfaces parallel to the midsurface and choose displacements of these surfaces as basic shell unknowns. Such choice allows one to represent the governing equations of the proposed higher order shell model in a very compact form and to solve the 3D static problems for thick plates and shells efficiently.

Exact 3D stress analysis of laminated composite plates by sampling surfaces method

A paper focuses on the use of the efficient approach to exact 3D elasticity solutions of cross-ply and angle-ply laminated composite plates. This approach is based on the new method of sampling surfaces (SaS) developed recently by the authors. We introduce inside the nth layer In not equally spaced SaS parallel to the midsurface of the plate and choose displacements of these surfaces as fundamental plate unknowns. Such an idea permits the representation of the proposed higher order layer-wise plate theory in a very compact form. This fact gives in turn the opportunity to derive the exact 3D solutions of elasticity for thick and thin laminated composite plates with a prescribed accuracy by utilizing a sufficiently large number of SaS, which are located at interfaces and Chebyshev polynomial nodes.