Tambov State Technical University

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Kulikov G.M.,Tambov State Technical University | Plotnikova S.V.,Tambov State Technical University
Computer Methods in Applied Mechanics and Engineering | Year: 2016

A hybrid-mixed ANS four-node quadrilateral plate element through the use of the sampling surfaces (SaS) technique is developed. The SaS formulation is based on choosing inside the nth layer In not equally spaced SaS parallel to the middle surface, in order to introduce the displacements of these surfaces as basic plate variables. Such choice of unknowns with utilizing the Lagrange polynomials of degree In-1 in the thickness direction for each layer leads to a very compact form of the governing equations. The SaS are located inside each layer at Chebyshev polynomial nodes that allows one to minimize uniformly the error due to the Lagrange interpolation. To avoid shear locking and have no spurious zero energy modes, the hybrid-mixed method and the ANS concept are employed. The developed four-node quadrilateral laminated plate element passes patch tests and exhibits a superior performance in the case of coarse distorted mesh configurations. It can be useful for the 3D stress analysis of thick and thin laminated composite plates because the SaS formulation gives the possibility to obtain the numerical solutions with a prescribed accuracy, which asymptotically approach the exact solutions of elasticity as the number of SaS tends to infinity. © 2016 Elsevier B.V.


Proskurin S.G.,Tambov State Technical University
Quantum Electronics | Year: 2011

The issues of detecting the inhomogeneities are studied aimed at mapping the distribution of orption and scattering in soft tissues. A modification of the method of diffuse optical tomography is proposed for detecting directly and determining the region of spatial localisation of such orbing and scattering inhomogeneities as a cyst, a hematoma, a tumour, as well as for measuring the degree of oxygenation or deoxygenation of blood, in which the late arriving photons that diffuse through the scattering object are used. © 2011 Kvantovaya Elektronika and Turpion Ltd.


Kulikov G.M.,Tambov State Technical University | Plotnikova S.V.,Tambov State Technical University
Composite Structures | Year: 2012

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 I n 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. © 2012 Elsevier Ltd.


Kulikov G.M.,Tambov State Technical University | Plotnikova S.V.,Tambov State Technical University
European Journal of Mechanics, A/Solids | Year: 2015

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 nth layer In 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. © 2014 Elsevier Masson SAS. All rights reserved.


Kulikov G.M.,Tambov State Technical University | Plotnikova S.V.,Tambov State Technical University
Composite Structures | Year: 2013

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. © 2013.


Kulikov G.M.,Tambov State Technical University | Plotnikova S.V.,Tambov State Technical University
Composite Structures | Year: 2013

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 I n 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. © 2012 Elsevier Ltd.


Kulikov G.M.,Tambov State Technical University | Plotnikova S.V.,Tambov State Technical University
International Journal of Solids and Structures | Year: 2013

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. © 2013 Elsevier Ltd. All rights reserved.


Kulikov G.M.,Tambov State Technical University | Plotnikova S.V.,Tambov State Technical University
International Journal of Solids and Structures | Year: 2013

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. © 2013 Elsevier Ltd. All rights reserved.


Kulikov G.M.,Tambov State Technical University | Plotnikova S.V.,Tambov State Technical University
Mechanics Research Communications | Year: 2014

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. © 2013 Elsevier Ltd. All rights reserved.


Kulikov G.M.,Tambov State Technical University | Plotnikova S.V.,Tambov State Technical University
International Journal of Solids and Structures | Year: 2014

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. © 2013 Elsevier Ltd. All rights reserved.

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