Grants

    Russian Science Foundation, Grant No. 24-21-00120 (2024-2025). Development of sampling surfaces method and differential quadrature method for solving three-dimensional problems of elasticity and electroelasticity for layered shells from composite and functionally graded piezoactive materials. Principal Investigator.
     The project focuses on the study of the fundamental problem of mechanics related to solving the three-dimensional problems of elasticity and electroelasticity for thin-walled composite structures. In recent years, devices and technical systems based on piezoactive materials penetrated in aerospace engineering and are widely used in adaptive thin-walled structures. Such structures with embedded piezoceramic materials can significantly change their technical characteristics in accordance with the operating conditions and allow controlling their deformations efficiently. The advantage of the piezoceramic material is that due to the direct and inverse piezoelectric effects it can fulfill simultaneously the functions of a sensor and an actuator as well. Thus, the analysis and modelling of thin-walled composite structures with piezoceramic sensors and actuators under electromechanical loading based on the three-dimensional theory of piezoelectricity is an important task. For this it is planned: (1) To develop a theory of laminated composite shells based on the sampling surfaces method by exactly satisfying the boundary conditions on the outer surfaces of the shell and the continuity conditions on the interfaces for the transverse components of the stress tensor. The sampling surfaces method, proposed by the authors for calculating the laminated elastic shells using the variational formulation, makes it possible to introduce an arbitrary number of sampling surfaces parallel to the middle surface into the shell and located at Chebyshev polynomial nodes in order to utilize the displacements of these surfaces as unknown functions. (2) To build a theory of laminated composite shells with embedded piezoceramic materials based on the sampling surfaces method by accurately fulfilling the boundary conditions on the outer surfaces of the shell and the continuity conditions on the interfaces for the transverse components of the stress tensor and the electric induction vector. The sampling surfaces method, adapted for the calculation of laminated piezoelectric shells, allows one to introduce sampling surfaces parallel to the middle surface in the shell in order to use the displacements and electric potentials of these surfaces as unknown functions. (3) To develop a version of the differential quadrature method for the three-dimensional analysis of laminated composite shells using Lagrange polynomials in spatial approximations of displacements, strains and stresses. (4) To build a version of the differential quadrature method for the three-dimensional analysis of laminated composite shells with continuously and discretely distributed functionally graded piezoactive materials on the outer surfaces using Lagrange polynomials in spatial approximations of displacements, strains, stresses, electric potential, electric field and electric induction vectors. (5) To study a coupling effect of the electric and mechanical fields in laminated shells made of composite and functionally graded piezoactive materials using the developed numerical algorithms. To describe spatial distributions of the transverse components of the stress tensor and the electric induction vector through the thickness of layers.

    Russian Science Foundation, Grant No. 22-21-00030 (2022-2023). Solution of three-dimensional geometrically nonlinear problems of thermoelectroelasticity for composite shells with piezoelectric sensors and actuators with temperature-dependent material properties. Principal Investigator.
     The project focuses on the study of the fundamental problem of mechanics related to solving the nonlinear problems of thermoelectroelasticity for thin-walled piezoelectric structures. In recent years, devices and technical systems based on piezoelectric materials have penetrated in aerospace engineering and are widely used in adaptive thin-walled structures. Such structures with embedded piezoceramic materials can significantly change their technical characteristics in accordance with the operating conditions and allow controlling their deformations efficiently. The advantage of the piezoceramic material is that due to the direct and inverse piezoelectric effects it can fulfill simultaneously the functions of a sensor and an actuator as well. The design of adaptive structures is a multifunctional activity including the investigation on the heat transfer, mechanics of composite materials and structures, sensors and actuators, optimization methods. Thus, the analysis and modelling of thin-walled composite structures with piezoceramic sensors and actuators under thermal and mechanical loading based on the three-dimensional theory of thermopiezoelectricity is an important task. Of particular practical interest is the solution of geometrically nonlinear problems for laminated composite shells with embedded piezoceramic materials with temperature-dependent properties. For this it is planned: (1) To develop geometrically linear and nonlinear models of the laminated composite shell with embedded piezoelectric materials with temperature-dependent properties based on the method of sampling surfaces. This method proposed by the authors of the project makes it possible to introduce sampling surfaces into the shell, which are parallel to the middle surface and located at Chebyshev polynomial nodes in order to use the temperatures, electric potentials and displacements of these surfaces as unknown functions. In particular, the choice of displacements of sampling surfaces allows one to obtain the Green-Lagrange strain-displacement relationships, which exactly represent arbitrarily large displacements of the shell as a rigid-body in curvilinear coordinates of the middle surface. (2) To construct geometrically exact hybrid finite elements of the laminated composite shell with continuously and discretely distributed sensors and actuators on the outer surfaces made of piezoelectric materials, which properties depend on temperature, using bilinear approximations of temperatures, temperature gradients, electric potentials, electric field vectors, displacements and strains of sampling surfaces as well as material properties on sampling surfaces that makes it possible to apply the effective algorithm of analytical integration throughout the finite element. The term “geometrically exact” means that the middle surface of the shell is described by analytically specified functions, including splines, i.e., the parametrization of the middle surface is known that in turn allows one to exactly calculate the coefficients of the first and second quadratic forms at the finite element nodes. (3) To investigate temperature, electric and mechanical fields in thin-walled composite structures with continuously and discretely distributed sensors and actuators on the outer surfaces using the developed geometrically exact solid-shell elements. To study the effect of piezoactive materials with temperature-dependent properties on the distribution of the symmetric Piola-Kirchhoff stress tensor and the electric induction vector through the thickness of layers in composite plates and shells undergoing arbitrarily large displacements and rotations. (4) To develop algorithms for optimizing the deformed shape of the thin-walled structure with piezoactive patches, the properties of which depend on temperature, under thermal and mechanical loading based on minimizing the basic functional with and without restrictions on the electric potentials applied to the electrodes of actuators.

    Russian Science Foundation, Grant No. 18-19-00092 (2018-2020). Development of the method of sampling surfaces and hybrid-mixed FEM model for solution of three-dimensional geometrically nonlinear problems of thermoelectroelasticity for piezoelectric shells with application to the analysis and modelling of adaptive thin-walled structures. Principal Investigator.
     In recent years, devices and systems on the basis of piezoelectric materials entered into many branches of modern engineering and are intensively used, in particular, in adaptive thin-walled structures subjected to thermomechanical loading. Such structures with embedded or discretely distributed on outers surfaces the piezoceramic materials can significantly change their technical characteristics in accordance with the operating conditions and allows controlling their deformations. Thus, the analysis and modelling of thinwalled composite structures with piezoelectric sensors and actuators on the basis of the 3D theory of thermoelectroelasticity is an actual task. The special interest has the solution of geometrically nonlinear problems for laminated composite shells made of piezoelectric functionally graded materials accounting for coupling electromechanical fields. The main purposes of the project are: (1) To develop new models of the layered composite shell with embedded or discretely distributed on outers surfaces the piezoelectric sensors and actuators based on the method of sampling surfaces. This method proposed by the authors of the project permits the introduction into a shell body of the arbitrary number of sampling surfaces parallel to the middle surface and located at Chebyshev polynomial nodes in order to use the displacements, temperature and electric potentials of these surfaces as unknown basic functions. Such choice of displacements gives an opportunity to derive the Green-Lagrange strain-displacement relationships, which exactly represent arbitrarily large displacements and rotations of the shell as a rigid-body in curvilinear coordinates of the middle surface. (2) To construct principally new geometrically exact hybrid finite elements of the laminated piezoelectric shell subjected to arbitrarily large rotations utilizing bilinear approximations of displacements, temperature and electric potentials of sampling surfaces and independent approximations of strains, stresses, temperature gradient and electric field vector that gives the possibility to implement effective analytical integration throughout the finite shell element. The term "geometrically exact" means that the middle surface of the shell is described by analytically given functions, i.e., the parametrization of the middle surface is known that in turn allows the exact calculation of coefficients of the first and second quadratic forms in finite element nodes. (3) To investigate the coupling of electric and mechanical fields in geometrically nonlinear laminated shells made of fiber reinforced composites and functionally graded piezoelectric materials subjected to thermal and electromechanical loading on the basis of proposed geometrically exact finite shell elements. (4) To analyze distributions of the symmetric Piola-Kirchhoff stress tensor and the Cauchy stress tensor through the layer thicknesses in deformed plates and shells with embedded piezoelectric sensors and actuators from functionally graded piezo-active materials under arbitrarily large rotations. (5) To elaborate through a nonlinear shell formulation the algorithm for optimization of deformed shapes of thin-walled structures with piezoelectric patches under thermomechanical loading based on minimization of the basic functional with and without restrictions on the voltage applied to the electrodes with application to adaptive space antennas and radio telescopes.

    Russian Ministry of Education and Science, Grant No. 9.4914.2017/ВУ (2017-2018). Organization of scientific research in Tambov State Technical University. Principal Investigator.
    Russian Ministry of Education and Science, Grant No. 9.1148.2017 (2017-2019). Nonlinear vibration control of adaptive thin-walled composite structures with discretely distributed sensors and actuators made of functionally graded piezoceramic materials based on the solution of three-dimensional dynamic problems of the geometrically nonlinear theory of electroelasticity. Principal Investigator.

    Russian Science Foundation, Grant No. 15-19-30002 (2015-2017). Shape and vibration control of adaptive thin-walled structures with segmented sensors and actuators made of functionally graded piezoelectric materials using geometrically exact solid-shell finite elements. Principal Investigator.
     In recent years, the technical systems based on piezoelectric materials have penetrated in many branches of modern mechanical engineering, particularly, in aerospace engineering and are widely used in adaptive thin-walled structures. Such structures with embedded piezoceramic materials can significantly change their technical characteristics in accordance with the operating conditions and enable to control their deformations and vibrations efficiently. The advantage of the piezoceramic material is that due to the direct and inverse piezoelectric effects it can fulfill simultaneously the functions of a sensor and a power drive (actuator) as well. The design of adaptive structures is a multifunctional activity including the investigation on mechanics of composite materials and structures, sensors and actuators, systems of automatic control and optimization methods. Thus, the calculation and modeling of static and dynamic problems for thin-walled composite structures with piezoelectric sensors and actuators based on the three-dimensional theory of electroelasticity is an important task. The special interest presents the solution of the control problem of deformed shapes and forced vibrations of laminated shells made of traditional fiber reinforced composite and functionally graded piezo-active materials accounting for the coupling of electromechanical fields. For this purpose, it is planned: (1) To develop a new mathematical models for the solution of coupled static and dynamic problems of electroelasticity for laminated composite shells with embedded piezoelectric sensors and actuators composed of functionally graded piezo-active materials based on the method of sampling surfaces. This method proposed recently by the authors of the project permits the introduction into a shell body of the arbitrary number of sampling surfaces parallel to the middle surface and located at Chebyshev polynomial nodes in order to use the displacements and electric potentials of these surfaces as unknown basic functions. (2) To construct a principally new geometrically exact hybrid finite elements of the laminated piezoelectric shell utilizing bilinear approximations of displacements and electric potentials of sampling surfaces and independent approximations of the strains, stress resultants and electric field vector that gives the possibility to implement effective analytical integration throughout the finite shell element. The term "geometrically exact" means that the middle surface of the shell is described by analytically given functions, i.e. the parametrization of the middle surface is known that in turn allows the exact calculation of coefficients of the first and second quadratic forms in finite element nodes. (3) To investigate the coupling of electric and mechanical fields in laminated orthotropic and anisotropic shells made of fiber reinforced composite and functionally graded piezoelectric materials in static and dynamic formulations on the basis of proposed geometrically exact finite shell elements. (4) To elaborate an algorithm for optimization of deformed shapes of thin-walled structures with piezoelectric patches under thermomechanical loading based on minimization of the basic functional with and without restrictions on the voltage applied to the electrodes with application to adaptive space antennas and radio telescopes. (5) To develop a technique of controlling the forced vibrations of intelligent thin-walled structures through the optimal location of sensors and actuators made of functionally graded piezo-active materials on the outer surfaces and determining the optimal voltages applied to the electrodes of piezoelectric patches with application to adaptive aircraft wings and helicopter blades.

    Russian Ministry of Education and Science, Grant No. 339 (2014-2016). Organization of scientific research in Tambov State Technical University. Principal Investigator.
    Russian Ministry of Education and Science, Grant No. 9.137.2014/K (2014-2016). Numerical three-dimensional modelling of quasistatic problems of geometrically non-linear thermoelectroelasticity for intelligent thin-walled structures with piezoelectric sensors and actuators composed of functionally graded materials. Principal Investigator.
    Russian Fund of Basic Research, Grant No. 13-01-00155 (2013-2015). Development of analytical and numerical methods for solution of coupled problems of three-dimensional thermoelectroelasticity for piezoelectric laminated shells. Principal Investigator.
    Russian Ministry of Education and Science, Grant No. 1.472/2011 (2012-2013). Modeling of dynamic behaviour of adaptive thin-walled piezoelectric structures on the basis of exact geometry solid-shell finite elements. Principal Investigator.
    Russian Ministry of Education and Science, Grant No 2.1.1/10003 (2011). Analysis of multilayered composite thin-walled structures subjected to thermoelectromechanical loading based on geometrically exact solid-shell elements. Principal Investigator.
    Russian Ministry of Education and Science, Grant No. 2.1.1/660 (2009-2010). Analysis of multilayered composite thin-walled structures subjected to thermoelectromechanical loading based on geometrically exact solid-shell elements. Principal Investigator.
    Russian Fund of Basic Research, Grant No. 08-01-00373 (2008-2010). Contact interaction of elastic multilayered composite shells undergoing arbitrarily large rotations. Principal Investigator.
    Russian Fund of Basic Research, Grant No. 04-01-00070 (2004-2006). Contact problem for elastic multilayered anisotropic shell undergoing arbitrarily large displacements and rotations. Principal Investigator.
    Deutsche Forschungsgemeinschaft and Russian Fund of Basic Research, Grant No. 98-01-04076 (1998-2000). Research of the static and dynamic contact of a geometrically non-linear multilayered anisotropic shell of revolution and deformed foundation with application to tire mechanics. Untersuchung des statischen und dynamischen Kontaktes mehrschichtiger anisotroper Rotationsschalen mit deformierbarem Untergrund in geometrisch nichtlinearer Aufgabenstellung mit Anwendung auf die Reifenmechanik. Principal Investigator.
    INTAS/FP6, Grant No. 95-0525 (1997-1999). Mathematical models and solving methods of the static and dynamic stress-strain state in composite shell structures for different purposes especially for problems in tire mechanics. Principal Investigator.