Showing papers by "Vladimir Sladek published in 2019"

Coupling effects in transient analysis of FGM plates bending in non-classical thermoelasticity

Abstract: Given that the thermal stresses mainly at the interface between two different materials are the significant factors of failure of the laminated composite structures, there is an enhanced request to replace laminated composite structures by structures made of micro-composite materials exhibiting the properties of continuously nonhomogeneous continua. In addition to elimination of interface discontinuities, the functional gradation (FG) of material coefficients brings new phenomena in bending of FGM plates as compared with homogeneous ones. There are known coupling effects between the in-plane deformations and bending modes even in plates subjected to stationary mechanical loadings. Another coupling can arise between thermal and mechanical fields in thermoelasticity. In the classical thermoelasticty, the heat conduction is described by the parabolic PDE when the temperature change propagates with infinite velocity. Much more realistic is the non-classical treatment with wave propagation of heat. In this paper, the unified formulation for bending of FGM plates under transient thermal loads is developed within the generalized thermoelasticity with taking into account the assumptions of the Lord-Shulman theory of thermoelasticty and the assumptions of the Kirchhoff-Love theory as well as the 1st and 3rd order shear deformation plate bending theories. Moreover, we can study various coupling effects by changing the parameters of functional gradations of particular material coefficients in numerical simulations. For numerical solution, the strong formulation is developed with meshless approximation of spatial variations of field variables. The time integration is carried out by the Wilson time stepping technique.

Gradient theory for crack problems in quasicrystals

Abstract: Constitutive equations in gradient theory of quasicrystals are written for phonon and phason stresses, and the higher-order stress tensor. They are expressed by the phonon and phason strains and the gradient of phonon strains. The higher-order elastic parameters are proportional to the conventional elastic stiffness coefficients by the internal length material parameter. Material parameters in constitutive equations correspond to the decagonal quasicrystals. The principle of virtual work is applied to derive governing equations and corresponding boundary conditions. The finite element method (FEM) is developed to solve general 2D boundary value problems in problems described by governing equations for strain-gradient theory of quasicrystals. The path-independent J -integral is also derived for fracture mechanics analysis of such solids. Numerical examples are presented to demonstrate the veracity of the formulations.

Perturbation finite element solution for chemo-elastic boundary value problems under chemical equilibrium

Abstract: Modeling the elastic behavior of solids in energy conversion and storage devices such as fuel cells and lithium-ion batteries is usually difficult because of the nonlinear characteristics and the coupled chemo-mechanical behavior of these solids. In this work, a perturbation finite element (FE) formulation is developed to analyze chemo-elastic boundary value problems (BVPs) under chemical equilibrium. The perturbation method is applied to the FE equations because of the nonlinearity in the chemical potential expression as a function of solute concentration. The compositional expansion coefficient is used as the perturbation parameter. After the perturbation expansion, a system of partial differential equations for the displacement and dimensionless solute concentration functions is obtained and solved in consecutive steps. The presence of a numerical solution enables modeling 3D chemo-elastic solids, such as battery electrodes or ionic gels, of any geometric shape with defects of different shapes. The proposed method is tested in several numerical examples such as plates with circular or elliptical holes, and cracks. The numerical examples showed how the shape of the defect can change the distribution of solute concentration around the defect. Cracks in chemo-elastic solids create sharp peaks in solute concentration around crack tips, and the intensity of these peaks increases as the far field solute concentration decreases.

Dynamic Wave Propagation in Fiber Reinforced Piezoelectric Composites with Cracks

Abstract: This paper presents the transient dynamic analysis of micro-cracks of arbitrary shape in two-dimensional, linear piezoelectric fiber reinforced composite materials. Interface cracks between fiber a...

Size Dependent Thermo-Piezoelectricity for In-Plane Cracks

Abstract: The finite element method (FEM) is developed to analyse the size effect (flexoeletricity) for 2-D crack problems in thermo-piezoelectricity. Flexoelectricity is observed in micro/nanoelectronic structures, where large strain gradients destroy the symmetric structure of atoms in crystals and thereby causing polarization, even in dielectric materials. In contrast to using classical Fourier heat conduction theory, a finite speed of the thermal wave is considered in the higher order transport equation. The variational principle is applied to derive the FEM equations and C1-continuous elements are employed in the implementation of the FEM. An example is presented to demonstrate the effect of the characteristic time parameter on the crack opening displacement and temperature distribution.

Bending of Piezo-Electric FGM Plates by a Mesh-Free Method

Abstract: Unified formulation for bending of elastic piezoelectric plates is derived with incorporating the assumptions of three plate bending theories, such as the Kirchhoff-Love theory, 1st order and 3rd order shear deformation plate theory. The functional gradation of material coefficients in the transversal as well as in-plane direction is allowed and the plate thickness can be variable. Both the governing equations and the boundary conditions are derived from the variational formulation of 3D electro-elasticity. For numerical solution a mesh-free method is developed with using the Moving Least Square approximation for spatial variations of field variables. The high order derivatives of field variables are eliminated by decomposing the original governing partial differential equations (PDE) into the system of PDEs with not higher than 2nd order derivatives. The numerical simulations are presented for illustration of coupling effects and verification of the developed theoretical and numerical formulations.