Slavomir Krahulec

Analyses of Circular Magnetoelectroelastic Plates with Functionally Graded Material Properties

A meshless method based on the local Petrov–Galerkin approach is proposed for plate bending analysis with material containing functionally graded magnetoelectroelastic properties. Material properties are considered to be continuously varying along the plate thickness. Axial symmetry of geometry and boundary conditions for a circular plate reduces the original 3D boundary value problem into a 2D problem in axial cross section. Both stationary and transient dynamic conditions for a pure mechanical load are considered in this article. The local weak formulation is employed on circular subdomains in the axial cross section. Subdomains surrounding nodes are randomly spread over the analyzed domain. The test functions are taken as unit step functions in derivation of the local integral equations (LIEs). The moving least-squares (MLS) method is adopted for the approximation of the physical quantities in the LIEs. After performing the spatial integrations, one obtains a system of ordinary differential equations for certain nodal unknowns. That system is solved numerically by the Houbolt finite-difference scheme as a time-stepping method.

Analyses of functionally graded plates with a magnetoelectroelastic layer

A meshless local Petrov–Galerkin (MLPG) method is presented for the analysis of functionally graded material (FGM) plates with a sensor/actuator magnetoelectroelastic layer localized on the top surface of the plate. The Reissner–Mindlin shear deformation theory is applied to describe the plate bending problem. The expressions for the bending moment, shear force and normal force are obtained by integration through the FGM plate and magnetoelectric layer for the corresponding constitutive equations. Then, the original three-dimensional (3D) thick-plate problem is reduced to a two-dimensional (2D) problem. Nodal points are randomly distributed over the mean surface of the considered plate. Each node is the center of a circle surrounding the node. The weak-form on small subdomains with a Heaviside step function as the test function is applied to derive local integral equations. After performing the spatial MLS approximation, a system of ordinary differential equations of the second order for certain nodal unknowns is obtained. The derived ordinary differential equations are solved by the Houbolt finite-difference scheme. Pure mechanical loads or electromagnetic potentials are prescribed on the top of the layered plate. Both stationary and transient dynamic loads are analyzed.

Enhancement of the magnetoelectric coefficient in functionally graded multiferroic composites

A meshless method based on the local Petrov–Galerkin approach is proposed to solve static and dynamic problems in functionally graded magnetoelectroelastic plates. Material properties on the bottom surface have a pure piezomagnetic behavior, and on the top surface, they are pure piezoelectric. Along the plate thickness, the material properties are continuously varying. The magnetoelectric coefficient is vanishing in pure piezoelectric as well as in pure piezomagnetic constituents. It is shown, however, that a finite electric potential in the functionally graded composite can be induced by an applied magnetic potential. It means that a finite magnetoelectric coefficient exists in a functionally graded composite plate made of different phases with vanishing magnetoelectric coefficients. It is a way to enhance the magnetoelectric coefficient in composites. Various gradations of material coefficients are considered to analyze their influence on the magnitude of magnetoelectric coefficients. Pure magnetic and combined magnetic–mechanical loads are analyzed. The meshless local Petrov–Galerkin is developed for the solution of boundary value problems in magnetoelectroelastic solids with continuously varying material properties.

Effect of Voids on a Magistral Crack in Piezoelectric Brittle Materials

A large (magistral) crack is analyzed in a voided piezoelectric solid. The representative volume element (RVE) is analyzed for determination of influence of voids on material properties. The whole domain is divided into two subdomains. At the crack tip vicinity it is considered a subdomain with the crack tip and circular voids. Material properties correspond to the piezoelectric skeleton there. The rest part of analyzed domain is modeled by effective material properties obtained from analyses on the RVE. The scaled boundary finite element method (SBFEM) is applied to solve all boundary value problems.

Numerical MLPG Analysis of Piezoelectric Sensor in Structures

Abstract The paper deals with a numerical analysis of the electro-mechanical response of piezoelectric sensors subjected to an external non-uniform displacement field. The meshless method based on the local Petrov-Galerkin (MLPG) approach is utilized for the numerical solution of a boundary value problem for the coupled electro-mechanical fields that characterize the piezoelectric material. The sensor is modeled as a 3-D piezoelectric solid. The transient effects are not considered. Using the present MLPG approach, the assumed solid of the cylindrical shape is discretized with nodal points only, and a small spherical subdomain is introduced around each nodal point. Local integral equations constructed from the weak form of governing PDEs are defined over these local subdomains. A moving least-squares (MLS) approximation scheme is used to approximate the spatial variations of the unknown field variables, and the Heaviside unit step function is used as a test function. The electric field induced on the sensor is studied in a numerical example for two loading scenarios.