P. Stanak

Three-Dimensional Meshless Modelling of Functionally Graded Piezoelectric Sensor

A meshless local Petrov-Galerkin (MLPG) method to analyse the electro-elastic response of functionally graded piezoelectric circular sensor is proposed. In this approach the analysed body is discretized using nodal points only, no finite element mesh is required. The moving least-squares (MLS) scheme is employed for the spatial approximation of unknown physical fields in terms of corresponding nodal quantities. Three-dimensional modelling enables asymmetric loading patterns to be used. The exponential gradation of material properties is proposed in the poling direction of the sensor. The effect of varying gradation coefficients on mechanical displacements and induced electric potential is investigated.

Meshless analysis of piezoelectric sensor embedded in composite floor panel

Piezoelectric materials are the key element in various sensors and sensory devices used in industry and research. In this article, we use the meshless local Petrov–Galerkin method to analyze a three-dimensional piezoelectric sensor that is embedded in a composite floor panel. Temporal variation of panel deformation is determined analytically and then prescribed as a boundary condition for the sensor. In the proposed formulation, quasi-static governing equations for the electric field and elastodynamic equations for mechanical fields are coupled together. Local integral equations are derived from the local weak form of the governing equations, using a Heaviside step function as the test function. Nodal points are distributed in the analyzed domain, and each node is the center of a small subdomain of spherical shape. The spatial variations of the displacement and electric potential are approximated by the moving least squares scheme. A system of ordinary differential equations is obtained after evaluation of all spatial integrals. The Houbolt finite-difference scheme is applied to solve this system of ordinary differential equations as a time-stepping method. The temporal variation of the induced electric field is finally obtained. It is shown that significant peak amplitudes of the electric field are detected at the top of the sensor.