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Jan Sládek, Vladimír Sládek and Peter Staňák

Analysis of Thermo-Piezoelectricity Problems by Meshless Method

In this paper meshless method based on the local Petrov-Galerkin approach is pesented for the solution of boundary value problems for coupled thermo-electro-mechanical fields. Transient dynamic governing equations are considered in analysis of the problems. Material properties of piezoelectric materials are influenced by a thermal field. It is leading to an induced nonhomogeneity and the governing equations are more complicated compared to a homogeneous counterpart. Two-dimensional analyzed domain is divided into small circular subdomains surrounding nodes that are randomly spread over the whole domain. A unit step function is used as the test functions in the local weak-form. The derived local integral equations (LIEs) have boundary-domain integral form. The moving least-squares (MLS) method is adopted for the approximation of the physical quantities in the LIEs and afterwards to obtain a system of ordinary differential equations (ODE) for unknown nodal quantities. To solve this system of ODE, Houbolt finite-difference scheme is applied as a time-stepping method.

Open access

Vladimir Sladek and Michal Ilčin

Abstract

Strong correlation of stabilization energies of π-stacked pyridine and fluorinated pyridine dimers with various relative orientations is presented. Four possible orientations of the monomers were considered. A SAPT decomposition of the interaction energies is presented and briefly discussed. The dominant electrostatic contribution to the stabilization energy is found in some dimers and its possible origin is addressed in the discussion. An outline of possible future studies is introduced.

Open access

Ladislav Sátor, Vladimír Sládek and Ján Sládek

Abstract

A numerical analysis based on the meshless local Petrov- Galerkin (MLPG) method is proposed for a functionally graded material FGM (FGMfunctionally graded material) beam. The planar bending of the beam is considered with a transversal gradation of Young's modulus and a variable depth of the beam. The collocation formulation is constructed from the equilibrium equations for the mechanical fields. Dirac's delta function is employed as a test function in the derivation of a strong formulation. The Moving Least Squares (MLS) approximation technique is applied for an approximation of the spatial variations of all the physical quantities. An investigation of the accuracy, the convergence of the accuracy, the computational efficiency and the effect of the level of the gradation of Young's modulus on the behaviour of coupled mechanical fields is presented in various boundary value problems for a rectangular beam with a functionally graded Young's modulus.

Open access

Vladimir Sladek, Lenka Rottmannová, Peter Škorňa, Michal Ilčin and Vladimír Lukeš

Abstract

A systematic comparative theoretical study has been performed on a series of fourteen metasubstituted selenophenols. The optimal geometries were calculated using the density functional theory (DFT) and the Nuclear Magnetic Resonance parameters were computed by applying the Gauge Including Atomic Orbital (GIAO) method. The calculated NMR shifts were correlated with the Hammett constants. The obtained results were also compared with the theoretical data obtained for thiophenols and phenols. Our results indicate the linear dependence between the gas-phase NMR shifts and Hammett constants. However, the presence of large selenium atoms is able to suppress significantly the substituent effect in meta position. Therefore six substituents (Me, OH, MeCO, COOMe, COOEt and CF3 groups) were excluded from the data evaluation. Correlations with the fundamental stretching vibration frequencies of the mode with the dominant Se-H vibration have not been found.

Open access

P. Stanak, A. Tadeu, J. Sladek and V. Sladek

Abstract

This paper presents a general 2.5D meshless MLPG methodology for the computation of the elastic response of longitudinally invariant structure subjected to the incident wave field. A numerical frequency domain model is established using the Fourier transform in time and longitudinal coordinate domains. This allows for significant reduction of computational effort required. In the MLPG method the Moving-Least Squares (MLS) scheme is employed for the approximation of the spatial variation of displacement field. No finite elements are required for the approximation or integration of unknowns. A small circular subdomain is introduced around each nodal point in the analyzed domain. Local integral equations derived from the governing equations are specified on these subdomains. Continuously non-homogeneous material properties are varying in the cross-section of the analyzed structure. A simple patch test is introduced to assess the accuracy and the convergence of developed numerical model. At the end of the paper, numerical examples illustrate the applicability of the proposed numerical formulation.

Open access

Peter Staňák, Ján Sládek, Vladimír Sládek and Slavomír Krahulec

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.

Open access

P. Staňák, J. Sládek, V. Sládek and S. Krahulec

Abstract

In this paper a computational homogenization technique is applied to thermal analyses in porous materials. A volume fraction of pores on the microstructural level is the key factor that changes the macroscopic thermal properties. Thus, the distribution of thermal fields at the macroscopic level is analysed through the incorporation of the microstructural response on the representative volume element (RVE) assuming a uniform distribution of pores. For the numerical analysis the scaled boundary finite element method (SBFEM) is introduced to compute the thermal response of RVE. The SBFEM combines the main advantages of the finite element method (FEM) and the boundary element method (BEM). In this method, only the boundary is discretized with elements leading to the reduction of spatial dimension by one, similarly as in the BEM. It reduces computational efforts in the mesh generation and CPU time. The proposed method is used to study square RVE with a circular and elliptic pore under the thermal load. Dimensions of the pore are varied to obtain different volume fractions of matrix material. Numerical results for effective thermal conductivities obtained via SBFEM modelling show an excellent agreement with the finite element analysis using commercial software COMSOL Multiphysics.