Piezoelectric Sensors and Quasicrystal Plate Problems by Localized Radial Basis Function Collocation Method
Date Issued
2015
Date
2015
Author(s)
Chiang, Yu-Chuan
Abstract
The advantage of the localized radial basis function collocation method (LRBFCM) is that we can easily utilize kinds of LRBFCM spatial differential operators for the approximation of the spatial derivatives from the governing equations and Neumann type boundary conditions. As a result, LRBFCM is a convenient strong form meshless method for researchers to conduct with complex physical problems numerically. In the past, LRBFCM are usually applied for solving computational fluid mechanics (CFD) problems. In order to extend LRBFCM into structure engineering problems, we focus on the two main problems: numerical studies of piezoelectric sensor and quasicrystal plate. Due to the inherent piezoelectricity, piezoelectric electric materials are recognized as intelligent materials which play an important role on the development of various sensors and smart materials applications. In this thesis, we use LRBFCM to analyze a piezoelectric sensor under a uniform compressive load. Piezoelectric sensors are often manufactured as thin cylindrical plates, therefore a 3D cylindrical model with multi-scale nodal distribution domain is applied here. This thesis will demonstrate the results of mechanical displacement and induced electric potential by the LRBFCM. Furthermore, we also take the FEM-ANSYS solutions as a benchmark to compare the results with meshless local-Petrov-Galerkin method (MLPG) from Professor Sladek’s group. For the second main problem, the LRBFCM is applied to analyze in a quasicrystal (QCs) plate under a uniform static loads. Due to the Reissner–Mindlin plate bending theory, the actual 3D plate problem can be reduced to a quasi-3D problem. Hence, we are allowed to simulate the phonon and phason displacements by 2D governing equations. The behavior of the simply supported and clamped quasicrystal plates will be discussed here. In addition, this study remakes this quasicrystal plate problem by a conventional mesh-dependent numerical method, finite difference method (FDM) and compare the FDM results and LRBFCM results in order to show the superiority of the LRBFCM. The last but not the least, this study points out the difficulties when we conduct with the cross term on the orthogonal uniform distribution domain in order to improve the stability and accuracy of the LRBFCM for further researches.
Subjects
localized radial basis function
piezoelectric sensor
piezoelectric effect
phonon and phason displacements
quasicrystal plate
Reissner-Mindlin theory
Type
thesis
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