Semi-analytical methods for analysis of prismatic structures with piezoelectric inclusions.

摘要

The objective of this research is to develop a semi-analytical method for analysis of prismatic structures with piezoelectric inclusions. This is achieved by decomposing the governing equations of exact three-dimensional piezoelasticity into cross-sectional and axial parts. Such decompositions allow the axial and the cross-sectional parts of the total solution to be obtained with analytic and interface-enriched Reproducing Kernel Particle Methods, respectively.; First, a semi-analytical finite element method is developed to analyze the behavior of a laminated circular piezoelectric cylinder under axisymmetric mechanical and electric loads. This method relies on finite element discretization over the thickness of the cylinder and analytical determination of the electromechanical fields along the other dimensions. Such an approach provides significant computational savings over fully-discrete numerical methods.; Since the proposed method is based on the extension of the relaxed formulation of Saint-Venant and Almansi-Michell problems, where the end conditions are given in terms of integral resultants of axial force, torque and electric flux, the second part of the research aims to quantify the end-effects due to self-equilibrated displacements, voltages, tractions, and/or electric displacements prescribed point-wise. The work brings the semi-analytic method for axisymmetric problems to full-generality.; An interface enriched Reproducing Kernel Particle Method (eRKPM) is developed in the third part of the research for two-dimensional (plane-strain or plane-stress) analysis of non-homogenous piezoelectric structures with arbitrarily shaped material interfaces. Special enrichment functions are introduced within the Reproducing Kernel Particle Method to capture discontinuities of strain and electric fields at the material interfaces.; The last part of the research is to extend the proposed semi-analytical method for analyzing piezoelectric prismatic structures with non-homogeneous, and arbitrarily shaped cross-sections. The proposed eRKPM discretization is utilized to obtain the cross-sectional behavior and the electromechanical fields along the axial direction are determined analytically.