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General solutions of plane problem in one-dimensional quasicrystal piezoelectric materials and its application on fracture mechanics

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Applied Mathematics and Mechanics(English Edition) 2015年第6期36卷 793-814页

作者： Jing YU Junhong GUO Ernian PAN Yongming XING School of Science Inner Mongolia University of Technology College of General Education Inner Mongolia Normal University Department of Civil Engineering University of Akron

Based on the fundamental equations of piezoelasticity of quasicrystals （QCs）, with the symmetry operations of point groups, the plane piezoelasticity theory of one- dimensional （1D） QCs with all point groups is investigated systematically. The gov- erning equations of the piezoelasticity problem for 1D QCs including monoclinic QCs, orthorhombic QCs, tetragonal QCs, and hexagonal QCs are deduced rigorously. The general solutions of the piezoelasticity problem for these QCs are derived by the opera- tor method and the complex variable function method. As an application, an antiplane crack problem is further considered by the semi-inverse method, and the closed-form so- lutions of the phonon, phason, and electric fields near the crack tip are obtained. The path-independent integral derived from the conservation integral equals the energy release rate.

关键词： quasicrystals （QCs） piezoelasticity fracture mechanics crack complexvariable method

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Complex variable method for an anti-plane elliptical cavity of one-dimensional hexagonal piezoelectric quasicrystals

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Chinese Journal of Aeronautics 2015年第4期28卷 1287-1295页

作者： Yu Jing Guo Junhong Xing Yongming School of Science Inner Mongolia University of Technology College of General Education Inner Mongolia Normal University

Based on the fundamental equations of piezoelasticity of quasicrystal media, using the symmetry operations of point groups, the linear piezoelasticity behavior of one-dimensional（1D）hexagonal quasicrystals is investigated and the piezoelasticity problem of 1D hexagonal quasicrystals is decomposed into two uncoupled problems, i.e., the classical plane elasticity problem of conventional hexagonal crystals and the phonon–phason-electric coupling elasticity problem of1 D hexagonal quasicrystals.The final governing equations are derived for the phonon–phasonelectric coupling anti-plane elasticity of 1D hexagonal quasicrystals.The complex variable method for an anti-plane elliptical cavity in 1D hexagonal piezoelectric quasicrystals is proposed and the exact solutions of complex potential functions, the stresses and displacements of the phonon and the phason fields, the electric displacements and the electric potential are obtained explicitly.Reducing the cavity into a crack, the explicit solutions in closed forms of electro–elastic fields,the field intensity factors and the energy release rate near the crack tip are derived.

关键词： Complex variable methodElliptical cavity Fracture mechanics piezoelasticity Quasicrystals

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3D mixed finite elements for curved,flat piezoelectric structures

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International Journal of Smart and Nano Materials 2019年第4期10卷 249-267页

作者： Martin Meindlhumer Astrid Pechstein Institute of Technical Mechanics Johannes Kepler University LinzLinzAustria

The Tangential-Displacement Normal-Normal-Stress(TDNNS)method is a finite element method that was originally introduced for elastic solids and later extended to piezoelectric materials.It uses tangential components of the displacement and normal components of the normal stress vector as degrees of freedom for elasticity.For the electric field,the electric potential is used.The TDNNS method has been shown to provide elements which do not suffer from shear locking.Therefore thin structures(e.***.piezoelectric patch actuators)can be modeled efficiently.Hexahedral and prismatic elements of arbitrary polynomial order are provided in the current contribution.We show that these elements can be used to discretize curved,shelllike geometries by curved elements of high aspect ratio.The order of geometry approximation can be chosen independently from the polynomial order of the shape functions.We present two examples of curved geometries,a circular patch actuator and a radially polarized piezoelectric semi-cylinder.Simulation results of the TDNNS method are compared to results gained in ABAQUS.We obtain good results for displacements and electric potential as well as for stresses,strains and electric field when using only one element in thickness direction.

关键词： piezoelasticity mixed finite elements curved elements locking free

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