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Investigation of Generalized SIFs of cracks in 3D piezoelectric media under various crack-face conditions

Frontiers of Structural and Civil Engineering 2020年第2期14卷 280-298页

作者： Jaroon RUNGAMORNRAT Bounsana CHANSAVANG Weeraporn PHONGTINNABOOT Chung Nguyen VAN Applied Mechanics and Structures Research Unit Department of Civil EngineeringFaculty of EngineeringChulalongkorn UniversityBangkok 10330Thailand Department of Civil Engineering Faculty of EngineeringSouphanouvong UniversityLoungprabang 06000Laos Department of Civil Engineering Faculty of EngineeringBurapha UniversityChonburi 20131Thailand Faculty of Civil Engineering Ho Chi Minh City of Technology and EducationHo Chi Minh 721400Vietnam

This paper investigates the influence of crack geometry,crack-face and loading conditions,and the permittivity of a medium inside the crack gap on intensity factors of planar and non-planar cracks in linear piezoelectric media.A weakly singular boundary integral equation method together with the near-front approximation is adopted to accurately determine the intensity *** results indicate that the non-flat crack surface,the electric field,and the permittivity of a medium inside the crack gap play a crucial role on the behavior of intensity *** mode-I stress intensity factors(K1)for two representative non-planar cracks under different crack-face conditions are found significantly different and they possess both upper and lower *** addition,K1 for impermeable and semi-permeable non-planar cracks treated depends strongly on the electric field whereas those of impermeable,permeable,and semi-permeable penny-shaped cracks are identical and independent of the electric *** stress/electric intensity factors predicted by permeable and energetically consistent models are,respectively,independent of and dependent on the electric field for the penny-shaped crack and the two representative non-planar ***,the permittivity of a medium inside the crack gap strongly affects the intensity factors for all crack configurations considered except for K1 of the semi-permeable pennyshaped crack.

关键词： crack-face conditions intensity factors non-flat cracks permittivity piezoelectric media SGBEM

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GENERALIZED 2D PROBLEM OF piezoelectric media CONTAINING COLLINEAR CRACKS

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Acta Mechanica Sinica 1999年第3期15卷 235-244页

作者：高存法王敏中 Department of Mechanics and Engineering Science Peking UniversityBeijing 100871China

The generalized 2D problem in piezoelectric media with collinear cracks is addressed based on Stroh's formulation and the exact electric boundary conditions on the crack faces. Exact solutions are obtained, respectively, for two special cases: one is that a piezoelectric solid withN collinear cracks is subjected to uniform loads at infinity, and the other is that a piezoelectric solid containing a single crack is subjected to a line load at an arbitrary point. It is shown when uniform loads are applied at infinity or on the crack faces that, the stress intensity factors are the same as those of isotropic materials, while the intensity factor of electric displacement is dependent on the material constants and the applied mechanical loads, but not on the applied electric loads. Moreover, it is found that the electric field inside any crack is not equal to zero, which is related to the material properties and applied mechanical-electric loads.

关键词： piezoelectric media cracks two-dimensional problem Stroh formulation

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THE FUNDAMENTAL SOLUTIONS FOR THE PLANE PROBLEM IN piezoelectric media WITH AN ELLIPTIC HOLE OR A CRACK

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Applied Mathematics and Mechanics(English Edition) 1998年第11期19卷 0-4044,0-0+0-0+0-0+0-0页

作者：高存法樊蔚勋 Department of Aircraft Nanjing University of Aeronautics and Astronautics Nanjing P. R. China

Based on the complex potential method, the Greed’s functions of the plane problem in transversely isotropic piezoelectric media with an elliptic hole are obtained in terms of exact electric boundary conditions at the rim of the hole. When foe elliptic hole degenerates into a crack, the fundamental solutions for the field intensity factors arc given. The general solutions for concentrated and distributed loads applied on the surface of the hole or crack are produced through the superposition of fundamental solutions With the aid of these solutions , some erroneous results provided previously in other works are pointed out More important is that these solutions can be used as the fundamental solutions of boundary element method to solve more practical problems in piezoelectric media.

关键词： piezoelectric media elliptic hole crack plane strain,fundamental solution

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GENERAL SOLUTION OF PLANE PROBLEM OF piezoelectric media EXPRESSED BY "HARMONIC FUNCTIONS

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Applied Mathematics and Mechanics(English Edition) 1997年第8期18卷 757-764页

作者：丁皓江王国庆陈伟球 Zhejiang University Hangzhou P. R. China

First, based on the basic equations of two-dimensional piezoelectroelasticity, a displacement function is introduced and the general solution is then derived. Utilizing the generalized Almansi's theorem, the general solution is so simplified that all physical quantities can be expressed by three 'harmonic functions'. Second, solutions of problems of a wedge loaded by point forces and point charge at the apex are also obtained in the paper. These solutions can be degenerated to those of problems of point forces and point charge acting on the line boundary of a piezoelectric half-plane.

关键词： piezoelectric media plane problem general solution wedge

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A symplectic eigensolution method in transversely isotropic piezoelectric cylindrical media

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2005年第9期6卷 922-927页

作者：徐新生顾佥梁以德郑建军 State Key Laboratory of Structure Analysis of Industrial Equipment and Department of Engineering Mechanics Dalian University of Technology Dalian 116024 China Department of Building and Construction City University of Hong Kong Hong Kong China

This paper reports establishment of a symplectic system and introduces a 3D sub-symplectic structure for transversely isotropic piezoelectric media. A complete space of eigensolutions is obtained directly. Thus all solutions of the problem are re- duced to finding eigenvalues and eigensolutions, which include zero-eigenvalue solutions and all their Jordan normal form of the corresponding Hamiltonian matrix and non-zero-eigenvalue solutions. The classical solutions are described by zero-eigen- solutions and non-zero-eigensolutions show localized solutions. Numerical results show some rules of non-zero-eigenvalue and their eigensolutions.

关键词： Symplectic method Hamiltonian system Transverse isotropic piezoelectric media Eigensolution

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PLANE PROBLEMS IN piezoelectric mediaWITH ELLIPTIC INCLUSION

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Applied Mathematics and Mechanics(English Edition) 1998年第2期19卷 147-155页

作者：侯密山杨其俊 University of Petroleum Dongying P. R. China

This paper expresses potential function of complex variable in Fabere series and the solution in closed form is provided for the plane stress problems in piezoelectric media with elliptic inclusion. It is shown from the solution that the stress, strain, electric field intensity and electric displacement in inclusion are all constant. In addition, the electromechanical behavior of piezoelectric influence at the elliptic rim of the infinite matrix with only acting mechanical or electric load is discussed with numerical examples.

关键词： piezoelectric media inclusion plane problem Faber series

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Free vibration of piezoelectric annular plate

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Journal of Zhejiang University Science 2003年第4期4卷 379-387页

作者：王云徐荣桥丁皓江 SchoolofMechanicalandElectronicEngineering HangzhouInstituteofElectronicEngineeringHangzhou310037China DepartmentofCivilEngineering ZhejiangUniversityHangzhou310027China)

General solutions for coupled three dimensional equations of piezoelectric media were used in this work to obtain some analytical solutions for free vibration of piezoelectric annular plates. These solutions not only satisfy the governing equations at every point in the concerned region but also satisfy the prescribed boundary conditions at every point on the boundaries. Therefore, they are three-dimensional exact. Numerical results are finally tabulated.

关键词： piezoelectric media Sectorial annular plate Free vibration

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