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GENERALIZED stroh formalism FOR ANISOTROPIC ELASTICITY FOR GENERAL BOUNDARY CONDITIONS

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Acta Mechanica Sinica 1992年第3期8卷 193-207页

作者：丁啟财王敏中 Department of Civil Engineering Mechanics and MetallurgyUniversity of Illinois at ChicagoBox 4348ChicagoIL 60680U.S.A. Department of Mechanics Peking UniversityBeijing 100871China

The stroh formalism is most elegant when the boundary conditions are simple, namely,they are prescribed in terms of traction or displacement.For mixed boundary conditions such as there for a slippery boundary,the concise matrix expressions of the stroh formalism are destroyed.We present a generalized stroh formalism which is applicable to a class of general boundary conditions.The general boundary conditions in- clude the simple and slippery boundary conditions as special cases.For Green's functions for the half space, the general solution is applicable to the case when the surface of the half-space is a fixed,a free,a slippery, or other more general boundary.For the Griffith crack in the infinite space,the crack can be a slit-like crack with free surfaces,a rigid line inclusion(which is sometimes called an anticrack),or a rigid line with slippery surface or with other general surface conditions.It is worth mention that the modifications required on the stroh formalism are minor.The generalized formalism and the final solutions look very similar to those of unmodified version.Yet the results are applicable to a rather wide range of boundary conditions.

关键词： anisotropic elasticity stroh formalism mixed boundary conditions

Green's functions of two-dimensional piezoelectric quasicrystal in half-space and bimaterials

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Applied Mathematics and Mechanics(English Edition) 2023年第2期44卷 237-254页

作者： Xiaoyu FU Xiang MU Jinming ZHANG Liangliang ZHANG Yang GAO College of Science China Agricultural UniversityBeijing 100083China College of Engineering China Agricultural UniversityBeijing 100083China

In this paper,we obtain Green’s functions of two-dimensional(2D)piezoelectric quasicrystal(PQC)in half-space and bimaterials.Based on the elastic theory of QCs,the stroh formalism is used to derive the general solutions of displacements and stresses.Then,we obtain the analytical solutions of half-space and bimaterial Green’s functions.Besides,the interfacial Green’s function for bimaterials is also obtained in the analytical form.Before numerical studies,a comparative study is carried out to validate the present solutions.Typical numerical examples are performed to investigate the effects of multi-physics loadings such as the line force,the line dislocation,the line charge,and the phason line force.As a result,the coupling effect among the phonon field,the phason field,and the electric field is prominent,and the butterfly-shaped contours are characteristic in 2D PQCs.In addition,the changes of material parameters cause variations in physical quantities to a certain degree.

关键词： Green’s function two-dimensional(2D)piezoelectric quasicrystal(PQC) stroh formalism half-space bimaterial

Theoretical analysis of surface waves in piezoelectric medium with periodic shunting circuits

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Applied Mathematics and Mechanics(English Edition) 2023年第8期44卷 1287-1304页

作者： Youqi ZHANG Rongyu XIA Jie XU Kefu HUANG Zheng LI State Key Laboratory for Turbulence and Complex Systems Department of Mechanics and Engineering SciencePeking UniversityBeijing 100871China Department of Mechanics and Aerospace Engineering Southern University of Science and TechnologyShenzhen 518055Guangdong ProvinceChina

The investigations of surface waves in the piezoelectric medium bring out great possibility in designing smart surface acoustic wave(SAW)devices.It is important to study the dispersion properties and manipulation mechanism of surface waves in the semi-infinite piezoelectric medium connected with periodic arrangement of shunting circuits.In this study,the extended stroh formalism is developed to theoretically analyze the dispersion relations of surface waves under different external circuits.The band structures of both the Rayleigh wave and the Bleustein-Gulyaev(BG)wave can be determined and manipulated with proper electrical boundary conditions.Furthermore,the electromechanical coupling effects on the band structures of surface waves are discussed to figure out the manipulation mechanism of adjusting electric circuit.The results indicate that the proposed method can explain the propagation behaviors of surface waves under the periodic electrical boundary conditions,and can provide an important theoretical guidance for designing novel SAW devices and exploring extensive applications in practice.

关键词： metamaterial phononic crystal surface wave piezoelectricity electromechanical coupling stroh formalism

FURTHER STUDIES ON stroh-TYPE formalismS FOR ANISOTROPIC PLATES WITH BENDING-EXTENSION COUPLING

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Acta Mechanica Solida Sinica 2007年第4期20卷 324-332页

作者： Pin Lu HaiBo Chen CAS Key Laboratory of Mechanical Behavior and Design of Materials Department of Modern Mechanics University of Science and Technology of China Hefei 230027 China Institute of High Performance Computing 1 SciencePark Road #01-01 The Capricorn Science Park II Singapore 117528

stroh-type formalisms for anisotropic thin plates in literature axe reviewed and discussed, and two kinds of hybrid stroh-type formalisms axe compared. It is seen that the two stroh-type formalisms are essentially equivalent. With simple transfer relations, they can be expressed each other. In addition, with properly defined notation systems, the two stroh-type formalisms can also be written in unified forms, which will be convenient in applications.

关键词： stroh formalism anisotropic plate stroh-type formalism composite laminates

An anisotropic micromechanics model for predicting the rafting direction in Ni-based single crystal superalloys

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Acta Mechanica Sinica 2016年第1期32卷 135-143页

作者： Shuang-Yu Li Wen-Ping Wu Ming-Xiang Chen Department of Engineering Mechanics School of Civil Engineering Wuhan University State Key Laboratory of Water Resources & Hydropower Engineering Science Wuhan University

An anisotropic micromechanics model based on the equivalent inclusion method is developed to investigate the rafting direction of Ni-based single crystal superalloys.The micromechanical model considers actual cubic structure and orthogonal anisotropy properties. The von Mises stress,elastic strain energy density, and hydrostatic pressure in different inclusions of micromechanical model are calculated when applying a tensile or compressive loading along the[001] direction. The calculated results can successfully predict the rafting direction for alloys exhibiting a positive or a negative mismatch, which are in agreement with pervious experimental and theoretical studies. Moreover, the elastic constant differences and mismatch degree of the matrix and precipitate phases and their influences on the rafting direction are carefully discussed.

关键词： Ni-based single crystal superalloys Rafting Equivalent inclusion theory stroh formalism

Strip-coalesced interior zone model for two unequal collinear cracks weakening piezoelectric media

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Applied Mathematics and Mechanics(English Edition) 2014年第10期35卷 1249-1260页

作者： R.R.BHARGAVA K.JANGID Department of Mathematics Indian Institute of Technology Roorkee

In this paper, a mathematical strip-saturation model is proposed for a poled transversely isotropic piezoelectric plate weakened by two impermeable unequal-collinear hairline straight cracks. Remotely applied in-plane unidirectional electromechanical loads open the cracks in mode-I such that the saturation zone developed at the interior tips of cracks gets coalesced. The developed saturation zones are arrested by distributing over their rims in-plane normal cohesive electrical displacement. The problem is solved using the stroh formalism and the complex variable technique. The expressions are derived for the stress intensity factors （SIFs）, the lengths of the saturation zones developed, the crack opening displacement （COD）, and the energy release rate. An illustrative numerical case study is presented for the poled PZT-5H ceramic to investigate the effect of prescribed electromechanical loads on parameters affecting crack arrest. Also, the effect of different lengths of cracks on the SIFs and the local energy release rate （LERR） has been studied. The results obtained are graphically presented and analyzed.

关键词： crack opening displacement （COD） energy release rate piezoelectric ce-ramic stroh formalism saturation zone unequal-collinear crack

ANALYSIS OF DYNAMIC INSTABILITY OF INTERFACIAL SLIP WAVES BASED ON THE SURFACE IMPEDANCE TENSOR

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Applied Mathematics and Mechanics(English Edition) 2004年第9期25卷 1022-1030页

作者：李楠汪越胜于桂兰 Institute of Engineering Mechanics Beijing Jiaotong University Department of Civil Engineering Beijing Jiaotong University

A new method relying on the stroh formulism and the theory of the surface impedance tensor was developed to investigate the dynamic instability of interfacial slip waves.The concept of the surface impedance tensor was extended to the case where the wave speed is of a complex value,and the boundary conditions at the frictionally contacting interface were expressed by the surface impedance tensor.Then the boundary value problem was transformed to searching for zeroes of a complex polynomial in the unit circle.As an example,the steady frictional sliding of an elastic half-space in contact with a rigid flat surface was considered in details.A quartic complex characteristic equation was derived and its solution behavior in the unit circle was discussed.An explicit expression for the instability condition of the interfacial slip waves was presented.

关键词： frictional contact slip wave instability stroh formalism surface impedance tensor

Study on a straight dislocation in an icosahedral quasicrystal with piezoelectric effects

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Applied Mathematics and Mechanics(English Edition) 2018年第9期39卷 1259-1266页

作者： Lianhe LI Guanting LIU College of Mathematics Science Inner Mongolia Normal University Inner Mongolia Key Laboratory of Nanoscience and Nanotechnology Inner Mongolia University

An electro-elastic analysis is performed on an icosahedral quasicrystal with piezoelectric effects containing a straight dislocation. The closed-form expressions for the elastic and electric fields are obtained using the extended stroh formalism. The effects of piezoelectric constant on the phonon displacement, phason displacement, and electric potential are discussed in detail.

关键词： icosahedral quasicrystal piezoelectric effect stroh formalism dislocation

COUPLED FIELDS OF TWO-DIMENSIONAL ANISOTROPIC MAGNETO-ELECTRO-ELASTIC SOLIDS WITH AN ELLIPTICAL INCLUSION

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Applied Mathematics and Mechanics(English Edition) 2000年第10期21卷 1213-1220页

作者：姜稚清刘金喜 Department of Civil Engineering Shijiazhuang Railway Institute Shijiazhuang P R China

The two-dimensional elliptical inclusion problems in infinite anisotropic magnetoelectro-elastic solids are considered. Based on the extended stroh formalism, the technique of conformal mapping and the concept of perturbation, the magneta-electro-elastic fields in both the matrix: and the inclusion are obtained explicitly. The results are of very importance for studying the effective properties of piezoelectric-piezomagnetic composite materials.

关键词： magneto-electro-elastic solid stroh formalism coupled field inclusion