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 equ...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.展开更多
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 conc...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.展开更多
A Zener-Stroh crack interacting with an edge dislocation is studied.The crack faces are assumed to be traction free.The applied 'generalized loading' for crack is the initial displacement jump and the interven...A Zener-Stroh crack interacting with an edge dislocation is studied.The crack faces are assumed to be traction free.The applied 'generalized loading' for crack is the initial displacement jump and the intervention of the edge dislocation.Through decomposing the problem into two subsimple problems,using the superposition principle,its solution is obtained.To demonstrate both the validity of the solution and its potential application,two simple examples related to the crack stress intensity factors are presented on the basis of the solution.The application of the solution to model crack initiations arising from dislocation-pileup is discussed.展开更多
With the assistance of Stroh formalism,the general solutions satisfying the basic laws of linear elastic theory are written in complex variable forms.To analyze the fracture behavior of two-dimensional decagonal piezo...With the assistance of Stroh formalism,the general solutions satisfying the basic laws of linear elastic theory are written in complex variable forms.To analyze the fracture behavior of two-dimensional decagonal piezoelectric quasicrystals,an elliptical hole model under different boundary conditions is established.The analytical expressions of generalized stress intensity factors(GSIFs)are obtained,respectively,for four general cases:a Griffith crack with generalized remote uniform loading,arbitrary loading on the crack surface,concentrated loading at any position of the crack surface,and multiple collinear periodic cracks under uniform loading at infinity.Numerical examples are given,and the effects of crack length,loading position,loading condition,and crack period on GSIFs are discussed.The derived analytical solutions of cracks play a significant role in understanding the phonon-phason and electromechanical coupled behavior in quasicrystals,and they also serve as criteria for fracture analysis.展开更多
This study aims to present exact multi-field coupling modeling and analysis of a simply-supported rectangular piezoelectric semiconductor(PSC)plate.Under the linear assumption of drift-diffusion current for a small el...This study aims to present exact multi-field coupling modeling and analysis of a simply-supported rectangular piezoelectric semiconductor(PSC)plate.Under the linear assumption of drift-diffusion current for a small electron concentration perturbation,the governing equations are solved by extending the classical Stroh formalism to involve all the physical fields of PSCs.The general solutions are obtained and then utilized to analyze three-dimensional(3D)problems of static deformation and free vibration of the PSC plate.To investigate the multi-physics interactions along the plate thickness,the distribution forms of electromechanical fields and electron concentration perturbation are given exactly,which are helpful for the development of the PSC plate theory.The differences between the PSC and purely piezoelectric as well as purely elastic counterparts are emphasized,in the context of evaluating the material performances with changing initial electron concentration.The results demonstrate that the PSC coupling exists only within a specific range of the initial electron concentration,where it exhibits a transition from the piezoelectric characteristics to the elastic ones.In addition,the dependence of coupling behaviors on the plate thickness is clarified.These results can not only be benchmarks in the development of PSC plate theories or other numerical methods,but also be guidance for the design of plate-based PSC devices.展开更多
The generalized two_dimensional problem of a dielectric rigid line inclusion, at the interface between two dissimilar piezoelectric media subjected to piecewise uniform loads at infinity, is studied by means of the St...The generalized two_dimensional problem of a dielectric rigid line inclusion, at the interface between two dissimilar piezoelectric media subjected to piecewise uniform loads at infinity, is studied by means of the Stroh theory. The problem was reduced to a Hilbert problem, and then closed_form expressions were obtained, respectively, for the complex potentials in piezoelectric media, the electric field inside the inclusion and the tip fields near the inclusion. It is shown that in the media, all field variables near the inclusion_tip show square root singularity and oscillatory singularity, the intensity of which is dependent on the material constants and the strains at infinity. In addition, it is found that the electric field inside the inclusion is singular and oscillatory too, when approaching the inclusion_tips from inside the inclusion.展开更多
基金Project supported by the National Natural Science Foundation of China (No.10102019).
文摘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.
文摘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.
基金supported by the National Basic Research Program of China(2007CB70770-5)Ph.D.Programs Foundation of Ministry of Education of Chinathe Fundamental Research Funds for the Central Universities
文摘A Zener-Stroh crack interacting with an edge dislocation is studied.The crack faces are assumed to be traction free.The applied 'generalized loading' for crack is the initial displacement jump and the intervention of the edge dislocation.Through decomposing the problem into two subsimple problems,using the superposition principle,its solution is obtained.To demonstrate both the validity of the solution and its potential application,two simple examples related to the crack stress intensity factors are presented on the basis of the solution.The application of the solution to model crack initiations arising from dislocation-pileup is discussed.
基金supported by the National Natural Science Foundation of China(Grant Nos.12272402,12102458,and 11972365)the China Agricultural University Education Foundation(No.1101-2412001).
文摘With the assistance of Stroh formalism,the general solutions satisfying the basic laws of linear elastic theory are written in complex variable forms.To analyze the fracture behavior of two-dimensional decagonal piezoelectric quasicrystals,an elliptical hole model under different boundary conditions is established.The analytical expressions of generalized stress intensity factors(GSIFs)are obtained,respectively,for four general cases:a Griffith crack with generalized remote uniform loading,arbitrary loading on the crack surface,concentrated loading at any position of the crack surface,and multiple collinear periodic cracks under uniform loading at infinity.Numerical examples are given,and the effects of crack length,loading position,loading condition,and crack period on GSIFs are discussed.The derived analytical solutions of cracks play a significant role in understanding the phonon-phason and electromechanical coupled behavior in quasicrystals,and they also serve as criteria for fracture analysis.
基金Project supported by the National Natural Science Foundation of China(Nos.U21A20430 and 12472155)the Science Research Project of Hebei Education Department of China(No.BJK2022055)+2 种基金the“333 Talents Project”of Hebei Province of China(No.C20231111)the Natural Science Foundation of Hebei Province of China(Nos.A2024210002 and A2023210064)the S&T Program of Hebei Province of China(No.225676162GH)。
文摘This study aims to present exact multi-field coupling modeling and analysis of a simply-supported rectangular piezoelectric semiconductor(PSC)plate.Under the linear assumption of drift-diffusion current for a small electron concentration perturbation,the governing equations are solved by extending the classical Stroh formalism to involve all the physical fields of PSCs.The general solutions are obtained and then utilized to analyze three-dimensional(3D)problems of static deformation and free vibration of the PSC plate.To investigate the multi-physics interactions along the plate thickness,the distribution forms of electromechanical fields and electron concentration perturbation are given exactly,which are helpful for the development of the PSC plate theory.The differences between the PSC and purely piezoelectric as well as purely elastic counterparts are emphasized,in the context of evaluating the material performances with changing initial electron concentration.The results demonstrate that the PSC coupling exists only within a specific range of the initial electron concentration,where it exhibits a transition from the piezoelectric characteristics to the elastic ones.In addition,the dependence of coupling behaviors on the plate thickness is clarified.These results can not only be benchmarks in the development of PSC plate theories or other numerical methods,but also be guidance for the design of plate-based PSC devices.
文摘The generalized two_dimensional problem of a dielectric rigid line inclusion, at the interface between two dissimilar piezoelectric media subjected to piecewise uniform loads at infinity, is studied by means of the Stroh theory. The problem was reduced to a Hilbert problem, and then closed_form expressions were obtained, respectively, for the complex potentials in piezoelectric media, the electric field inside the inclusion and the tip fields near the inclusion. It is shown that in the media, all field variables near the inclusion_tip show square root singularity and oscillatory singularity, the intensity of which is dependent on the material constants and the strains at infinity. In addition, it is found that the electric field inside the inclusion is singular and oscillatory too, when approaching the inclusion_tips from inside the inclusion.
