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
准晶因其性能良好而广泛应用于发动机等设备的表面涂层中。由于准晶材料非常脆,因而对准晶部件应力集中处的应力场分析已引起广泛关注。本文利用复边界元法研究八次对称二维准晶中的椭圆形刚性夹杂问题。首先,通过推广的Stroh公式推导...准晶因其性能良好而广泛应用于发动机等设备的表面涂层中。由于准晶材料非常脆,因而对准晶部件应力集中处的应力场分析已引起广泛关注。本文利用复边界元法研究八次对称二维准晶中的椭圆形刚性夹杂问题。首先,通过推广的Stroh公式推导出在集中点力作用下,含椭圆刚性夹杂八次对称二维准晶平面弹性问题的Green函数。其次,基于不计体力的平衡方程和椭圆形刚性夹杂问题所对应的边界条件,构建边界积分方程,最后,通过Guass数值积分公式离散该边界积分方程并求解,分别获得了声子场和相位子场的孔边应力值。数值实例讨论了椭圆形刚性夹杂所引起的孔边应力变化,与含孔洞问题相比,内部夹杂的存在使基体孔边应力集中处的应力值减弱。Quasicrystals are widely used in surface coatings for devices such as engines due to their excellent properties. Because quasicrystal materials are very brittle, the analysis of the stress field at stress concentration areas of quasicrystal components has attracted widespread attention. The plane elastic problem of octagonal symmetric two-dimensional quasicrystals containing an elliptical rigid inclusion is considered by using the complex boundary element method. First, Green’s functions are obtained utilizing the extended Stroh formalism under concentrated force. Second, based on the equilibrium equation satisfying body force free and the boundary conditions corresponding to the elliptical rigid inclusion problem, a boundary integral equation is constructed, which is discretized and solved using the Guass’s formula of numerical integration. The stresses of the phonon field and the phason field on the boundary of an elliptic hole are obtained. The effect of the elliptical rigid inclusion on the stress is also discussed by comparing with the problem of containing an elliptic hole, and the presence of the internal inclusion weakens the stress values at the stress concentration points.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.
文摘准晶因其性能良好而广泛应用于发动机等设备的表面涂层中。由于准晶材料非常脆,因而对准晶部件应力集中处的应力场分析已引起广泛关注。本文利用复边界元法研究八次对称二维准晶中的椭圆形刚性夹杂问题。首先,通过推广的Stroh公式推导出在集中点力作用下,含椭圆刚性夹杂八次对称二维准晶平面弹性问题的Green函数。其次,基于不计体力的平衡方程和椭圆形刚性夹杂问题所对应的边界条件,构建边界积分方程,最后,通过Guass数值积分公式离散该边界积分方程并求解,分别获得了声子场和相位子场的孔边应力值。数值实例讨论了椭圆形刚性夹杂所引起的孔边应力变化,与含孔洞问题相比,内部夹杂的存在使基体孔边应力集中处的应力值减弱。Quasicrystals are widely used in surface coatings for devices such as engines due to their excellent properties. Because quasicrystal materials are very brittle, the analysis of the stress field at stress concentration areas of quasicrystal components has attracted widespread attention. The plane elastic problem of octagonal symmetric two-dimensional quasicrystals containing an elliptical rigid inclusion is considered by using the complex boundary element method. First, Green’s functions are obtained utilizing the extended Stroh formalism under concentrated force. Second, based on the equilibrium equation satisfying body force free and the boundary conditions corresponding to the elliptical rigid inclusion problem, a boundary integral equation is constructed, which is discretized and solved using the Guass’s formula of numerical integration. The stresses of the phonon field and the phason field on the boundary of an elliptic hole are obtained. The effect of the elliptical rigid inclusion on the stress is also discussed by comparing with the problem of containing an elliptic hole, and the presence of the internal inclusion weakens the stress values at the stress concentration points.
