It is shown, using analytical methodologies, that the velocity field blow-up suffered by vertically ascending acoustic waves in an isothermal atmosphere can be eliminated via the introduction of fine particles. Assuming the inhomogeneous generalization of the particle-laden flow model known as the (linearized) Marble–Thompson model-1, it is established that bounded, exponentially decreasing, shock amplitudes can be obtained provided the mass fraction of particles exceeds a critical value, for which an exact expression is derived. Lastly, supporting numerical results are presented, special cases are discussed, and possible follow-on studies are noted.
{"title":"Acoustic propagation in inhomogeneous fluids: regularization via the introduction of fine particles","authors":"P. Jordan","doi":"10.24423/AOM.3370","DOIUrl":"https://doi.org/10.24423/AOM.3370","url":null,"abstract":"It is shown, using analytical methodologies, that the velocity field blow-up suffered by vertically ascending acoustic waves in an isothermal atmosphere can be eliminated via the introduction of fine particles. Assuming the inhomogeneous generalization of the particle-laden flow model known as the (linearized) Marble–Thompson model-1, it is established that bounded, exponentially decreasing, shock amplitudes can be obtained provided the mass fraction of particles exceeds a critical value, for which an exact expression is derived. Lastly, supporting numerical results are presented, special cases are discussed, and possible follow-on studies are noted.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42813605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The dynamics of elastic plane waveguides is studied on the basis of the extended formulation of the plate theory of N th order. The plate model is based on the Lagrangian formalism of analytical dynamics combined with the dimensional reduction approach and the biorthogonal expansion of the spatial distribution of the displacement. The boundary conditions shifted from the faces onto the base plane are interpreted as constraints for the variational formulation of two-dimensional plate models. The normal wave dispersion in plates is modelled, the convergence of the approximate solutions is studied using the known exact solution for a plane layer as a reference. The proposed plate theory is used to analyse the normal wave dispersion in power graded waveguides of both symmetric and asymmetric structures, the locking phase frequencies for various power indices are computed.
{"title":"Use of the higher-order plate theory of I. N. Vekua type in problems of dynamics of heterogeneous plane waveguides","authors":"O. Egorova, L. Rabinskiy, S. Zhavoronok","doi":"10.24423/AOM.3074","DOIUrl":"https://doi.org/10.24423/AOM.3074","url":null,"abstract":"The dynamics of elastic plane waveguides is studied on the basis of the extended formulation of the plate theory of N th order. The plate model is based on the Lagrangian formalism of analytical dynamics combined with the dimensional reduction approach and the biorthogonal expansion of the spatial distribution of the displacement. The boundary conditions shifted from the faces onto the base plane are interpreted as constraints for the variational formulation of two-dimensional plate models. The normal wave dispersion in plates is modelled, the convergence of the approximate solutions is studied using the known exact solution for a plane layer as a reference. The proposed plate theory is used to analyse the normal wave dispersion in power graded waveguides of both symmetric and asymmetric structures, the locking phase frequencies for various power indices are computed.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41695517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The combined stochastic-deterministic approach, which may be applied to the numerical analysis of a wide range of scalar elliptic problems of civil engineering, is presented in this paper. It is based on the well-known Monte Carlo concept with a random walk procedure, in which series of random paths are constructed. Additionally, it incorporates selected features of the meshless finite difference method, especially star selection criteria and a local weighted function approximation. The approach leads to the explicit stochastic formula relating one unknown function value with all a-priori known data parameters. Therefore, it allows for a fast and effective estimation of the solution value at the selected point(s), without the necessity of generation of large systems of equations, combining all unknown values. In such a manner, the proposed approach develops and extends the original standard Monte Carlo one toward analysis of boundary value problems with more complex shape geometry, natural boundary conditions, non-homogeneous right-hand sides as well as anisotropic and non-linear material models. The paper is illustrated with numerical results of selected elliptic problems, including a torsion problem of a prismatic bar, a stationary heat flow analysis with anisotropic and non-linear material functions, as well as an inverse heat problem. Moreover, the appropriate coupling with other deterministic methods (e.g., the finite element method) is considered.
{"title":"Application of the Monte Carlo method with meshless random walk procedure to selected scalar elliptic problems","authors":"S. Milewski","doi":"10.24423/AOM.3111","DOIUrl":"https://doi.org/10.24423/AOM.3111","url":null,"abstract":"The combined stochastic-deterministic approach, which may be applied to the numerical analysis of a wide range of scalar elliptic problems of civil engineering, is presented in this paper. It is based on the well-known Monte Carlo concept with a random walk procedure, in which series of random paths are constructed. Additionally, it incorporates selected features of the meshless finite difference method, especially star selection criteria and a local weighted function approximation. The approach leads to the explicit stochastic formula relating one unknown function value with all a-priori known data parameters. Therefore, it allows for a fast and effective estimation of the solution value at the selected point(s), without the necessity of generation of large systems of equations, combining all unknown values. In such a manner, the proposed approach develops and extends the original standard Monte Carlo one toward analysis of boundary value problems with more complex shape geometry, natural boundary conditions, non-homogeneous right-hand sides as well as anisotropic and non-linear material models. The paper is illustrated with numerical results of selected elliptic problems, including a torsion problem of a prismatic bar, a stationary heat flow analysis with anisotropic and non-linear material functions, as well as an inverse heat problem. Moreover, the appropriate coupling with other deterministic methods (e.g., the finite element method) is considered.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49165809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
R. Pacevič, R. Kačianauskas, A. Kačeniauskas, G. Kaklauskas, R. Barauskas
The paper presents the development of the GPU-based discrete element method (DEM) code for simulating damage and fracture of cohesive solids with application to reinforced concrete at the scale of reinforcement ribs. The solid volume of concrete and steel is modelled by bonded spherical particles. Very fine discretization, containing more than million particles, is applied to describe the 3D reinforcement bar geometry at the scale of ribs and to investigate cracking behaviour of concrete near the reinforcement bar. The numerical model is validated by using experimental results of the double pull-out test. Influence of the discretization scale to the numerical solution is evaluated by using the reinforcement strain profiles and the cracking patterns. The developed GPU-based DEM algorithm efficiently handles interaction of particles, does not require any atomic operation and allows performing fast damage and fracture simulations with large number of particles. The performance measured on GPU is compared with that attained on different CPUs for varying number of particles. The high value of the Cundall number (particle number multiplied by time steps computed per second) equal to 4.3E+07 is measured on NVIDIA® Tesla™ P100 GPU in the case of 1858560 particles.
{"title":"Fast GPU simulation of reinforced concrete at the scale of reinforcement ribs by the discrete element method","authors":"R. Pacevič, R. Kačianauskas, A. Kačeniauskas, G. Kaklauskas, R. Barauskas","doi":"10.24423/AOM.3148","DOIUrl":"https://doi.org/10.24423/AOM.3148","url":null,"abstract":"The paper presents the development of the GPU-based discrete element method (DEM) code for simulating damage and fracture of cohesive solids with application to reinforced concrete at the scale of reinforcement ribs. The solid volume of concrete and steel is modelled by bonded spherical particles. Very fine discretization, containing more than million particles, is applied to describe the 3D reinforcement bar geometry at the scale of ribs and to investigate cracking behaviour of concrete near the reinforcement bar. The numerical model is validated by using experimental results of the double pull-out test. Influence of the discretization scale to the numerical solution is evaluated by using the reinforcement strain profiles and the cracking patterns. The developed GPU-based DEM algorithm efficiently handles interaction of particles, does not require any atomic operation and allows performing fast damage and fracture simulations with large number of particles. The performance measured on GPU is compared with that attained on different CPUs for varying number of particles. The high value of the Cundall number (particle number multiplied by time steps computed per second) equal to 4.3E+07 is measured on NVIDIA® Tesla™ P100 GPU in the case of 1858560 particles.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43271696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
B. Berisha, S. Hirsiger, H. Hippke, P. Hora, A. Mariaux, David Leyvraz, C. Bezençon
Modeling of anisotropic behavior as well as hardening behavior based on micromechanical quantities in combination with a spectral solver is the focus of this study. A deep drawing steel as well as two different aluminum alloys are investigated. Prediction capabilities of the proposed modeling strategy are discussed and the benefits of the micromechanical model are highlighted. Further, a comparison of the crystal plasticity (CP) results with the well established macroscopic model YLD2000-2d underlines the importance of the CP as a complementary modeling technique to the macroscopic modeling. Both models – the microscopic as well as the macroscopic – are validated on experimental data mainly gained from uniaxial and biaxial tests. In the second part of this study, strong inhomogeneous microstructures are investigated from a modeling point of view. For this purpose, a Hall–Petch phenomenological model is implemented in the CP open-source code DAMASK to take the grain size effects into account. Appropriate combinations of the grain sizes in a bimodal microstructure are presented in order to increase the strength as well as ductility of a generic aluminium alloy. The proposed numerical strategy of coupling the CP and efficient FFT-based spectral solver supports the development of new materials in an optimal way.
{"title":"Modeling of anisotropic hardening and grain size effects based on advanced numerical methods and crystal plasticity","authors":"B. Berisha, S. Hirsiger, H. Hippke, P. Hora, A. Mariaux, David Leyvraz, C. Bezençon","doi":"10.24423/AOM.3150","DOIUrl":"https://doi.org/10.24423/AOM.3150","url":null,"abstract":"Modeling of anisotropic behavior as well as hardening behavior based on micromechanical quantities in combination with a spectral solver is the focus of this study. A deep drawing steel as well as two different aluminum alloys are investigated. Prediction capabilities of the proposed modeling strategy are discussed and the benefits of the micromechanical model are highlighted. Further, a comparison of the crystal plasticity (CP) results with the well established macroscopic model YLD2000-2d underlines the importance of the CP as a complementary modeling technique to the macroscopic modeling. Both models – the microscopic as well as the macroscopic – are validated on experimental data mainly gained from uniaxial and biaxial tests. In the second part of this study, strong inhomogeneous microstructures are investigated from a modeling point of view. For this purpose, a Hall–Petch phenomenological model is implemented in the CP open-source code DAMASK to take the grain size effects into account. Appropriate combinations of the grain sizes in a bimodal microstructure are presented in order to increase the strength as well as ductility of a generic aluminium alloy. The proposed numerical strategy of coupling the CP and efficient FFT-based spectral solver supports the development of new materials in an optimal way.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46904951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The probabilistic solutions of the elastic stretched beam are studied under the excitation of Kanai–Tajimi ground motion. Finite difference scheme is adopted to formulate the nonlinear multi-degree-of-freedom system about the random vibration of the beam. The state-space-split is employed to make the high-dimensional Fokker–Planck–Kolmogorov equation reduced to 4-dimensional Fokker–Planck–Kolmogorov equations which are solved by the exponential polynomial closure method for the probabilistic solutions of the system responses. The rules for selecting the state variables are proposed in order to reduce the dimensionality of Fokker–Planck–Kolmogorov equation by the state-space-split method. The numerical results obtained by the state-space-split and exponential polynomial closure method, Monte Carlo simulation method, and equivalent linearization method are presented and compared to show the computational efficiency and numerical accuracy of the state-space-split and exponential polynomial closure method in analyzing the probabilistic solutions of the strongly nonlinear stretched beam systems formulated by a finite difference scheme and excited by the Kanai–Tajimi ground motion.
{"title":"Probabilistic solutions of a stretched beam discretized with finite difference scheme and excited by Kanai-Tajimi ground motion","authors":"G. Er, V. Iu, Hai-En Du","doi":"10.24423/AOM.3145","DOIUrl":"https://doi.org/10.24423/AOM.3145","url":null,"abstract":"The probabilistic solutions of the elastic stretched beam are studied under the excitation of Kanai–Tajimi ground motion. Finite difference scheme is adopted to formulate the nonlinear multi-degree-of-freedom system about the random vibration of the beam. The state-space-split is employed to make the high-dimensional Fokker–Planck–Kolmogorov equation reduced to 4-dimensional Fokker–Planck–Kolmogorov equations which are solved by the exponential polynomial closure method for the probabilistic solutions of the system responses. The rules for selecting the state variables are proposed in order to reduce the dimensionality of Fokker–Planck–Kolmogorov equation by the state-space-split method. The numerical results obtained by the state-space-split and exponential polynomial closure method, Monte Carlo simulation method, and equivalent linearization method are presented and compared to show the computational efficiency and numerical accuracy of the state-space-split and exponential polynomial closure method in analyzing the probabilistic solutions of the strongly nonlinear stretched beam systems formulated by a finite difference scheme and excited by the Kanai–Tajimi ground motion.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45584759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A mixed finite element formulation is developed for the general 2D plane strain, linear isotropic gradient elasticity problem. Form II of the dipolar strain gradient theory for micro-structured solids is considered. The main variables are the double stress tensor μ and the displacement field vector u . Standard C 0 −continuous, high polynomial order hierarchical basis functions are employed for the finite element solution spaces (p-extension). The formulation is numerically validated against the standard axial tension patch test and the Mode I crack problem. The theoretical convergence rates of the uniform h - and p -extensions are confirmed using a benchmark problem where only double stresses appear. Results for the crack problem demonstrate that proper mesh refinement at areas of steep gradients ensures reproduction of the exact solution behaviour at different length scales. More specifically, the asymptotic exponents of the crack face opening displacement and the crack head true stress solutions of the Mode I crack problem are recovered. Finally, the upper bound of the true tensile normal stress near the crack tip is estimated. This upper bound is of major importance since the nature of the exact solution may change radically as we proceed from the macro- to micro-scale.
{"title":"p-Extension of C0 continuous mixed finite elements for plane strain gradient elasticity","authors":"S. Markolefas, T. Papathanasiou, S. Georgantzinos","doi":"10.24423/AOM.3219","DOIUrl":"https://doi.org/10.24423/AOM.3219","url":null,"abstract":"A mixed finite element formulation is developed for the general 2D plane strain, linear isotropic gradient elasticity problem. Form II of the dipolar strain gradient theory for micro-structured solids is considered. The main variables are the double stress tensor μ and the displacement field vector u . Standard C 0 −continuous, high polynomial order hierarchical basis functions are employed for the finite element solution spaces (p-extension). The formulation is numerically validated against the standard axial tension patch test and the Mode I crack problem. The theoretical convergence rates of the uniform h - and p -extensions are confirmed using a benchmark problem where only double stresses appear. Results for the crack problem demonstrate that proper mesh refinement at areas of steep gradients ensures reproduction of the exact solution behaviour at different length scales. More specifically, the asymptotic exponents of the crack face opening displacement and the crack head true stress solutions of the Mode I crack problem are recovered. Finally, the upper bound of the true tensile normal stress near the crack tip is estimated. This upper bound is of major importance since the nature of the exact solution may change radically as we proceed from the macro- to micro-scale.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43105045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A single layer shear deformation plate theory with superposed shape functions for laminated composite plates has been proposed. Some of the previously developed, five degrees of freedom shear deformation theories, including parabolic [1], hyperbolic [2], exponential [3] and trigonometric [4] plate theories have been superposed by applying different theories in the different in- plane directions of the composite plate. Statics and dynamics of composite plate problems have been investigated. It was obtained that using different shape functions in the different in-plane directions may decrease the percentage error of stress and deflection. Present hyperbolic-exponential and parabolic-exponential theories predict stiffer properties (give lower bending and stress values, and higher frequency, and buckling loads when compared to the 3-D elasticity). Some improvements were determined for y-z component of the transverse shear stress using hyperbolic-exponential and parabolic-exponential theories for symmetric cross-ply composite plates when compared to available single shape function plate models. Global behaviours (vibration frequency and critical buckling loads) are predicted within %5 accuracy similar to plate theories with single shape functions.
{"title":"An equivalent single layer shear deformation plate theory with superposed shape functions for laminated composite plates","authors":"M. Aydogdu","doi":"10.24423/AOM.3170","DOIUrl":"https://doi.org/10.24423/AOM.3170","url":null,"abstract":"A single layer shear deformation plate theory with superposed shape functions for laminated composite plates has been proposed. Some of the previously developed, five degrees of freedom shear deformation theories, including parabolic [1], hyperbolic [2], exponential [3] and trigonometric [4] plate theories have been superposed by applying different theories in the different in- plane directions of the composite plate. Statics and dynamics of composite plate problems have been investigated. It was obtained that using different shape functions in the different in-plane directions may decrease the percentage error of stress and deflection. Present hyperbolic-exponential and parabolic-exponential theories predict stiffer properties (give lower bending and stress values, and higher frequency, and buckling loads when compared to the 3-D elasticity). Some improvements were determined for y-z component of the transverse shear stress using hyperbolic-exponential and parabolic-exponential theories for symmetric cross-ply composite plates when compared to available single shape function plate models. Global behaviours (vibration frequency and critical buckling loads) are predicted within %5 accuracy similar to plate theories with single shape functions.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44744783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A size-dependent model for cross-ply composite laminated plate bonded with PZT actuators is developed by using re-modified couple stress theory (RMCST), which only uses two material length scale parameters to describe the size-dependent effect. An equivalent bending moment model and a refined model are developed by using two different ways. The analytical solution of equivalent bending moment model for simply supported composite laminated plate is obtained. The equilibrium equation of motion and corresponding boundary constraints of the refined model are established from the potential energy principle. The Ritz approximate solution of transverse deflection of the refined model indicates that the size-effect cannot be ignored in micro-scale. Numerical examples are given to account for the effect of material length scale parameters and dimensions of piezoelectric actuators on the defection of composite laminated plate.
{"title":"Size-dependent deflection of cross-ply composite laminated plate induced by piezoelectric actuators based on a re-modified couple stress theory","authors":"Hongtao Wang, Z. Li, S. Zheng","doi":"10.24423/AOM.3047","DOIUrl":"https://doi.org/10.24423/AOM.3047","url":null,"abstract":"A size-dependent model for cross-ply composite laminated plate bonded with PZT actuators is developed by using re-modified couple stress theory (RMCST), which only uses two material length scale parameters to describe the size-dependent effect. An equivalent bending moment model and a refined model are developed by using two different ways. The analytical solution of equivalent bending moment model for simply supported composite laminated plate is obtained. The equilibrium equation of motion and corresponding boundary constraints of the refined model are established from the potential energy principle. The Ritz approximate solution of transverse deflection of the refined model indicates that the size-effect cannot be ignored in micro-scale. Numerical examples are given to account for the effect of material length scale parameters and dimensions of piezoelectric actuators on the defection of composite laminated plate.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48918079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present an analytical solution to the problem of a screw dislocation in a four-phase piezoelectric laminate composed of two piezoelectric layers of equal thickness sandwiched between two semi-infinite piezoelectric media. A new version of the complex variable formulation is proposed such that the 2 × 2 real symmetric matrix appearing in the formulation becomes dimensionless. Using analytic continuation, the original boundary value problem is reduced to the identification of a single 2D analytic vector function which is completely determined following rigorous solution of the resulting linear recurrence relations in matrix form. An explicit expression for the image force acting on the piezoelectric screw dislocation is obtained once the single 2 × 2 real matrix function is identified. We also discuss the solution for a screw dislocation in an N -phase piezoelectric laminate composed of N − 2 piezoelectric layers of equal thickness sandwiched between two semi-infinite piezoelectric media.
{"title":"Screw dislocations in piezoelectric laminates with four or more phases","authors":"X. Wang, L. Chen, P. Schiavone","doi":"10.24423/AOM.3218","DOIUrl":"https://doi.org/10.24423/AOM.3218","url":null,"abstract":"We present an analytical solution to the problem of a screw dislocation in a four-phase piezoelectric laminate composed of two piezoelectric layers of equal thickness sandwiched between two semi-infinite piezoelectric media. A new version of the complex variable formulation is proposed such that the 2 × 2 real symmetric matrix appearing in the formulation becomes dimensionless. Using analytic continuation, the original boundary value problem is reduced to the identification of a single 2D analytic vector function which is completely determined following rigorous solution of the resulting linear recurrence relations in matrix form. An explicit expression for the image force acting on the piezoelectric screw dislocation is obtained once the single 2 × 2 real matrix function is identified. We also discuss the solution for a screw dislocation in an N -phase piezoelectric laminate composed of N − 2 piezoelectric layers of equal thickness sandwiched between two semi-infinite piezoelectric media.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44451893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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