Pub Date : 2004-12-01DOI: 10.1142/S1465876304002678
M. Rashid, V. Tvergaard
A model problem is considered in which a crack propagates under ductile conditions through an edge-notched plane-strain tension strip. The strip consists of two monolithic material regions joined transversely by a thin graded layer. The material regions are elastically identical but dissimilar in their plastic and fracture-toughness properties. A range of initial crack configurations is studied, including cracks at various angles to the graded layer and with various initial positions in relation to it. A finite-element-based computational procedure containing a number of novel features is used to study the curvilinear crack growth that occurs in this problem. For the problem parameters under consideration, net-section yielding is induced in the more ductile of the two materials, even when the crack trajectory lies well inside the more brittle material. In general, it is found that the brittle material strongly attracts the crack trajectory, and that the presence of the lower-flow-stress material in conjun...
{"title":"Effect of a Graded Interface on a Crack Approaching at an Oblique Angle","authors":"M. Rashid, V. Tvergaard","doi":"10.1142/S1465876304002678","DOIUrl":"https://doi.org/10.1142/S1465876304002678","url":null,"abstract":"A model problem is considered in which a crack propagates under ductile conditions through an edge-notched plane-strain tension strip. The strip consists of two monolithic material regions joined transversely by a thin graded layer. The material regions are elastically identical but dissimilar in their plastic and fracture-toughness properties. A range of initial crack configurations is studied, including cracks at various angles to the graded layer and with various initial positions in relation to it. A finite-element-based computational procedure containing a number of novel features is used to study the curvilinear crack growth that occurs in this problem. For the problem parameters under consideration, net-section yielding is induced in the more ductile of the two materials, even when the crack trajectory lies well inside the more brittle material. In general, it is found that the brittle material strongly attracts the crack trajectory, and that the presence of the lower-flow-stress material in conjun...","PeriodicalId":331001,"journal":{"name":"Int. J. Comput. Eng. Sci.","volume":"111 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132563128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2004-12-01DOI: 10.1142/S146587630400268X
Yi Zhong, Y. Bansal, M. Pindera
Functionally graded materials are characterized by spatially variable microstructures introduced to satisfy given performance requirements. The graded microstructure gives rise to continuously or discretely changing properties, complicating the analysis of these materials. The majority of the computational techniques use the so-called uncoupled approach which ignores the effect of microstructural gradation by employing specific spatial material property variations that are either assumed or obtained by local homogenization. In contrast, the higher-order theory for functionally graded materials is a coupled approach which takes the effect of microstructural gradation into consideration and does not ignore the local-global interaction of the spatially variable inclusion phase(s). Despite its demonstrated utility, however, the original formulation of the higher-order theory is computationally intensive. Herein, an efficient reformulation of the higher-order theory for thermal problems, based on the local/glo...
{"title":"Efficient Reformulation of the Thermal Higher-order Theory for Fgms with Locally Variable Conductivity","authors":"Yi Zhong, Y. Bansal, M. Pindera","doi":"10.1142/S146587630400268X","DOIUrl":"https://doi.org/10.1142/S146587630400268X","url":null,"abstract":"Functionally graded materials are characterized by spatially variable microstructures introduced to satisfy given performance requirements. The graded microstructure gives rise to continuously or discretely changing properties, complicating the analysis of these materials. The majority of the computational techniques use the so-called uncoupled approach which ignores the effect of microstructural gradation by employing specific spatial material property variations that are either assumed or obtained by local homogenization. In contrast, the higher-order theory for functionally graded materials is a coupled approach which takes the effect of microstructural gradation into consideration and does not ignore the local-global interaction of the spatially variable inclusion phase(s). Despite its demonstrated utility, however, the original formulation of the higher-order theory is computationally intensive. Herein, an efficient reformulation of the higher-order theory for thermal problems, based on the local/glo...","PeriodicalId":331001,"journal":{"name":"Int. J. Comput. Eng. Sci.","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133641213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2004-12-01DOI: 10.1142/S1465876304002666
J. Aliaga, J. Reddy
Linear and nonlinear thermomechanical response of the functionally graded (metal-ceramic) plates subjected to static and dynamic loads is studied. The third-order plate theory of Reddy with the von Karman geometric nonlinearity is used for the kinematic and kinetic descriptions, and two constitutent power-law distribution through the plate thickness is employed. A displacement finite element model is developed with the Newmark time integration scheme, and the Newton-Raphson iterative procedure is used for the solution of nonlinear algebraic equations. While the model is general enough to be used for any boundary conditions, the simply supported and clamped boundary conditions are used to study the parametric effect of the power-law index and surface temperatures and mechanical loads on the thermomechanical response. The most significant finding of this study is that the deflection response does not fall intermediate to those of the metal or ceramic plates. This is due to the nonlinear coupling of mechanical and thermal contributions.
{"title":"Nonlinear Thermoelastic Analysis of Functionally Graded Plates Using the Third-order Shear Deformation Theory","authors":"J. Aliaga, J. Reddy","doi":"10.1142/S1465876304002666","DOIUrl":"https://doi.org/10.1142/S1465876304002666","url":null,"abstract":"Linear and nonlinear thermomechanical response of the functionally graded (metal-ceramic) plates subjected to static and dynamic loads is studied. The third-order plate theory of Reddy with the von Karman geometric nonlinearity is used for the kinematic and kinetic descriptions, and two constitutent power-law distribution through the plate thickness is employed. A displacement finite element model is developed with the Newmark time integration scheme, and the Newton-Raphson iterative procedure is used for the solution of nonlinear algebraic equations. While the model is general enough to be used for any boundary conditions, the simply supported and clamped boundary conditions are used to study the parametric effect of the power-law index and surface temperatures and mechanical loads on the thermomechanical response. The most significant finding of this study is that the deflection response does not fall intermediate to those of the metal or ceramic plates. This is due to the nonlinear coupling of mechanical and thermal contributions.","PeriodicalId":331001,"journal":{"name":"Int. J. Comput. Eng. Sci.","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134646602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2004-12-01DOI: 10.1142/S146587630400271X
Y. Shabana, N. Noda
By utilizing the finite element method, the macroscopic as well as the microscopic thermal stress behaviors of a functionally graded material rectangular plate (FGP) subjected to partial heating conditions in a transient state are presented. The FGP has non-homogeneous thermal and mechanical material properties in the thickness direction, and consists of the particle-reinforced composite in the regions near both surfaces and a composite mixture in the intermediate region. A microscopic constitutive equation and the macroscopic analysis are used to treat the particle-reinforced regions and the intermediate region, respectively. Therefore, the FGP is analyzed by a combination of the macroscopic and the microscopic analyses. The elasto-plasticity and the temperature-dependent properties of the constituent materials as well as the residual stresses arising from the fabrication process are taken into account. The effects of the heating length of the partial heating conditions and the non-homogeneity function of the constituents are discussed in order to find out the optimum form of the gradation function for the FGM subjected to partial heating conditions in transient state. The two-dimensional transient temperature and two-dimensional transient thermal stresses, which include the macroscopic and microscopic components, for the FGP are analyzed and shown in figures. The character (tension or compression) of the macroscopic stresses is dependent on the functional form of gradation.
{"title":"Thermo-elasto-plastic Stresses in Functionally Graded Ceramic/metal Composites with Two-dimensional Temperature Gradient","authors":"Y. Shabana, N. Noda","doi":"10.1142/S146587630400271X","DOIUrl":"https://doi.org/10.1142/S146587630400271X","url":null,"abstract":"By utilizing the finite element method, the macroscopic as well as the microscopic thermal stress behaviors of a functionally graded material rectangular plate (FGP) subjected to partial heating conditions in a transient state are presented. The FGP has non-homogeneous thermal and mechanical material properties in the thickness direction, and consists of the particle-reinforced composite in the regions near both surfaces and a composite mixture in the intermediate region. A microscopic constitutive equation and the macroscopic analysis are used to treat the particle-reinforced regions and the intermediate region, respectively. Therefore, the FGP is analyzed by a combination of the macroscopic and the microscopic analyses. The elasto-plasticity and the temperature-dependent properties of the constituent materials as well as the residual stresses arising from the fabrication process are taken into account. The effects of the heating length of the partial heating conditions and the non-homogeneity function of the constituents are discussed in order to find out the optimum form of the gradation function for the FGM subjected to partial heating conditions in transient state. The two-dimensional transient temperature and two-dimensional transient thermal stresses, which include the macroscopic and microscopic components, for the FGP are analyzed and shown in figures. The character (tension or compression) of the macroscopic stresses is dependent on the functional form of gradation.","PeriodicalId":331001,"journal":{"name":"Int. J. Comput. Eng. Sci.","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134094929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2004-12-01DOI: 10.1142/S1465876304002708
N. Dumont, R. Chaves, G. Paulino
Since the introduction of the hybrid boundary element method in 1987, it has been applied to various problems of elasticity and potential theory, including time-dependent problems. This paper focuses on establishing the conceptual framework for applying both the variational formulation and a simplified version of the hybrid boundary element method to nonhomogeneous materials. Several classes of fundamental solutions for problems of potential are derived. Thus, the boundary-only feature of the method is preserved even with a spatially varying material property. Several numerical examples are given in terms of an efficient patch test including irregularly bounded, unbounded, and multiply connected regions submitted to high gradients.
{"title":"The Hybrid Boundary Element Method Applied to Problems of Potential Theory in Nonhomogeneous Materials","authors":"N. Dumont, R. Chaves, G. Paulino","doi":"10.1142/S1465876304002708","DOIUrl":"https://doi.org/10.1142/S1465876304002708","url":null,"abstract":"Since the introduction of the hybrid boundary element method in 1987, it has been applied to various problems of elasticity and potential theory, including time-dependent problems. This paper focuses on establishing the conceptual framework for applying both the variational formulation and a simplified version of the hybrid boundary element method to nonhomogeneous materials. Several classes of fundamental solutions for problems of potential are derived. Thus, the boundary-only feature of the method is preserved even with a spatially varying material property. Several numerical examples are given in terms of an efficient patch test including irregularly bounded, unbounded, and multiply connected regions submitted to high gradients.","PeriodicalId":331001,"journal":{"name":"Int. J. Comput. Eng. Sci.","volume":"210 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114222015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2004-12-01DOI: 10.1142/S1465876304002691
G. Paulino, Jeong-Ho Kim
Poisson's ratio is an important factor for fracture of functionally graded materials (FGMs). It may have significant influence on fracture parameters (e.g. stress intensity factors and T-stress) for a crack in FGMs under mixed-mode loading conditions, while its effect on such parameters is negligible in homogeneous materials. For instance, when tension load is applied in the direction parallel to material gradation, the fracture parameters may show significant influence on the Poisson's ratio. This paper uses a new formulation, so-called non-equilibrium formulation, of the interaction integral method. It also presents a few numerical examples where Poisson's ratio is assumed either constant or linearly varying function, and Young's modulus is assumed to be exponential or hyperbolic-tangent function.
{"title":"On the Poisson's Ratio Effect on Mixed-mode Stress Intensity Factors and T-stress in Functionally Graded Materials","authors":"G. Paulino, Jeong-Ho Kim","doi":"10.1142/S1465876304002691","DOIUrl":"https://doi.org/10.1142/S1465876304002691","url":null,"abstract":"Poisson's ratio is an important factor for fracture of functionally graded materials (FGMs). It may have significant influence on fracture parameters (e.g. stress intensity factors and T-stress) for a crack in FGMs under mixed-mode loading conditions, while its effect on such parameters is negligible in homogeneous materials. For instance, when tension load is applied in the direction parallel to material gradation, the fracture parameters may show significant influence on the Poisson's ratio. This paper uses a new formulation, so-called non-equilibrium formulation, of the interaction integral method. It also presents a few numerical examples where Poisson's ratio is assumed either constant or linearly varying function, and Young's modulus is assumed to be exponential or hyperbolic-tangent function.","PeriodicalId":331001,"journal":{"name":"Int. J. Comput. Eng. Sci.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122520949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2004-09-01DOI: 10.1142/S1465876304002587
E. Garusi, A. Tralli, A. Cazzani
In the present paper a simple mixed-hybrid element for the linear analysis of Reissner-Mindlin plates is discussed. The element is derived from a modified Reissner functional and standard bilinear (isoparametric) interpolation for displacement and rotations is assumed whereas local stresses (rather than stress resultants and moments) are explicitly modelled. It is assumed that in plane shear stresses are not a priori symmetric. This choice allows to decouple the equilibrium equations, and involves introducing an in-plane infinitesimal rotation field, corresponding to drilling degrees of freedom. Out-of-plane shear stresses are then obtained such that equilibrium equations are exactly satisfied. The proposed element does not exhibit locking effects at all: i.e. the shear deformation energy is zero in the thin plate limit. Details of the formulation are provided, and the performances of the element are assessed with reference to well-established benchmark problems.
{"title":"An unsymmetric stress formulation for reissner-mindlin plates: a simple and locking-free rectangular element","authors":"E. Garusi, A. Tralli, A. Cazzani","doi":"10.1142/S1465876304002587","DOIUrl":"https://doi.org/10.1142/S1465876304002587","url":null,"abstract":"In the present paper a simple mixed-hybrid element for the linear analysis of Reissner-Mindlin plates is discussed. The element is derived from a modified Reissner functional and standard bilinear (isoparametric) interpolation for displacement and rotations is assumed whereas local stresses (rather than stress resultants and moments) are explicitly modelled. It is assumed that in plane shear stresses are not a priori symmetric. This choice allows to decouple the equilibrium equations, and involves introducing an in-plane infinitesimal rotation field, corresponding to drilling degrees of freedom. Out-of-plane shear stresses are then obtained such that equilibrium equations are exactly satisfied. The proposed element does not exhibit locking effects at all: i.e. the shear deformation energy is zero in the thin plate limit. Details of the formulation are provided, and the performances of the element are assessed with reference to well-established benchmark problems.","PeriodicalId":331001,"journal":{"name":"Int. J. Comput. Eng. Sci.","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115144528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2004-09-01DOI: 10.1142/S1465876304002630
J. Ramos
The propagation of fronts in two–dimensional, anisotropic, nonlinear reactive–diffusive media with cross–diffusion is analyzed by means of implicit time–linearized factorization techniques. Four factorization methods are considered; the first one disregards the approximate factorization errors and treats the mixed second–order derivatives explicitly, whereas the other three account for either the approximate factorization errors or the mixed second–order derivative terms in an iterative manner. The four techniques involve the solution of one–dimensional operators and require the solution of linear algebraic systems with block–tridiagonal matrices. It is shown that anisotropy and cross–diffusion deform the reaction front and affect the front velocity. It is also shown that the approximate factorization method that treats the mixed second–order derivative terms iteratively provide much more accurate transient results than techniques that account for the approximate factorization errors and treat the mixed s...
{"title":"Implicit factorization techniques for two-dimensional, anisotropic, reactive-diffusive media with cross-diffusion effects","authors":"J. Ramos","doi":"10.1142/S1465876304002630","DOIUrl":"https://doi.org/10.1142/S1465876304002630","url":null,"abstract":"The propagation of fronts in two–dimensional, anisotropic, nonlinear reactive–diffusive media with cross–diffusion is analyzed by means of implicit time–linearized factorization techniques. Four factorization methods are considered; the first one disregards the approximate factorization errors and treats the mixed second–order derivatives explicitly, whereas the other three account for either the approximate factorization errors or the mixed second–order derivative terms in an iterative manner. The four techniques involve the solution of one–dimensional operators and require the solution of linear algebraic systems with block–tridiagonal matrices. It is shown that anisotropy and cross–diffusion deform the reaction front and affect the front velocity. It is also shown that the approximate factorization method that treats the mixed second–order derivative terms iteratively provide much more accurate transient results than techniques that account for the approximate factorization errors and treat the mixed s...","PeriodicalId":331001,"journal":{"name":"Int. J. Comput. Eng. Sci.","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117308918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2004-09-01DOI: 10.1142/S1465876304002617
W. Li, Shuhong Xu, Ong Eng Teo, Gang Zhao
This paper presents two robust algorithms for calculating the orientation and inclusion of simple polygons, respectively. By finding a maximum vertex of a simple polygon, a very fast convex vertex searching method is proposed and the orientation of the polygon can be uniquely determined. To decide the relationship between a point and a simple polygon, the concept of visible edge is put forward and an efficient visible edge searching algorithm is presented.
{"title":"Orientation and point inclusion tests for simple polygons","authors":"W. Li, Shuhong Xu, Ong Eng Teo, Gang Zhao","doi":"10.1142/S1465876304002617","DOIUrl":"https://doi.org/10.1142/S1465876304002617","url":null,"abstract":"This paper presents two robust algorithms for calculating the orientation and inclusion of simple polygons, respectively. By finding a maximum vertex of a simple polygon, a very fast convex vertex searching method is proposed and the orientation of the polygon can be uniquely determined. To decide the relationship between a point and a simple polygon, the concept of visible edge is put forward and an efficient visible edge searching algorithm is presented.","PeriodicalId":331001,"journal":{"name":"Int. J. Comput. Eng. Sci.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126838335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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