This paper investigates numerically and experimentally the influence of initial geometric imperfections on the critical loads of initially stretched thick hyperelastic cylindrical shells under increasing uniform internal pressure. Imperfections in shells can have a global or local character. First, two types of local imperfections are considered: (1) a local axially symmetric imperfection in the form of a ring and (2) a small rectangular imperfection. The influence of the imperfection thickness, position and size are analysed in detail. Results show that the critical load decreases as the imperfections increase in size or thickness and as they move from the boundaries to the centre of the shell. The influence of multiple local imperfections is also studied in the present paper. Finally, the influence of global imperfections is considered with the imperfections described as a variation of the shell curvature in the axial direction. The results show that thick hyperelastic shells may be sensitive to local and global imperfections. In all cases the experimental results are in good agreement with the numerical ones, corroborating the conclusions.
{"title":"Influence of initial geometric imperfections on the stability of thick cylindrical shells under internal pressure","authors":"S.R.X. Lopes, P. Gonçalves, D. Pamplona","doi":"10.1002/CNM.916","DOIUrl":"https://doi.org/10.1002/CNM.916","url":null,"abstract":"This paper investigates numerically and experimentally the influence of initial geometric imperfections on the critical loads of initially stretched thick hyperelastic cylindrical shells under increasing uniform internal pressure. Imperfections in shells can have a global or local character. First, two types of local imperfections are considered: (1) a local axially symmetric imperfection in the form of a ring and (2) a small rectangular imperfection. The influence of the imperfection thickness, position and size are analysed in detail. Results show that the critical load decreases as the imperfections increase in size or thickness and as they move from the boundaries to the centre of the shell. The influence of multiple local imperfections is also studied in the present paper. Finally, the influence of global imperfections is considered with the imperfections described as a variation of the shell curvature in the axial direction. The results show that thick hyperelastic shells may be sensitive to local and global imperfections. In all cases the experimental results are in good agreement with the numerical ones, corroborating the conclusions.","PeriodicalId":51245,"journal":{"name":"Communications in Numerical Methods in Engineering","volume":"23 1","pages":"577-597"},"PeriodicalIF":0.0,"publicationDate":"2006-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/CNM.916","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51600646","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}
J. Aquino, A. Francisco, F. Pereira, H. P. A. Souto, F. Furtado
We present a new numerical scheme for the approximation of solutions of transient water infiltration problems in heterogeneous soils. The two-phase (water and air) flow problem is governed by a pressure-velocity equation coupled to a saturation equation. The numerical scheme combines a non-oscillatory, second-order, conservative central finite differencing scheme for the saturation equation with mixed finite elements for the pressure-velocity equation. An operator splitting technique allows for the use of distinct time steps for the solution of the equations of the governing system. One and two-dimensional numerical experiments show that the proposed scheme is able to capture accurately and efficiently sharp fronts in two-phase water-air problem. The simulations were carried out taking into account the effects of gravity and capillary diffusion forces.
{"title":"Numerical simulation of transient water infiltration in heterogeneous soils combining central schemes and mixed finite elements","authors":"J. Aquino, A. Francisco, F. Pereira, H. P. A. Souto, F. Furtado","doi":"10.1002/CNM.905","DOIUrl":"https://doi.org/10.1002/CNM.905","url":null,"abstract":"We present a new numerical scheme for the approximation of solutions of transient water infiltration problems in heterogeneous soils. The two-phase (water and air) flow problem is governed by a pressure-velocity equation coupled to a saturation equation. The numerical scheme combines a non-oscillatory, second-order, conservative central finite differencing scheme for the saturation equation with mixed finite elements for the pressure-velocity equation. An operator splitting technique allows for the use of distinct time steps for the solution of the equations of the governing system. One and two-dimensional numerical experiments show that the proposed scheme is able to capture accurately and efficiently sharp fronts in two-phase water-air problem. The simulations were carried out taking into account the effects of gravity and capillary diffusion forces.","PeriodicalId":51245,"journal":{"name":"Communications in Numerical Methods in Engineering","volume":"23 1","pages":"491-505"},"PeriodicalIF":0.0,"publicationDate":"2006-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/CNM.905","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51600230","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}
Stable and accurate finite element methods are presented for Darcy flow in heterogeneous porous media with an interface of discontinuity of the hydraulic conductivity tensor, Accurate velocity fields are computed through global or local post-processing formulations that use previous approximations of the hydraulic potential. Stability is provided by combining Galerkin and least squares (GLS) residuals of the governing equations with an additional stabilization on the interface that incorporates the discontinuity on the tangential component of the velocity field in a strong sense. Numerical analysis is outlined and numerical results are presented to illustrate the good performance of the proposed methods, Convergence studies for a heterogeneous and anisotropic porous medium confirm the same rates of convergence predicted for homogeneous problem with smooth solutions, for both global and local post-processings.
{"title":"Stabilized velocity post‐processings for Darcy flow in heterogeneous porous media","authors":"M. R. Correa, A. Loula","doi":"10.1002/CNM.904","DOIUrl":"https://doi.org/10.1002/CNM.904","url":null,"abstract":"Stable and accurate finite element methods are presented for Darcy flow in heterogeneous porous media with an interface of discontinuity of the hydraulic conductivity tensor, Accurate velocity fields are computed through global or local post-processing formulations that use previous approximations of the hydraulic potential. Stability is provided by combining Galerkin and least squares (GLS) residuals of the governing equations with an additional stabilization on the interface that incorporates the discontinuity on the tangential component of the velocity field in a strong sense. Numerical analysis is outlined and numerical results are presented to illustrate the good performance of the proposed methods, Convergence studies for a heterogeneous and anisotropic porous medium confirm the same rates of convergence predicted for homogeneous problem with smooth solutions, for both global and local post-processings.","PeriodicalId":51245,"journal":{"name":"Communications in Numerical Methods in Engineering","volume":"23 1","pages":"461-489"},"PeriodicalIF":0.0,"publicationDate":"2006-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/CNM.904","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51600225","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}
The solution of the fully non-linear time-dependent two-dimensional shallow water equations is considered. Dispersive effects due to the Coriolis forces are taken into account. Such effects are of major importance in geophysical fluid dynamics applications. The recently proposed string gradient weighted moving finite element method is extended for this class of problems. This method simultaneously determines, at each time step, the solution of the governing partial differential equations and an optimal location of the finite element nodes. It has previously been applied to non-dispersive wave problems; here its performance under the demanding conditions of large Coriolis forces, inducing large mesh and field rotation, is studied. Optimal rates of convergence are obtained. Results for some example problems of water hump release are presented. Non-linear and linearized solutions are compared.
{"title":"Solution of non-linear dispersive wave problems using a moving finite element method","authors":"A. Wacher, D. Givoli","doi":"10.1002/CNM.897","DOIUrl":"https://doi.org/10.1002/CNM.897","url":null,"abstract":"The solution of the fully non-linear time-dependent two-dimensional shallow water equations is considered. Dispersive effects due to the Coriolis forces are taken into account. Such effects are of major importance in geophysical fluid dynamics applications. The recently proposed string gradient weighted moving finite element method is extended for this class of problems. This method simultaneously determines, at each time step, the solution of the governing partial differential equations and an optimal location of the finite element nodes. It has previously been applied to non-dispersive wave problems; here its performance under the demanding conditions of large Coriolis forces, inducing large mesh and field rotation, is studied. Optimal rates of convergence are obtained. Results for some example problems of water hump release are presented. Non-linear and linearized solutions are compared.","PeriodicalId":51245,"journal":{"name":"Communications in Numerical Methods in Engineering","volume":"23 1","pages":"253-262"},"PeriodicalIF":0.0,"publicationDate":"2006-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/CNM.897","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51600406","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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