Hybridized dual-mixed hp-finite element model for shells of revolution

[1]  P. M. Naghdi,et al.  FOUNDATIONS OF ELASTIC SHELL THEORY , 1962 .

[2]  I. Babuska,et al.  Mixed-hybrid finite element approximations of second-order elliptic boundary-value problems. Interim report , 1975 .

[3]  B. D. Veubeke.  Stress function approach , 1975 .

[4]  L. D. Marini,et al.  Two families of mixed finite elements for second order elliptic problems , 1985 .

[5]  Eduardo N. Dvorkin,et al.  A formulation of general shell elements—the use of mixed interpolation of tensorial components† , 1986 .

[6]  R. Stenberg.  A family of mixed finite elements for the elasticity problem , 1988 .

[7]  T. Hughes,et al.  On mixed finite element methods for axisymmetric shell analysis , 1989 .

[8]  E. Stein,et al.  Mechanical conditions for stability and optimal convergence of mixed finite elements for linear plane elasticity , 1990 .

[9]  Michel Fortin,et al.  Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

[10]  D. Braess,et al.  Error indicators for mixed finite elements in 2-dimensional linear elasticity , 1995 .

[11]  K. Bathe.  Finite Element Procedures , 1995 .

[12]  E. Stein,et al.  A regularized dual mixed element for plane elasticity implementation and performance of the BDM element , 1995 .

[13]  M. Fortin,et al.  Dual hybrid methods for the elasticity and the Stokes problems: a unified approach , 1997 .

[14]  C. Schwab.  P- and hp- finite element methods : theory and applications in solid and fluid mechanics , 1998 .

[15]  Alexander G Iosilevich,et al.  An evaluation of the MITC shell elements , 2000 .

[16]  C. Schwab,et al.  Fourier mode analysis of layers in shallow shell deformations , 2001 .

[17]  C. Bottasso,et al.  The discontinuous Petrov–Galerkin method for elliptic problems , 2002 .

[18]  Juhani Pitkäranta.  Mathematical and historical reflections on the lowest-order finite element models for thin structures , 2003 .

[19]  F. Gruttmann,et al.  A linear quadrilateral shell element with fast stiffness computation , 2005 .

[20]  D. Arnold,et al.  RECTANGULAR MIXED FINITE ELEMENTS FOR ELASTICITY , 2005 .

[21]  M. Suri.  Stable hp mixed finite elements based on the Hellinger-Reissner principle , 2005 .

[22]  E. Rank,et al.  High order finite elements for shells , 2005 .

[23]  P. G. Ciarlet,et al.  An Introduction to Differential Geometry with Applications to Elasticity , 2006 .

[24]  L. Demkowicz.  One and two dimensional elliptic and Maxwell problems , 2006 .

[25]  Ernst Rank,et al.  Finite cell method , 2007 .

[26]  Douglas N. Arnold,et al.  Mixed finite element methods for linear elasticity with weakly imposed symmetry , 2007, Math. Comput..

[27]  S. Nicaise,et al.  Dual mixed finite element methods for the elasticity problem with Lagrange multipliers , 2008 .

[28]  Antti H. Niemi,et al.  Approximation of shell layers using bilinear elements on anisotropically refined rectangular meshes , 2008 .

[29]  L. Demkowicz,et al.  Mixed hp-Finite Element Method for Linear Elasticity with Weakly Imposed Symmetry: Stability Analysis , 2009, SIAM J. Numer. Anal..

[30]  Bernardo Cockburn,et al.  A new elasticity element made for enforcing weak stress symmetry , 2010, Math. Comput..

[31]  O. Millet,et al.  Singularities in shell theory: Anisotropic error estimates and numerical simulations , 2010 .

[32]  K. Wiśniewski.  Finite Rotation Shells: Basic Equations and Finite Elements for Reissner Kinematics , 2010 .

[33]  Jamie A. Bramwell,et al.  Discontinuous Petrov–Galerkin method with optimal test functions for thin-body problems in solid mechanics , 2011 .

[34]  Phill-Seung Lee,et al.  Measuring the convergence behavior of shell analysis schemes , 2011 .

[35]  Bernardo Cockburn,et al.  High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics , 2011, J. Comput. Phys..

[36]  I. Babuska,et al.  Introduction to Finite Element Analysis: Formulation, Verification and Validation , 2011 .

[37]  J. Schöberl,et al.  TANGENTIAL-DISPLACEMENT AND NORMAL–NORMAL-STRESS CONTINUOUS MIXED FINITE ELEMENTS FOR ELASTICITY , 2011 .

[38]  Ngoc Cuong Nguyen,et al.  Hybridizable discontinuous Galerkin methods for partial differential equations in continuum mechanics , 2012, J. Comput. Phys..

[39]  B. Tóth,et al.  Dual‐mixed hp finite element model for elastic cylindrical shells , 2012 .

[40]  K. Wisniewski,et al.  Two improvements in formulation of nine‐node element MITC9 , 2013 .

[41]  B. Tóth,et al.  Comparison of dual-mixed h- and p-version finite element models for axisymmetric problems of cylindrical shells , 2013 .

[42]  B. Tóth.  Dual‐mixed variational formulation and hp finite element method for axisymmetric shell problems in elastodynamics , 2013 .

[43]  Douglas N. Arnold,et al.  Mixed Methods for Elastodynamics with Weak Symmetry , 2013, SIAM J. Numer. Anal..

[44]  I. Ecsedi,et al.  Curved composite beam with interlayer slip loaded by radial load , 2015 .

[45]  Hyun Joong Yoon,et al.  Free vibration analysis for shells of revolution based on p-version mixed finite element formulation , 2015 .

[46]  G. Y. Li,et al.  A nodal integration axisymmetric thin shell model using linear interpolation , 2016 .

[47]  L. Demkowicz,et al.  The DPG methodology applied to different variational formulations of linear elasticity , 2016, 1601.07937.

[48]  B. Tóth.  Multi-field Dual-Mixed Variational Principles Using Non-symmetric Stress Field in Linear Elastodynamics , 2016 .

[49]  Andreas Schröder,et al.  A posteriori error control and adaptivity of hp-finite elements for mixed and mixed-hybrid methods , 2017, Comput. Math. Appl..

[50]  Patrick Le Tallec,et al.  Coupled variational formulations of linear elasticity and the DPG methodology , 2016, J. Comput. Phys..

[51]  Phill-Seung Lee,et al.  Performance of the MITC3+ and MITC4+ shell elements in widely-used benchmark problems , 2017 .

[52]  B. Tóth.  Dual and mixed nonsymmetric stress-based variational formulations for coupled thermoelastodynamics with second sound effect , 2018 .

[53]  K. Wiśniewski,et al.  Improved nine-node shell element MITC9i with reduced distortion sensitivity , 2018 .

[54]  A. Schröder,et al.  Hybridization and stabilization for hp-finite element methods , 2019, Applied Numerical Mathematics.