ALTERNATE STRESS AND CONJUGATE STRAIN MEASURES, AND MIXED VARIATIONAL FORMULATIONS INVOLVING RIGID ROTATIONS, FOR COMPUTATIONAL ANALYSES OF FINITELY DEFORMED SOLIDS, WITH APPLICATION TO PLATES AND SHELLS-I

Keywords

Stress resultants, Plane stress, Mathematics, Finite element method, Rotation (mathematics)

References

• The stationary principle of complementary work in nonlinear theory of elasticity: PMM vol.34, n≗2. 1970, pp. 241–245Л. М. Зубов — 1970
• Finite rotations and Lagrangean description in the non-linear theory of shellsWojciech Pietraszkiewicz — 1979
• Variational Methods in Elasticity and PlasticityK. Washizu — 1982
• Nonlinear Shell Theory With Finite Rotation and Stress-Function VectorsJ. G. Simmonds, D. A. Danielson — 1972
• A tensorial Hencky measure of strain and strain rate for finite deformationsJames E. Fitzgerald — 1980
• Finite elements, finite rotations and small strains of flexible shellsGerald Wempner — 1969
• Theoretical Formulation of Finite-Element Methods in Linear-Elastic Analysis of General Shells∗Satyanadham Atluri, T. H. H. Pian — 1972
• Invariant Stress and Deformation Functions for Doubly Curved ShellsA. Libai — 1967
• On Finite Symmetrical Deflections of Thin Shells of RevolutionE. Reissner — 1969
• On constitutive inequalities for simple materials—IR. Hill — 1968
• Notes on nonlinear shell theory.Bernard Budiansky — 1968
• Objectivity of incremental constitutive relations over finite time steps in computational finite deformation analysesRobert Rubinstein, Satya N. Atluri — 1983
• Mechanics of Incremental DeformationM. A. Biot, D. C. Drucker — 1965
• On Some New General and Complementary Energy Theorems for the Rate Problems in Finite Strain. Classical ElastoplasticitySatya N. Atluri — 1980
• Finite rotation effects in numerical integration of rate constitutive equations arising in large‐deformation analysisThomas J.R. Hughes, James M. Winget — 1980
• Nonlinear theory of continuous mediaA. Cemal Eringen, P. R. Paslay — 1962
• A new variational principle for finite elastic displacementsBaudouin Fraeijs de Veubeke — 1972
• NONLINEAR THEORIES FOR THIN SHELLSJ. L. Sanders — 1963
• On the Equations of Nonlinear Shallow Shell TheoryE. Reissner — 1969
• New General and Complementary Energy Theorems, Finite Strain, Rate Sensitive Inelasticity and Finite Elements: Some Computational StudiesS. Atluri, H. Murakawa — 1981

Cited by

• Indeterminacy of first order stress functions and the stress- and rotation-based formulation of linear elasticityE. Bert�ti — 1994
• The Biot stresses in nonlinear elasticity and the associated generalized variational principlesH. Bufler — 1985
• Development of Large Strain Shell Elements for Woven Fabrics with Application to Clothing Pressure Distribution ProblemMasato Tanaka, Hiroshi Noguchi, Masaki FUJIKAWA — 2010
• An Improved Quadrilateral Flat Element with Drilling Degrees of Freedom for Shell Structural AnalysisHieu Nguyen‐Van, N. Mai‐Duy, T. Tran‐Cong — 2009
• The Computations of Large Rotation Through an Index Two Nilpotent EquationChein‐Shan Liu — 2006
• Large Deformation Analyses of Space-Frame Structures, Using Explicit Tangent Stiffness Matrices, Based on the Reissner variational principle and a von Karman Type Nonlinear Theory in Rotated Reference FramesY.C. Cai, Jeom Kee Paik, Satya N. Atluri — 2009
• Vibration Analysis of Curved Shell using B-spline Wavelet on the Interval (BSWI) Finite Elements Method and General Shell TheoryZhibo Yang, Xuefeng Chen, Bing Li — 2012
• Dynamic Instabilities in Slender Space Launch Vehicles under Propulsive Thrust and Aerodynamic ForcesManish Trikha, S. Gopalakrishnan, D. Roy Mahapatra — 2009
• Eshelby Stress Tensor T: a Variety of Conservation Lawsfor T in Finite Deformation Anisotropic Hyperelastic Solid& Defect Mechanics, and the MLPG-Eshelby Method inComputational Finite Deformation Solid Mechanics-Part IZhiyun Han, Satyanadham Atluri — 2014
• Theory and numerics of thin elastic shells with finite rotationsFriedrich Gruttmann, E. Stein, Peter Wriggers — 1989
• Advances in Finite Rotations in Structural MechanicsM. Iura, Satya N. Atluri — 2003
• On the (Meshless Local Petrov-Galerkin) MLPG-EshelbyMethod in Computational Finite Deformation SolidMechanics - Part IIZ. D. Han, Satya N. Atluri — 2014
• On finite element analysis of fluid flows fully coupled with structural interactionsSandra Rugonyi, Klaus‐Jürgen Bathe — 1999
• Estimation of Isotropic Hyperelasticity ConstitutiveModels to Approximate the Atomistic Simulation Data forAluminium and Tungsten MonocrystalsMarcin Maździarz, Marcin Gajewski — 2015
• Hybrid Elements for Modelling Squeeze Film Effects Coupled with Structural Interactions in Vibratory MEMS DevicesAnish Roychowdhury, Arup Nandy, CS Jog — 2015
• Development of Intrinsic Formulation of W.-Z. Chien of the Geometrically Nonlinear Theory of Thin Elastic ShellsWojciech Pietraszkiewicz — 2011
• Théorie géométriquement exacte des coques en rotations finies et son implantation éléments finisAdnan Ibrahimbegović — 1997
• Unified nonlinear analysis for nonhomogeneous anisotropic beams with closed cross sectionsAli Rana Atılgan, Dewey H. Hodges — 1991
• Mathematical Modeling and Numerical Simulation of the Dynamics of Flexible Structures Undergoing Large Overall MotionsJ.C. Simo — 1991
• A Meshfree Thin Shell for Arbitrary Evolving Cracks Based on An Extrinsic BasisTimon Rabczuk, P. Areias — 2006

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