Mathematical Analysis of Thin Plate Models - Softcover

Destuynder, Philippe; Salaun, Michel

Softcover

ISBN 10: 3642517625 ISBN 13: 9783642517624

Publisher: Springer, 2014

Synopsis

I - Plate models for thin structures.- I.0 - A short description of the chapter.- I.1 - The three dimensionnal elastic-model.- I.1.1 - About the kinematics.- I.1.2 - About the Principle of virtual work.- I.1.3 - About the constitutive relationship.- I.1.4 - Existence uniqueness of the solution to the elastic model.- I.2 - The Kirchhoff-Love assumption.- I.3 - The Kirchhof f-Love plate model.- I.3.1 - Existence and uniqueness of a solution to the Kirchhof f-Love model.- I.3.2 - The local equations satisfied by the Kirchhoff-Love plate model.- I.3.3 - The transverse shear stress in Kirchhoff-Love theory.- I.4 - The Naghdi model revisited using mixed variational formulation.- I.4.1 - Existence and uniqueness of a solution to the revisited Naghdi model.- I.4.2 - Local equations of the Naghdi model.- I.5 - About the rest of the book.- References of Chapter I.- II - Variational formulations for bending plates.- II.0 - A brief summary of the chapter.- II. 1 - Why a mixed formulation for plates.- II.2 - The primal variational formulation for Kirchhoff-Love model.- II.2.1 - Double Stokes formula for plates.- II.2.2 - The variational formulation.- II.2.3 - Another variational formulation.- II.2.4 - Interest of formulation (II. 12).- II.3 - The Reissner-Mindlin-Naghdi model for plates.- II.3.1 - The penalty method applied to the Kirchhoff-Love model.- II.3.2 - A correction to the penalty method.- II.4 - Natural duality techniques for the bending plate model.- II.4.1 - A mixed variational formulation for Kirchhoff-Love model.- II.4.2 - Existence and uniqueness of solution to the mixed formulation.- II.4.3 - Computation of the deflection u3.- II.4.4 - How to be sure we solved the right model (interpretation of the model).- II.4.5 - What is the meaning of ? and when is it zero?.- II.4.6 - Non-homogeneous boundary conditions.- II.4.7 - The revisited modified Reissner-Mindlin-Naghdi model.- II.4.8 - Extension to a multi-connected boundary.- II.5 - A comparison between the mixed method and the one of section II.2.4.- References of Chapter II.- III - Finite element approximations for several plate models.- III.0 - A summary of the chapter.- III. 1 - Basic results in finite element approximation.- III. 1.1 - Several useful definitions.- III. 1.2 - A brief recall concerning error estimates.- III.2 - C1 elements.- III.3 - Primal finite element methods for bending plates.- III.4 - The penalty-duality finite element method for the bending plate model.- III.4.1 - Stability with respect to the penalty parameter of the R.M.N. solution.- III.4.2 - A finite element scheme and error estimates for the R.M.N. model.- III.4.3 - Practical aspects in solving the R.M.N. finite element model.- III.4.4 - About the famous QUAD4 element.- III.5 - Numerical approximation of the mixed formulation for a bending plate.- III.5.1 - General error estimates between (0,A) and (?, ?h).- III.5.2 - Theoretical estimates on u3 - u3h.- III.5.3 - A first choice of finite elements.- HI.5.4 - A second choice of finite elements.- References of Chapter III.- IV - Numerical tests for the mixed finite element schemes.- IV.0 - A brief description of the chapter.- IV. 1 - Precision tests for the mixed formulation.- IV. 1.1 - A recall of the equations to be solved.- IV. 1.2 - Numerical tests.- IV. 1.3 - A few remarks relative to the above numerical results.- IV.2 Vectorial and parallel algorithms for mixed elements.- IV.2.1 - Three strategies for solving the system (IV. 18).- IV.2.2 - Optimization of Crout factorization.- IV.2.3 - Optimization of node renumbering.- IV.2.4 - Numerical tests.- IV.3 - Concluding remarks.- References of Chapter IV.- V - A Numerical model for delamination of composite plates.- V.O - A brief description of the chapter.- V. 1 - What is delamination of thin multilayered plates.- V.2 - The three-dimensional multilayered composite plate model with delamination.- V.3 - A plate model for large delamination.- V.4 - The three-dimensional energy release rate.- V.4.1 - T

Edition details

• Publisher: Springer
• Publication date: 2014
• Language: English
• ISBN 10: 3642517625
• ISBN 13: 9783642517624
• Binding: Paperback
• Number of pages: 252