Mathematical Analysis of Thin Plate Models

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 - The energy release rate..- V.4.2 - The energy release rate for delaminated plates.- V.5 - The mechanical example and the numerical method.- V.5.1 - The specimen studied.- V.6 - Concluding remarks.- References of Chapter V.