Plate and Shell Models

This book presents, in a variational form, very many two dimensional models which have been developed to overcome some weaknesses of the Kirchhoff-Love and Reissner-Mindlin's models. More precisely the N-T and N models are particularly treated because they clearly show the impact of the change in the third fundamental form whose contribution to the strain energy becomes important when the characteristic ratio of the shell is roughly greater than 0.3. Transverse stresses through-the-thickness are calculated. Gradient Recovery and Strain deformation approach with Curve triangular and Shifted Lagrange elements are implemented. These new FEM appear to be memory less greedy.

Presents the different models in a variational form suitable to implement FEM

Covers Gradient Recovery and Strain Deformation methods

Defines governing equations on transverse stresses through the thickness

Auteur

Prof. Nzengawa has been teaching in masters level, for many years now, in engineering advance schools such as The Ecole Nationale Supérieure Polytechnique de Yaoundé where he was the head of the department of civil engineering, The Ecole Nationale Supérieure Polytechnique de Douala, former Faculty of Industrial Engineering, where he was the Dean and the head of the department of construction engineering. These results are also used in the engineering office that he runs.

Contenu
Dedication List of Figures

List of Tables

Acknowledgements

1 CURVILINEAR MEDIA

1.1 GEOMETRY OF A 3D CURVILINEAR MEDIA

1.2 SURFACE GEOMETRY

2 EQUILIBRIUM EQUATIONS

2.1 GEOMETRY OF A SHELL

2.2 EULER'S EQUATIONS AND VARIATIONAL FORMULATION

3 DYNAMIC EVOLUTION OF SHELLS

3.1 DYNAMIC EQUILIBRIUM EQUATION OF THE N-T MODEL . . . . . . 3.2 FREE VIBRATIONS 3.3 THE MODEL "N" OF THICK SHELLS. . . . . . . . . . . . . . . . .

4 THIN SHELLS

4.1 THEORY OF THIN SHELLS

4.2 THE MEMBRANE THEORY OF THIN SHELLS. . . . . . . . . . .

.4.3 THE MIXED THEORY (MEMBRANE-BENDING) OF THIN SHELLS 4.4 THEORY OF PLATES 4.5 THEORY OF ORTHOTROPIC PLATES

5 NUMERICAL METHODS

5.1 GENERALITIES OF THE 2D FEM. . . . . . . . . . . . . . . . . . .

5.2 C 0 FINITE ELEMENTS. . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 CURVED TRIANGULAR ELEMENTS AND ASSUMED STRAIN APPROACH FOR SHELLS. . . . . . . . . . . . . . . . . . . . . . . .

5.4 APPLICATIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6 OTHER MODELS

6.1 STIFFENED,THERMOELASTIC AND HOMOGENEOUS ANISOTROPIC SHELLS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.2 HETEROGENEOUS SHELLS. . . . . . . . . . . . . . . . . . . . .

6.3 SOME SEMI-ANALYTIC MODELS. . . . . . . . . . . . . . . . . .

6.4 COSSERAT THICK SHELLS. . . . . . . . . . . . . . . . . . . . . .

Bibliography