Poroelastic Structures (eBook)

G. Cederbaum, L. P. Li, K. Schulgasser (Herausgeber)

eBook Download: PDF

2000 | 1. Auflage
168 Seiten
Elsevier Science (Verlag)
978-0-08-053927-0 (ISBN)

Infos

Poroelasticity is a continuum theory for the analysis of a porous media consisting of an elastic matrix containing interconnected fluid-saturated pores. In physical terms the theory postulates that when a porous material is subjected to stress, the resulting matrix deformation leads to volumetric changes in the pores.
This book is devoted to the analysis of fluid-saturated poroelastic beams, columns and plates made of materials for which diffusion in the longitudinal direction(s) is viable, while in the perpendicular direction(s) the flow can be considered negligible because of the micro-geometry of the solid skeletal material. Many microstructures and fabrication schemes could be imagined, which would produce bulk materials with the postulated behavior. The book provides a methodology and a theoretical basis for investigating the mechanical behaviors of the structural elements made of such materials. It is recognized that the response of the poroelastic structural element to loading is sensitive to the properties of the fluid and to the diffusion boundaries, which can be easily altered in practice. Therefore, such structural elements and thus their features are potentially controllable. In other words, it could be possible to convert such elements into intelligent or smart structures. If this is so, it would be interesting that such structural elements could work as both sensors and actuators, e.g. the fluid can feel the change of the temperature by changing its viscosity and this results in a change of the behavior of the structure.
The present book is the first of its kind, there does not exist in the professional literature any book which deals with this subject.
Chapter 1 is a general introduction and overview. The governing equations for beams are presented in Chapter 2. Chapter 3 then presents analytical solutions for the quasi-static bending problem. Series solutions are found for normal loading with various mechanical and diffusion boundary conditions. The finite element method is developed and employed for the quasi-static beams and columns with small deflections in Chapter 4. In Chapter 5 solutions are found for free and forced vibrations of poroelastic beams. Chapter 6 deals with large deflections of beams. The stability of poroelastic columns is investigated in Chapter 7. Three problems are considered: buckling, post-buckling, and dynamic stability. Formulations are found in Chapter 8 for fluid-saturated poroelastic plates consisting of a material, for which the diffusion is possible in the in-plane directions only, both for bending and for in-plane loading.
This book attempts to constitute a reasonably self-contained presentation of a wide spectrum of problems related to the analysis of the type of poroelastic structure considered.

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Poroelasticity is a continuum theory for the analysis of a porous media consisting of an elastic matrix containing interconnected fluid-saturated pores. In physical terms the theory postulates that when a porous material is subjected to stress, the resulting matrix deformation leads to volumetric changes in the pores. This book is devoted to the analysis of fluid-saturated poroelastic beams, columns and plates made of materials for which diffusion in the longitudinal direction(s) is viable, while in the perpendicular direction(s) the flow can be considered negligible because of the micro-geometry of the solid skeletal material. Many microstructures and fabrication schemes could be imagined, which would produce bulk materials with the postulated behavior. The book provides a methodology and a theoretical basis for investigating the mechanical behaviors of the structural elements made of such materials. It is recognized that the response of the poroelastic structural element to loading is sensitive to the properties of the fluid and to the diffusion boundaries, which can be easily altered in practice. Therefore, such structural elements and thus their features are potentially controllable. In other words, it could be possible to convert such elements into intelligent or smart structures. If this is so, it would be interesting that such structural elements could work as both sensors and actuators, e.g. the fluid can "e;feel"e; the change of the temperature by changing its viscosity and this results in a change of the behavior of the structure. The present book is the first of its kind; there does not exist in the professional literature any book which deals with this subject.Chapter 1 is a general introduction and overview. The governing equations for beams are presented in Chapter 2. Chapter 3 then presents analytical solutions for the quasi-static bending problem. Series solutions are found for normal loading with various mechanical and diffusion boundary conditions. The finite element method is developed and employed for the quasi-static beams and columns with small deflections in Chapter 4. In Chapter 5 solutions are found for free and forced vibrations of poroelastic beams. Chapter 6 deals with large deflections of beams. The stability of poroelastic columns is investigated in Chapter 7. Three problems are considered: buckling, post-buckling, and dynamic stability. Formulations are found in Chapter 8 for fluid-saturated poroelastic plates consisting of a material, for which the diffusion is possible in the in-plane directions only, both for bending and for in-plane loading. This book attempts to constitute a reasonably self-contained presentation of a wide spectrum of problems related to the analysis of the type of poroelastic structure considered.

Inhalt

Cover 1
Contents 8
Chapter 1. Introduction 10
Chapter 2. Modeling of poroelastic beams 18
2.1. Basic equations 18
2.2. Characteristic times 24
2.3. Note on a beam impermeable at both ends 25
2.4. Equations in non-dimensional form 26
Chapter 3. Analytical solutions for quasi-static beams 28
3.1. Simply-supported beams with permeable ends 28
3.2. Beams subjected to loads suddenly applied and constant thereafter 29
Chapter 4. Finite element formulation and solutions for quasi-static beams 42
4.1. Introduction 42
4.2. Variational principles 43
4.3. Finite element formulation 46
4.4. Examples and discussion 50
Chapter 5. Vibrations of poroelastic beams 62
5.1. Initial value problems 62
5.2. Forced harmonic vibrations 72
5.3. Closure 74
Chapter 6. Large deflection analysis of poreolastic beams 76
6.1. Governing equations 76
6.2. Equations in non-dimensional form whene0=0 80
6.3. Numerical formulation 81
6.4. Numerical procedure for the finite difference method 86
6.5. Examples and discussion 88
Chapter 7. Stability of poroelastic columns 98
7.1. Buckling of columns 98
7.2. Limits of critical load 99
7.3. Time-dependence of critical load and deflections 101
7.4. Post-buckling: formulation 105
7.5. Post-buckling: results and discussion 108
7.6. Imperfection sensitivity 111
7.7. Dynamic stability of poroelastic columns 113
7.8. Stability boundaries and critical load amplitude 116
Chapter 8. Analysis of poroelastic plates 120
8.1. Basic equations for thin plates 120
8.2. Bending equations in non-dimensional form 127
8.3. Analytical solutions for quasi-static bending 128
8.4. Transverse vibrations of simply supported plates 137
Chapter 9. Closure 144
REFERENCES 150
Appendix A. Proof of the variational principles 154
Appendix B. A finite element for poroelastic beams 158
Appendix C. Several useful Laplace inverse transformations 160
Appendix D. Coefficients in difference formulas 162
Appendix E. Determination of boundary values at x1 for the finite difference method 164
SUBJECT INDEX 166

Produkt-Details

• Erscheint lt. Verlag: 12.7.2000
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Chemie
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Mineralogie / Paläontologie
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 0-08-053927-0 / 0080539270
• ISBN-13: 978-0-08-053927-0 / 9780080539270