Mechanics of Curved Composites

This book is the frrst to focus on mechanical aspects of fibrous and layered composite material with curved structure. By mechanical aspects we mean statics, vibration, stability loss, elastic and fracture problems. By curved structures we mean that the reinforcing layers or fibres are not straight: they have some initial curvature, bending or distortion. This curvature may occur as a result of design, or as a consequence of some technological process. During the last two decades, we and our students have investigated problems relating to curved composites intensively. These investigations have allowed us to study stresses and strains in regions of a composite which are small compared to the curvature wavelength. These new, accurate, techniques were developed in the framework of continuum theories for piecewise homogeneous bodies. We use the exact equations of elasticity or viscoelasticity for anisotropic bodies, and consider linear and non-linear problems in the framework of this continuum theory as well as in the framework of the piecewise homogeneous model. For the latter the method of solution of related problems is proposed. We have focussed our attention on self-balanced stresses which arise from the curvature, but have provided sufficient information for the study of other effects. We assume that the reader is familiar with the theory of elasticity for anisotropic bodies, with partial differential equations and integral transformations, and also with the Finite Element Method.

Klappentext

This book is the first to focus on mechanical aspects of fibrous and layered composite materials with curved structure. By mechanical aspects it is meant that the reinforcing layers or fibres have some initial curvature, bending or distortion which may occur as a result of design, or as a consequence of some technological process. The new, accurate techniques were developed in the framework of continuum theories for piecewise homogeneous bodies. Linear and non-linear problems in the framework of this continuum theory as well as in the framework of the piecewise homogeneous body model are considered. It is assumed that the reader is familiar with the theory of elasticity for anisotropic bodies, with partial differential equations and integral transformations, and also with the FEM. This book is designed for graduate researchers, for mechanical engineers designing composite materials for automobiles, trucks, flywheels etc., and for civil, aerospace, and biomedical engineers.

Inhalt
1.1. Types of composite materials.- 1.2. Specific curving of reinforcing elements.- 1.3. Background and brief review.- 1. Plane-curved Composites.- 1.1. Classical theories.- 1.2. Basic equations and boundary conditions.- 1.3. Constitutive relations.- 1.4. Displacement equations; formulation and solution.- 1.5. Example for exact solution.- 1.6. Vibration problems.- 1.7. Quasi-homogeneous stress states corresponding to pure shears.- 1.8. Quasi-homogeneous states corresponding to tension-compression.- 1.9. Some detailed results on quasi-homogeneous states.- 1.10. Composites with large-scale curving.- 1.11. Bibliographical notes.- 2. General curved composites.- 2.1. Some preliminary remarks on geometry.- 2.2. Constitutive relations.- 2.3. Explicit constitutive relations for small curving.- 2.4. Displacements equations for small curving; formulation and solution.- 2.5. Example of the small parameter method.- 2.6. An exact solution.- 2.7. Pure shear of composite materials.- 2.8. Quasi-homogeneous stress state corresponding to triaxial tension-compression.- 2.9. Approximate results for layered composites.- 2.10. The applicability of the proposed approach.- 2.11. Bibliographical notes.- 3. Problems for curved composites.- 3.1. Bending of a strip.- 3.2. Bending of a rectangular plate.- 3.3. Vibration problems.- 3.4. Bibliographical notes.- 4. Plane-strain state in periodically curved composites.- 4.1. Formulation.- 4.2. Method of solution.- 4.3. Stress distribution in composites with alternating layers.- 4.4. Stress distribution in composites with partially curved layers.- 4.5. Viscoelastic composites.- 4.6. Stress distribution in composites with viscoelastic layers.- 4.7. Composite materials with anisotropic layers.- 4.8. Numerical results: rectilinear anisotropy.- 4.9. Numerical results: curvilinear anisotropy.- 4.10. Bibliographical notes.- 5. Composites with spatially periodic curved layers.- 5.1. Formulation.- 5.2. The equation of contact surfaces.- 5.3. The presentation of the governing relations in series form.- 5.4. Method of solution.- 5.5. Stress distribution.- 5.6. Bibliographical notes.- 6. Locally-curved composites.- 6.1. Formulation.- 6.2. Method of solution.- 6.3. Composite with alternating layers.- 6.4. The influence of local curving form.- 6.5. Bibliographical notes.- 7. Fibrous composites.- 7.1. Formulation.- 7.2. Method of solution for lower fiber concentration.- 7.3. Method of solution for higher fiber concentrations.- 7.4. Numerical results.- 7.5. Screwed fibers in an elastic matrix.- 7.6. Bibliographical notes.- 8. Geometrically non-linear problems.- 8.1. Formulation. Governing relations and equations.- 8.2. Method of solution.- 8.3. Numerical results.- 8.4. Bibliographical notes.- 9. Normalized modulus elasticity.- 9.1. Basic equations.- 9.2. Normalized moduli.- 9.3. Numerical results.- 9.4. Bibliographical notes.- 10. Fracture problems.- 10.1. Fiber separation.- 10.2. Crack problems.- 10.3. Fracture in compression.- 10.4. Bibliographical notes.- Supplement 1. Viscoelastic unidirectional composites in compression.- 5.1.1. Fracture of unidirectional viscoelastic composites in compression.- 5.1.2. Compressive strength in compression of viscoelastic unidirectional composites.- 5.1.3. Bibliographical notes.- Supplement 2. Geometrical non-linear and stability problems.- 5.2.1. Geometrical non-linear bending of the strip.- 5.2.2. Stability loss of the strip.- 5.2.3. Bibliographical notes.- References.- References Supplement.