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2004 | Buch

Classification of Composite Materials Kapitel lesen Erstes Kapitel lesen

Mechanics of Composite Structural Elements

verfasst von: Prof. Dr.-Ing. habil. Holm Altenbach, Prof. Dr.-Ing. habil. Dr. h.c. Johannes Altenbach, Prof. Dr.-Ing. habil. Wolfgang Kissing

Verlag: Springer Berlin Heidelberg

Enthalten in: Professional Book Archive

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Über dieses Buch

Laminate and sandwich structures are typical lightweight elements with rapidly ex­ panding application in various industrial fields. In the past, these structures were used primarily in aircraft and aerospace industries. Now, they have also found ap­ plication in civil and mechanical engineering, in the automotive industry, in ship­ building, the sport goods industries, etc. The advantages that these materials have over traditional materials like metals and their alloys are the relatively high specific strength properties (the ratio strength to density, etc). In addition, the laminate and sandwich structures provide good vibration and noise protection, thermal insulation, etc. There are also disadvantages - for example, composite laminates are brittle, and thejoining of such elements is not as easy as with classical materials. The recycling of these materials is also problematic, and a viable solution is yet to be developed. Since the application of laminates and sandwiches has been used mostly in new technologies, governmental and independent research organizations, as well as big companies, have spent a lot of money for research. This includes the development of new materials by material scientists, new design concepts by mechanical and civil engineers as well as new testing procedures and standards. The growing de­ mands of the industry for specially educated research and practicing engineers and material scientists have resulted in changes in curricula of the diploma and master courses. More and more universities have included special courses on laminates and sandwiches, and training programs have been arranged for postgraduate studies.

Inhaltsverzeichnis

Frontmatter
1. Classification of Composite Materials
Abstract
Fibre reinforced polymer composite systems have become increasing important in a variety of engineering fields. The rapid growth in the use of composite materials in structures has required the development of structure mechanics for modelling the mechanical behavior and the analysis of structural elements made of composite material as laminate or sandwich beams, plates and shells. The main topics of this textbook are
  • a short introduction into the linear mechanics of deformable solids with anisotropic material behavior,
  • the mechanical behavior of composite materials as unidirectional reinforced single layers or laminated composite materials, the analysis of effective moduli, some basic mechanisms and criteria of failure,
  • the modelling of the mechanical behavior of laminates and sandwiches, general assumptions of various theories, classical laminate theory (CLT), effect of stacking of the layers of laminates and the coupling of stretching, bending and twisting, first order shear deformation theory (FOSDT), an overview on refined equivalent single layer plate theories and on multilayered plate modelling,
  • modelling and analysis of laminate and sandwich beams, plates and shells, problems of bending, vibration and buckling and
  • modelling and analysis of fibre reinforced long thin-walled folded-plated structural elements.
Holm Altenbach, Johannes Altenbach, Wolfgang Kissing
2. Linear Anisotropic Materials
Abstract
The classical theory of linear elastic deforrnable solids is based on the following restrictions to simplify the modelling and analysis:
  • The body is an ideal linear elastic body.
  • All strains are small.
  • The material behavior is homogeneous.
  • The deforrnable solid is isotropic.
Holm Altenbach, Johannes Altenbach, Wolfgang Kissing
3. Effective Material Moduli for Composites
Abstract
Composite materials have at least two different material components which are bonded. The material response of a composite is determined by the material moduli of all constituents, the volume or mass fractions of the single constituents in the composite material, by the quality of their bonding, i.e. of the behavior of the interfaces, and by the arrangement and distribution of the fibre reinforcement, i.e. the fibre architecture.
Holm Altenbach, Johannes Altenbach, Wolfgang Kissing
4. Elastic Behavior of Laminate and Sandwich Composites
Abstract
A lamina has been defined as a thin single layer of composite material. A lamina or ply is a typical sheet of composite materials, which is generally of a thickness of the order 1 mm. A laminate is constructed by stacking a number of laminae in the direction of the lamina thickness. The layers are usually bonded together with the same matrix material as in the single lamina. A laminate bonded of n (n = 2) laminae of nearly the same thickness. A sandwich can be defined as a special case of a laminate with n = 3. Generally, the sandwich is made of a material of low density for the inner layer, the core or the supporting pith respectively, and of high strength material for the outer layers, the cover or face sheets. The thickness of the core is generally much greater than the thickness of the sheets and core and sheets are bonded to each other at the surfaces.
Holm Altenbach, Johannes Altenbach, Wolfgang Kissing
5. Classical and Improved Theories
Abstract
In this chapter, the theoretical background for two commonly used structural theories for the modelling and analysis of laminates and sandwiches is considered, namely the classical laminate theory and the first-order shear deformation theory. The classical laminate theory (CLT) and the first-order shear deformation theory (FSDT) are the most commonly used theories for analyzing laminated or sandwiched beams, plates and shells in engineering applications. The CLT is an extension of Kirchhoff’s classical plate theory for homogeneous isotropic plates to laminated composite plates with a reasonable high width-to-thickness ratio. For homogeneous isotropic plates the Kirchhoff’s theory is limited to thin plates with ratios of maximum plate deflection w to plate thickness h < 0.2 and plate thickness/ minimum in-plane dimensions < 0.1. Unlike homogeneous isotropic structure elements, laminated plates or sandwich structures have a higher ratio of in-plane Young’s moduli to the interlaminar shear moduli, i.e. such composite structure elements have a lower transverse shear stiffness and often have significant transverse shear deformations at lower thickness-to span ratios < 0.05. Otherwise the maximum deflections can be considerable larger than predicted by CLT. Furthermore, the CLT cannot yield adequate correct through-the-thickness stresses and failure estimations. As a result of these considerations it is appropriate to develop higher-order laminated and sandwich theories which can be applied to moderate thick structure elements, e.g. the FSDT. CLT and FSDT are so-called equivalent single-layer theories (ESLT).
Holm Altenbach, Johannes Altenbach, Wolfgang Kissing
6. Failure Mechanisms and Criteria
Abstract
Failure of structural elements can be defined in a different manner. As in the case of buckling, a structural element may be considered failure though the material is still intact, but there are excessive deformations. In Chap. 6 failure will be considered to be the loss of integrity of the composite material itself.
Holm Altenbach, Johannes Altenbach, Wolfgang Kissing
7. Modelling and Analysis of Beams
Abstract
In Chap. 1 the classification of composite materials, the significance, advantages and limitations of composite materials and structures and the material characteristics of the constituents of composite materials were considered. Chapter 2 gave a short introduction to the governing equations of the linear theory of anisotropic material behavior. Chapter 3 defined effective material moduli of composites including elementary mixture rules and improved formulas. Chapter 4 developed in detail the modelling of the mechanical behavior of laminates and sandwiches in the frame of classical theories including thermal and hygroscopic effects. The constitutive equations, describing the relationships between stress resultants and in-plane strains and mid-surface curvatures were developed for unidirectional laminae, laminates and sandwiches with the assumptions of the classical laminate theory. Further the calculation of in-plane and through-the-thickness stresses was considered. Chapter 5 gave an introduction to classical and refined laminate theories. In Chap. 6 selected failure mechanisms and criteria were briefly discussed. These parts of the book give the basic knowledge, how the design engineer can tailor composite materials to obtain the desired properties by the appropriate choice of the fibre and matrix constituents, a laminate or a sandwich material, the stacking sequence of layers, etc. This basic knowledge can be utilized to develop the modelling and analysis of structural elements and structures composed of composite materials.
Holm Altenbach, Johannes Altenbach, Wolfgang Kissing
8. Modelling and Analysis of Plates
Abstract
The modelling and analysis of plates constituted of laminate or sandwich material is a problem of more complexity than that of beams, considered in Chap. 7. Generally, plates are two-dimensional thin structure elements with a plane middle surface. The thickness h is small relatively to the two other dimensions a, b (Fig. 8.1). In Chap. 8 all derivatives are as a matter of priority restricted to rectangular plates including the special case of a plate strip, i.e. a rectangular plate element which is very long, for instance in the x 2 -direction and has finite dimension in the x 1 direction. When the transverse plate loading, the plate stiffness, and the boundary conditions for the plate edges x 1 = const are independent of the coordinate x 2 , the plate strip modelling can be reduced to a one-dimensional problem. The analysis is nearly the same as in the beam theory. Chapter 8 gives a first introduction to the classical plate theory and the plate theory including transverse shear deformations. The derivations of the principal equations for plates relies upon the basic considerations of Chap. 5.
Holm Altenbach, Johannes Altenbach, Wolfgang Kissing
9. Modelling and Analysis of Circular Cylindrical Shells
Abstract
In the previous Chaps. 7 and 8 we have considered beams and plates, i.e. one- and two-dimensional structural elements with straight axes and plane reference surfaces. Thin-walled laminated or sandwich shells can be also modelled as two-dimensional structural elements but with single or double curved reference surfaces. To cover shells of general shape a special book is necessary, because a general treatment of shells of any geometry demands a detailed application of differential geometry relations.
Holm Altenbach, Johannes Altenbach, Wolfgang Kissing
10. Modelling and Analysis of Thin-walled Folded Structures
Abstract
The analysis of real structures always is based on a structural and mathematical modelling. It is indispensable for obtaining realistic results that the structural model represents sufficiently accurate the characteristic structure behavior.
Holm Altenbach, Johannes Altenbach, Wolfgang Kissing
11. Finite Element Analysis
Abstract
The Finite Element Method (FEM) is one of the most effective methods for the numerical solution of field problems formulated in partial differential equations. The basic idea of the FEM is a discretization of the continuous structure into substructures. This is equivalent to replacing a domain having an infinite number of degrees of freedom by a system having a finite number of degrees of freedom. The actual continuum or structure is represented as an assembly of subdivisions called finite elements. These elements are considered to be interconnected at specified joints which are called nodes. The discretization is defined by the so-called finite element mesh made up of elements and nodes.
Holm Altenbach, Johannes Altenbach, Wolfgang Kissing
A. Matrix Operations
Abstract
The following short review of the basic matrix definitions and operations will provide a quick reference and ensure that the particular use of vector-matrix notations in this textbook is correct understood.
Holm Altenbach, Johannes Altenbach, Wolfgang Kissing
B. Stress and strain transformations
Holm Altenbach, Johannes Altenbach, Wolfgang Kissing
C. Differential Operators for Rectangular Plates (Classical Plate Theory)
Holm Altenbach, Johannes Altenbach, Wolfgang Kissing
D. Differential Operators for Rectangular Plates (Shear Deformation Theory)
Holm Altenbach, Johannes Altenbach, Wolfgang Kissing
E. Differential Operators for Circular Cylindrical shells (Classical Shell Theory)
Holm Altenbach, Johannes Altenbach, Wolfgang Kissing
F. Differential Operators for Circular Cylindrical Shells (Shear Deformation Theory)
Holm Altenbach, Johannes Altenbach, Wolfgang Kissing
G. Solution Forms of the Differential Equation
Holm Altenbach, Johannes Altenbach, Wolfgang Kissing
H. Material’s properties
Abstract
Below material properties for classical materials, for the constituents of various composites and for unidirectional layers are presented. The information about the properties were taken from different sources. Among others the following Handbooks, Textbooks and Monographs are used:
1.
W. Beitz, K.-H. Kiittner (Eds): Dubbel — Taschenbuch für den Maschinenbau. Springer: Berlin et al., 1990
 
2.
J.-M- Berthelot: Composite Materials. Springer: New York, 1999
 
3.
H. Czichos (Ed.): Hütte — Die Grundlagen der Ingenieurwissenschaften Springer: Berlin et al., 1991
 
4.
M.W. Hyer: Stress Analysis of Fiber-Reinforced Composite Materials. — Boston et al.: McGraw-Hill, 1998
 
5.
V.V. Vasiliev and E.V. Morozov: Mechanics and Analysis of Composite Materials. — Amsterdam: Elsevier, 2001
 
6.
G.I. Zagainov and G.E. Lozino-Lozinski (Eds): Composite Materials in Aerospace Design. — London et al.: Chapman & Hall, 1996
 
Holm Altenbach, Johannes Altenbach, Wolfgang Kissing
I. References
Holm Altenbach, Johannes Altenbach, Wolfgang Kissing
Backmatter
Metadaten
Titel
Mechanics of Composite Structural Elements
verfasst von
Prof. Dr.-Ing. habil. Holm Altenbach
Prof. Dr.-Ing. habil. Dr. h.c. Johannes Altenbach
Prof. Dr.-Ing. habil. Wolfgang Kissing
Copyright-Jahr
2004
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-662-08589-9
Print ISBN
978-3-642-07411-0
DOI
https://doi.org/10.1007/978-3-662-08589-9