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1998 | Buch

Some results from continuum mechanics Kapitel lesen Erstes Kapitel lesen

Finite Element Analysis for Composite Structures

verfasst von: Lazarus Teneketzis Tenek, John Argyris

Verlag: Springer Netherlands

Buchreihe : Solid Mechanics and Its Applications

Enthalten in: Professional Book Archive

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Über dieses Buch

This book is an adventure into the computer analysis of three dimensional composite structures using the finite element method (FEM). It is designed for Universities, for advanced undergraduates, for graduates, for researchers, and for practising engineers in industry. The text advances gradually from the analysis of simple beams to arbitrary anisotropic and composite plates and shells; it treats both linear and nonlinear behavior. Once the basic philosophy of the method is understood, the reader may expand its application and modify the computer programs to suit particular needs. The book arose from four years research at the University of Stuttgart, Germany. We present the theory and computer programs concisely and systematically so that they can be used both for teaching and applications. We have tried to make the book simple and clear, and to show the underlying physical and mathematical ideas. The FEM has been in existence for more than 50 years. One of the authors, John Argyris, invented this technique in World War II in the course of the check on the analysis of the swept back wing of the twin engined Meteor Jet Fighter. In this work, he also consistently applied matrix calculus and introduced triangular membrane elements in conjunction with two new definitions of triangular stresses and strains which are now known as the component and total measures. In fact, he was responsible for the original formulation of the matrix force and displacement methods, the forerunners of the FEM.

Inhaltsverzeichnis

Frontmatter
Chatper 1. Some results from continuum mechanics
Abstract
A clear, full account of the analysis of stress may be found in Chapter 2 of Sokolnikoff’s Mathematical Theory of Elasticity [1]. Here we give an abbreviated account.
Lazarus Teneketzis Tenek, John Argyris
Chapter 2. A brief history of FEM
Abstract
An analysis of complex structures and other systems in a matrix formulation is now unthinkable without the finite element method. Our personal belief is that the origins of such a rich and applicable method cànnot be attributed solely to one person or school of thought but rather to a synergy of various scientific developments at various research establishments. The notion of geometrical division can be traced back to the Greek natural philosopher Archimedes who in order to compute the area of a complex shape divided it into triangles and quadrilaterals whose area could be easily computed; the assembly of the individual areas provided the total area of the complex shape. More recently, Courant used variational and minimization arguments for the solution of physical problems. Courant [5], and Prager and Synge [6] had both proposed the concept of regional discretization which is essentially equivalent to the assumption of constant strain fields within the elements. The adaptation, however, and development of these concepts for structural analysis and other physical and technical problems was not conceptually achieved until during and shortly after World War II.
Lazarus Teneketzis Tenek, John Argyris
Chapter 3. Natural modes for finite elements
Abstract
In the natural mode method we express the deformation u(x, y, z) at any point in a finite element as a linear combination of the nodal cartesian displacements r e
$$ \mathop u\limits_{(3x1)} (x,y,z) = \mathop C\limits_{(3xn)} (x,y,z)\mathop {{r_e}}\limits_{(nx1)} $$
(3.1)
where n represents the nodal degrees of freedom. A finite element e can deform in n different modes. Then, the total deformation of the element may be expressed as a linear combination of the imposed n modes so that
$$ u = {u_1} + {u_2} + ... + {u_n} $$
(3.2)
Lazarus Teneketzis Tenek, John Argyris
Chapter 4. Composites
Abstract
Composite materials are one of the great technological advances of the last half of the twentieth century [26]. By the term composite we usually refer to materials that are combinations of two or more organic or inorganic components, of which one serves as a matrix and the other as fibers. The fibers provide virtually all the strength and stiffness. The purpose of the matrix is to bind the fibers together and keep them in proper orientation, transfer the load to and between them and distribute it evenly, protect the fibers from hazardous environments and handling, provide resistance to crack propagation and damage, provide all the interlaminar shear strength of the composite, and offer resistance to high temperatures and corrosion. Polymer composites are defined as reinforcement fibers supported by a polymer matrix. Individual fibers are usually referred to as filaments; sometimes the fibers are called the reinforcement and the matrix the binder. In structural polymer composites, the fiber is stiffer and stronger than the matrix. The most powerful concept behind composites is that the fibers and the matrix can blend into a new material with properties that are better than those of the constituent parts. In addition, by changing the orientation of the fibers, we can optimize composites for strength, stiffness, fatigue, heat and moisture resistance, etc. It is therefore feasible to tailor the material to meet specific design needs.
Lazarus Teneketzis Tenek, John Argyris
Chapter 5. Composite beam element
Abstract
Beams are autonomous or secondary load bearing members of many structures. They are used extensively in the formation of linkages, shafts and frames and as reinforcements on plate and shell panels. They are also used in robotics and high speed machinery. Laminated composite beams are integral parts of lightweight structures that require high strength over weight ratios. In general, laminated beams have been studied to a lesser degree than laminated plates and shells. This may not come as a surprise considering the fact that some aspects of the theory of beams are more intricate than aspects of plate and shell theory. For example, the geometrical stiffness of a shell element, required for buckling and large deflection analyses, is sufficiently developed using membrane stresses. However, for beam elements other forces or moments may contribute to the geometrical stiffness, albeit not significantly. In the latter case, the geometrical stiffness is more difficult to derive than for plate and shell elements.
Lazarus Teneketzis Tenek, John Argyris
Chapter 6. Composite plate and shell element
Abstract
Shells are used in many modern structures because of their efficiency and economy, their ability to retain their form, and because of other features stemming from their reaction to certain loads. Their shape allows certain membrane stress systems to develop parallel to their tangential plane and become prime carriers of the deformation. Indeed the analysis of many thin shells is solely based on the membrane theory of shells which neglects their bending rigidity. On the other hand, bending becomes important in the presence of rapidly changing loads (e.g. concentrated loads, line loads etc.), near edge constraints, near discontinuities in the shell geometry and in nonlinear deformations. The development of a general membrane and bending theory as well as related numerical implementations are subjects of intense research efforts which aim at providing deeper understanding of the mechanics of load carrying. The literature on this subject has been growing at a rapid pace over the last decades.
Lazarus Teneketzis Tenek, John Argyris
Chapter 7. Computational statistics
Abstract
Following the theoretical formulation and computational validation of our finite element methodology we now address some computational aspects of our method. the cylindrical composite shell of Fig. 6.28 is selected as a model problem to assess the computational advantages of the methodology and obtain an indication about the efficiency of the computer program. The cylindrical panel of Fig. 6.28 (the mesh is shown in Fig. 6.29) includes 800 elements for a total of 2398 degrees of freedom. The elastic and geometrical stiffnesses contain 295969 elements which are stored in skyline form as one dimensional arrays. Of interest is the estimation of the first four elastic buckling modes of the composite shell structure. In order to compute the critical loads both static and eigenvalue analyses are required. The code is executed on a CRAY-C94 supercomputer, and special compilation directives are issued in order to measure the performance of all routines used in the estimation of the buckling loads. Following execution, a statistics report is issued by the computer in which the breakdown of the computing time per routine is shown. This report is provided in the following section.
Lazarus Teneketzis Tenek, John Argyris
Chapter 8. Nonlinear analysis of anisotropic shells
Abstract
In the presence of large deflections, bifurcations, and load and displacement limit points, the analysis of arbitrary anisotropic shells requires the adoption of incremental and iterative procedures. In many cases the load-displacement curves may exhibit unstable branches followed by stable equilibrium paths. The true response is dynamic in nature. However, a full dynamic analysis is impractical and expensive. Thus in most cases a fully static solution or a combined static and dynamic solution is performed. The latter must be able to predict and pass critical limit points and predict collapse loads. The state of the art in current solution algorithms is given by Papadrakakis [80] and Crisfield [81].
Lazarus Teneketzis Tenek, John Argyris
Chapter 9. Programming aspects
Abstract
In this chapter we introduce some programming aspects of our method and explane key elements of the computer program included with the book. We will describe the general structure of the computer program which is based on generic finite element programming concepts. We stress that the basic code structure is similar for beam and shell elements, or for any other finite element type per se. Only key parts of the code will be highlighted here. We believe that the reader, using basic knowledge of Fortran 77 [86] and having understood the principles of our method can easily follow the structure of the computer program.
Lazarus Teneketzis Tenek, John Argyris
Backmatter
Metadaten
Titel
Finite Element Analysis for Composite Structures
verfasst von
Lazarus Teneketzis Tenek
John Argyris
Copyright-Jahr
1998
Verlag
Springer Netherlands
Electronic ISBN
978-94-015-9044-0
Print ISBN
978-90-481-4975-9
DOI
https://doi.org/10.1007/978-94-015-9044-0