Preface
Engineered structures are almost as old as human civilization and undoubtedly began with rudimentary tools and the first dwellings outside caves. Great progress has been made over thousands of years, and our world is now filled with engineered struc- tures from nano-scale machines to soaring buildings.
Aerospace structures ranging from fragile human-powered aircraft to sleek jets and thundering rockets are, in our opinion, among the most challenging and creative examples of these efforts.
The study of mechanics and structural analysis has been an important area of en-gineering over the past 300 years, and some of the greatest minds have contributed to its development.
Newton formulated the most basic principles of equilibrium in the 17th century, but fundamental contributions have continued well into the 20th century. Today, structural analysis is generally considered to be a mature field with.
well-established principles and practical tools for analysis and design. A key rea- son for this is, without doubt, the emergence of the finite element method and its widespread application in all areas of structural engineering. As a result, much of today’s emphasis in the field is no longer on structural analysis, but instead is on the use of new materials and design synthesis.
The field of aerospace structural analysis began with the first attempts to build flying machines, but even today, it is a much smaller and narrower field treated in far fewer textbooks as compared to the fields of structural analysis in civil and mechan-ical engineering. Engineering students have access to several excellent texts such as those by Donaldson and Megson, but many other notable textbooks are now out of print.
This textbook has emerged over the past two decades from our efforts to teach in aerospace engineering. By the time students enroll in the undergraduate course, they have studied statics and covered introductory mechanics of deformable bodies dealing primarily with beam bending.
These introductory courses are taught using texts devoted largely to applications in civil and mechanical engineering, leaving our students with little appreciation for some of the unique and challenging features of aerospace structures, which often involve thin-walled structures made of fiber- reinforced composite materials.
In addition, while in widespread use in industry and tures from nano-scale machines to soaring buildings. Aerospace structures ranging core courses in advanced structural analysis to undergraduate and graduate students.
VIII Preface
the subject of numerous specialized textbooks, the finite element method is only slowly finding its way into general structural analysis texts as older applied methods and special analysis techniques are phased out.
The book is divided into four parts. The first part deals with basic tools and concepts that provide the foundation for the other three parts. It begins with an intro-duction to the equations of linear elasticity, which underlie all of structural analysis.
A second chapter presents the constitutive laws for homogeneous, isotropic and lin- early elastic material but also includes an introduction to anisotropic materials and particularly to transversely isotropic materials that are typical of layered composites.
The first part
concludes with chapter 4, which defines isostatic and hyperstatic prob- lems and introduces the fundamental solution procedures of structural analysis: the displacement method and the force method.
Part 2
develops Euler-Bernoulli beam theory with emphasis on the treatment of beams presenting general cross-sectional configurations. Torsion of circular cross- sections is discussed next, along with Saint-Venant torsion theory for bars of arbitrary shape. A lengthy chapter is devoted to thin-walled beams typical of those used in aerospace structures. Coupled bending-twisting and nonuniform torsion problems are also addressed.
Part 3
introduces the two fundamental principles of virtual work that are the ba-sis for the powerful and versatile energy methods. They provide tools to treat more realistic and complex problems in an efficient manner. A key topic in Part 3 is the de- velopment of methods to obtain approximate solution for complex problems.
First, the Rayleigh-Ritz method is introduced in a cursory manner; next, applications of the weak statement of equilibrium and of energy principles are presented in a more formal manner; finally, the finite element method applied to trusses and beams ispresented. Part 3 concludes with a formal introduction of variational methods and general statements of the energy principles introduced earlier in more applied con-texts.
Part 4
covers a selection of advanced topics of particular relevance to aerospace structural analysis. These include introductions to plasticity and thermal stresses, buckling of beams, shear deformations in beams and Kirchhoff plate theory. In our experience, engineering students generally grasp concepts more quickly.
when presented first with practical examples, which then lead to broader generaliza-tions. Consequently, most concepts are first introduced by means of simple examples; more formal and abstract statements are presented later, when the student has a better grasp of the significance of the concepts. Furthermore, each chapter provides numer- ous examples to demonstrate the application of the theory to practical problems.
Some of the examples are re-examined in successive chapters to illustrate alternative or more versatile solution methods. Step-by-step descriptions of important solution procedures are provided. As often as possible, the analysis of structural problems is approached in a unified manner.
First, kinematic assumptions are presented that describe the structure’s dis-placement field in an approximate manner; next, the strain field is evaluated based on the strain-displacement relationships; finally, the constitutive laws lead to the stress field for which equilibrium equations are then established.
In our experience, this ap-proach reduces the confusion that students often face when presented with develop ments that don’t seem to follow any obvious direction or strategy but yet, inevitably lead to the expected solution.
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