Mechanics of Aircraft Structures E-Book

C. T. Sun

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 358

Veröffentlichungsjahr: 2021

Beschreibung

MECHANICS OF AIRCRAFT STRUCTURES

Explore the most up-to-date overview of the foundations of aircraft structures combined with a review of new aircraft materials

The newly revised Third Edition of Mechanics of Aircraft Structures delivers a combination of the fundamentals of aircraft structure with an overview of new materials in the industry and a collection of rigorous analysis tools into a single one-stop resource. Perfect for a one-semester introductory course in structural mechanics and aerospace engineering, the distinguished authors have created a textbook that is also ideal for mechanical or aerospace engineers who wish to stay updated on recent advances in the industry.

The new edition contains new problems and worked examples in each chapter and improves student accessibility. A new chapter on aircraft loads and new material on elasticity and structural idealization form part of the expanded content in the book. Readers will also benefit from the inclusion of:

• A thorough introduction to the characteristics of aircraft structures and materials, including the different types of aircraft structures and their basic structural elements
• An exploration of load on aircraft structures, including loads on wing, fuselage, landing gear, and stabilizer structures
• An examination of the concept of elasticity, including the concepts of displacement, strain, and stress, and the equations of equilibrium in a nonuniform stress field
• A treatment of the concept of torsion

Perfect for senior undergraduate and graduate students in aerospace engineering, Mechanics of Aircraft Structures will also earn a place in the libraries of aerospace engineers seeking a one-stop reference to solidify their understanding of the fundamentals of aircraft structures and discover an overview of new materials in the field.

Leseprobe

MECHANICS OF AIRCRAFT STRUCTURES

THIRD EDITION

C. T. Sun and Ashfaq Adnan

This edition first published 2021© 2021 John Wiley and Sons, Inc.

Edition historyJohn Wiley & Sons, Inc (2e, 2006; 1e 1998)

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The right of C.T. Sun and Ashfaq Adnan to be identified as the authors of this work has been asserted in accordance with law.

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Library of Congress Cataloging‐in‐Publication Data Applied for:

ISBN: 9781119583912

Cover Design: WileyCover Image: © guvendemir/iStock/Getty Images Plus

To my wife, Iris, and my children, Edna, Clifford, and Leslie – C.T. Sun

To my loving parents Afroza Nasreen and Dr. Md. Golbar Hussain, my beautiful wife, Most, and my sons, Aayan and Aayat – A. Adnan

Preface to the Third Edition

The purpose of the third edition is to correct some typographical errors in the second edition, add 3D elasticity equations, describe methods for structural idealization, and add a number of worked out and exercise problems. The Chapter 1 in the second edition is broken to two chapters. The Chapter 1 in the new edition includes discussions on the role of structural analysis in aircraft component design process, an overview on (i) fixed wing (ii) rotor craft (iii) lighter than air vehicles, and (iv) drones, a show the road map for developing simplified geometry for structural analysis, basic structural elements and control surfaces and materials. Example problems are added. Chapter 2 provides a brief overview of various types of mechanical loads such as axial, shear, torsion, and bending. Solved example problems include simple design problems including designing a pressurized thin walled cylinder (as simplified fuselage), thin cantilever beam (as simplified wing), designing against joint failure, etc. In Chapter 3, the concept of elasticity is elaborately discussed. A new road map is added to show how the concepts of statics, solid mechanics and elasticity are connected. The role of elasticity in aircraft structure design and its limitation are added. In Chapter 4, a discussion is added on the limitation of solid mechanics in describing torsion problems for noncircular section. Additional problems are added. In Chapter 5, a new discussion is added to describe structural idealizations. New example problems are added. The expansions in the remaining chapters are concentrated on new examples and exercise problems.

The authors are indebted to many students and colleagues for some corrections and valuable suggestions. In particular, Ashfaq Adnan is indebted to his former colleague late Dr. Wen Chan. Ashfaq Adnan is thankful to Aayan Adnan for his assistance in making many new drawings. Ms. Rajni Chahal and Dr. Wei‐Tsen (Eric) Lu are acknowledged for their contributions in the worked‐out problems and instruction materials.

Preface to the Second Edition

The purpose of the second edition is to correct a number of typographical errors in the first edition, add more examples and problems for the student, and introduce a few new topics, including primary warping, effects of boundary constraints, Saint‐Venant’s principle, the concept of shear lag, the Timoshenko beam theory, and a brief introduction to the effect of plasticity on fracture. All these additions are direct extensions of the existing contents in the first edition. Consequently, the background‐building chapters, Chapters 1 and 2, need no modification. The expansions are concentrated in Chapters 3, 4, and 6 and amount to about a 25% increase in the number of pages.

The author is indebted to many students and colleagues for numerous corrections and valuable suggestions. He is indebted also to Dr. G. Huang for his assistance in making many new drawings.

Preface to the First Edition

This book is intended for junior or senior level aeronautical engineering students with a background in the first course of mechanics of solids. The contents can be covered in a semester at a normal pace.

The selection and presentation of materials in the course of writing this book were greatly influenced by the following developments. First, commercial finite element codes have been used extensively for structural analyses in recent years. As a result, many simplified ad hoc techniques that were important in the past have lost their useful roles in structural analyses. This development leads to the shift of emphasis from the problem‐solving drill to better understanding of mechanics, developing the student’s ability in formulating the problem, and judging the correctness of numerical results. Second, fracture mechanics has become the most important tool in the study of aircraft structure damage tolerance and durability in the past thirty years. It seems highly desirable for undergraduate students to get some exposure to this important subject, which has traditionally been regarded as a subject for graduate students. Third, advanced composite materials have gained wide acceptance for use in aircraft structures. This new class of materials is substantially different from traditional metallic materials. An introduction to the characteristic properties of these new materials seems imperative even for undergraduate students.

In response to the advent of the finite element method, consistent elasticity approach is employed. Multidimensional stresses, strains, and stress–strain relations are emphasized. Displacement, rather than strain or stress, is used in deriving the governing equations for torsion and bending problems. This approach will help the student understand the relation between simplified structural theories and 3‐D elasticity equations.

The concept of fracture mechanics is brought in via the original Griffith’s concept of strain energy release rate. Taking advantage of its global nature and its relation to the change of the total strain energies stored in the structure before and after crack extension, the strain energy release rate can be calculated for simple structures without difficulty for junior and senior level students.

The coverage of composite materials consists of a brief discussion of their mechanical properties in Chapter 1, the stress–strain relations for anisotropic solids in Chapter 2, and a chapter (Chapter 8) on analysis of symmetric laminates of composite materials. This should be enough to give the student a background to deal correctly with composites and to avoid regarding a composite as an aluminum alloy with the Young’s modulus taken equal to the longitudinal modulus of the composite. Such a brief introduction to composite materials and laminates is by no means sufficient to be used as a substitute for a course (or courses) dedicated to composites.

A classical treatment of elastic buckling is presented in Chapter 7. Besides buckling of slender bars, the postbuckling concept and buckling of structures composed of thin sheets are also briefly covered without invoking an advanced background in solid mechanics. Postbuckling strengths of bars or panels are often utilized in aircraft structures. Exposure, even very brief, to this concept seems justified, especially in view of the mathematics employed, which should be quite manageable for student readers of this book.

The author expresses his appreciation to Mrs. Marilyn Engel for typing the manuscript and to James Chou and R. Sergio Hasebe for making the drawings.

C.T. Sun

About the Companion Website

This book is accompanied by a companion website:

www.wiley.com/go/Sun/aircraftstructures3

This website includes:

Lecture slides

A solutions manual

Scan this QR code to visit the companion website.

1Characteristics of Aircraft Structures and Materials

1.1 INTRODUCTION

An aircraft is a vehicle that is used for flight in the air. A vehicle like this is typically built by assembling many component structures such as wing, fuselage, landing gears, stabilizers, etc. Each component structure is typically built by assembling many substructures. Each substructure can be made out of different materials. The main difference between aircraft structures and materials and civil engineering structures and materials lies in their weight. The main driving force in aircraft structural design and aerospace material development is to reduce weight. In general, materials with high stiffness, high strength, and light weight are most suitable for aircraft applications.

Aircraft structures must be designed to ensure that every part of the material is used to its full capability. A typical aircraft design cycle involves three major steps – (i) conceptual design, (ii) preliminary design, and (iii) detail design. In any of these design stages, different factors such as aerodynamics, avionics, propulsion, and structural integrity are simultaneously taken into account. As such, aircraft structures are not designed for structural safety and integrity only; many nonstructural requirements impose additional restrictions in designing aircraft structural components. For instance, an airfoil is chosen according to aerodynamic lift and drag characteristics. As such, the size and shape of an aircraft structural component are usually predetermined. Such restrictions significantly limit the number of solutions for structural problems in terms of global configurations. Often, the solutions resort to the use of special materials developed for applications in aerospace vehicles.

The nonstructural and weight‐saving design requirements generally lead to the use of shell‐like structures (monocoque constructions) and stiffened shell structures (semimonocoque constructions). The geometrical details of aircraft structures are much more complicated than those of civil engineering structures. They usually require the assemblage of thousands of parts. Technologies for joining the parts are especially important for aircraft construction.

Because of their high stiffness/weight and strength/weight ratios, aluminum and titanium alloys have been the dominant aircraft structural materials for many decades. However, the recent advent of advanced fiber‐reinforced composites has changed the outlook. Composites may now achieve weight savings of 30–40% over aluminum or titanium counterparts. As a result, composites have been used increasingly in aircraft structures.

1.2 TYPES OF AIRCRAFT STRUCTURES

Most aircraft are built as fixed‐wing vehicles and are commonly known as airplanes. Other categories include rotorcrafts, glider, lighter‐than‐air vehicles, etc. Presence of air is essential for generating lift on these vehicles. As such, structural design of such vehicles depends on how airload is transmitted to the structural elements.

1.2.1 Fixed‐Wing Aircraft

A fixed‐wing aircraft is a kind of air vehicle that is heavier‐than‐air but can fly in the air by generating lift using the wings. An aircraft with a powered engine is generally called an airplane (Figure 1.1a). The unpowered version of fixed‐wing aircraft is called gliders (Figure 1.1b).

1.2.2 Rotorcraft

A rotorcraft (Figure 1.1c) or rotary‐wing aircraft is a heavier‐than‐air vehicle that generates lift using rotary wings or rotor blades, which revolve around a rotor. Depending on how rotor blades function, rotorcrafts are categorized as helicopters, autogyros, or gyrodynes. Recently, small‐scale multirotor rotorcrafts are widely used for surveillance or video‐capturing purposes. Designing blades for the rotorcraft is far more complex than designing a fixed‐wing aircraft because of the complex aerodynamic forces.

1.2.3 Lighter‐than‐Air Vehicles

Aircraft such as balloons, nonrigid blimps, and airships (also known as dirigibles) are designed to contain sufficient amount of lighter‐than‐air gases (typically helium) so that lift can be generated from the lifting gas (Figure 1.2).

1.2.4 Drones

Drones (Figure 1.3) are small‐scale air vehicles that can be fixed‐wing type or rotary‐wing type. The size of a drone is significantly smaller than a typical airplane or rotorcraft. As such, most drones are powered by electrical sources. Other than their size, the lifting mechanism of a drone is similar to the conventional fixed‐wing or rotary‐wing vehicles.

Fig. 1.1 (a) Powered fixed‐wing aircraft, (b) glider, and (c) rotorcraft.

Fig. 1.2 Various lighter‐than‐air vehicles: (a) hot‐air balloon, (b) blimp, and (c) dirigible.

Fig. 1.3 (a) Fixed‐wing drone; (b) multirotor rotary wing drone.

1.3 BASIC STRUCTURAL ELEMENTS IN AIRCRAFT STRUCTURE

An aircraft has many integrated parts, as shown in Figure 1.4. In general, these parts can be categorized into basic structural elements such as wing, fuselage, landing gears, tail units (horizontal and vertical stabilizers), and control surfaces such as aileron, rudder, and elevator.

1.3.1 Fuselage

The fuselage is the main structural element of a fixed‐wing aircraft. It provides space for cargo, control system and pilots, passengers and cabin crews, and other accessories and equipment. In single‐engine aircraft, the fuselage also carries the power plant. As shown in Figure 1.5, a fuselage can be constructed in various configurations such as truss, semimonocoque, and monocoque.

1.3.2 Wing

The main function of the wing is to pick up the air and power plant loads and transmit them to the fuselage. The wing cross‐section takes the shape of an airfoil, which is designed based on aerodynamic considerations. In general, wings are constructed based on monospar, multispar, or box beam configurations, as shown in Figure 1.6. These three design configurations are considered as the basic designs, and aircraft manufacturers may adopt a modified configuration. In the monospar wing configuration, only one main spanwise member is present. Ribs or bulkheads are used to provide the necessary aerodynamic contour or shape to the airfoil. The multispar wing configuration has more than one main longitudinal member in its construction. To attain the desired aerodynamic shape, ribs or bulkheads are often included. The box beam wing configuration has two main longitudinal members and connecting bulkheads to attain the required airfoil contour.

Fig. 1.4 Fixed‐wing aircraft parts.

Fig. 1.5 Various fuselage configurations: (a) truss type, (b) semimonocoque type, and (c) monocoque type.

Fig. 1.6 Various wing configurations: (a) monospar (b) multispar type and (c) box beam type.

1.3.3 Landing Gear

The landing gear is used to support an aircraft during landing and while it is on the ground. Small aircraft flying at low speeds generally have fixed gear. On the other hand, faster and more complex aircraft have retractable landing gear. To avoid parasite drag forces, the landing gear is retracted into the fuselage or wings after take‐off.

1.3.4 Control Surfaces

Since an aircraft is free to rotate around three mutually perpendicular axes (longitudinal, transverse, and vertical) intersecting at its center of gravity (CG), a pilot must be able to control rotation about each of these axes to control overall position and direction of the aircraft. Aircraft flight control surfaces are aerodynamic devices that allow a pilot to maneuver and control the aircraft's flight in midair. As shown in Figure 1.4, there are three basic control surfaces, namely aileron, rudder, and elevator. Rotation about the transverse axis, defined by the line that passes through an aircraft from wingtip to wingtip, is called pitch. The elevators are the major control surfaces for pitch. Ailerons control the rotation about the longitudinal axis, called roll. This axis passes through the aircraft from nose to tail. The rotation about the vertical axis is called yaw, and the primary control of yaw is done with the rudder.

1.4 AIRCRAFT MATERIALS

Traditional metallic materials used in aircraft structures are aluminum, titanium, and steel alloys. In the past three decades, applications of advanced fiber composites have rapidly gained momentum. To date, some new commercial jets, such as the Boeing 787, already contain composite materials up to 50% of their structural weight.

Selection of aircraft materials depends on many considerations that can, in general, be categorized as cost and structural performance. Cost includes initial material cost, manufacturing cost, and maintenance cost. The key material properties that are pertinent to maintenance cost and structural performance are as follows:

Density (weight)

Stiffness (Young's modulus)

Strength (ultimate and yield strengths)

Durability (fatigue)

Damage tolerance (fracture toughness and crack growth)

Corrosion.

Seldom is a single material able to deliver all desired properties in all components of the aircraft structure. A combination of various materials is often necessary. Table 1.1 lists the basic mechanical properties of some metallic aircraft structural materials.

1.4.1 Steel Alloys

Among the three metallic materials, steel alloys have highest densities, and are used only where high strength and high yield stress are critical. Examples include landing gear units and highly loaded fittings. The high strength steel alloy 300 M is commonly used for landing gear components. This steel alloy has a strength of 1.9 GPa (270 ksi) and a yield stress of 1.5 GPa (220 ksi).

Besides being heavy, steel alloys are generally poor in corrosion resistance. Components made of these alloys must be plated for corrosion protection.

Table 1.1Mechanical properties of metals at room temperature in aircraft structures.

Material

Property

a

E

v

σ

u

σ

Y

ρ

GPa (msi)

MPa (ksi)

MPa (ksi)

g/cm

3

(lb/in

3

)

Aluminum

2024‐T3

72 (10.5)

0.33

449 (65)

324 (47)

2.78 (0.10)

7075‐T6

71 (10.3)

0.33

538 (78)

490 (71)

2.78 (0.10)

Titanium

Ti‐6Al‐4V

110 (16.0)

0.31

925 (134)

869 (126)

4.46 (0.16)

Steel

AISI4340

200 (29.0)

0.32

1790 (260)

1483 (212)

7.8 (0.28)

300 M

200 (29.0)

0.32

1860 (270)

1520 (220)

7.8 (0.28)

aσu, tensile ultimate stress; σY, tensile yield stress.

1.4.2 Aluminum Alloys

Aluminum alloys have played a dominant role in aircraft structures for many decades. They offer good mechanical properties with low weight. Among the aluminum alloys, the 2024 and 7075 alloys are perhaps the most used. The 2024 alloys (2024‐T3, T42) have excellent fracture toughness and slow crack growth rate as well as good fatigue life. The code number following T for each aluminum alloy indicates the heat treatment process. The 7075 alloys (7075‐T6, T651) have higher strength than the 2024 but lower fracture toughness. The 2024‐T3 is used in the fuselage and lower wing skins, which are prone to fatigue due to applications of cyclic tensile stresses. For the upper wing skins, which are subjected to compressive stresses, fatigue is less of a problem, and 7075‐T6 is used.

The recently developed aluminum lithium alloys offer improved properties over conventional aluminum alloys. They are about 10% stiffer and 10% lighter and have superior fatigue performance.

1.4.3 Titanium Alloys

Titanium such as Ti–6Al–4V (the number indicates the weight percentage of the alloying element) with a density of 4.5 g/cm3 is lighter than steel (7.8 g/cm3) but heavier than aluminum (2.7 g/cm3). See Table 1.1. Its ultimate and yield stresses are almost double those of aluminum 7075‐T6. Its corrosion resistance in general is superior to both steel and aluminum alloys. While aluminum is usually not for applications above 350 °F, titanium, on the other hand, can be used continuously up to 1000 °F.

Titanium is difficult to machine, and thus the cost of machining titanium parts is high. Near net shape forming is an economic way to manufacture titanium parts. Despite its high cost, titanium has found increasing use in military aircraft. For instance, the F‐15 contained 26% (structural weight) titanium.

1.4.4 Fiber‐Reinforced Composites