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The Behavior of
, ~# Y9 b0 c0 J5 ZStructures Composed of
$ [, f, t$ q) A" m* RComposite Materials
/ {: ~' g( X3 i# p6 A2 H5 M$ Y4 f4 kSecond Edition
/ y+ t( P$ `0 @# d1 t* Yby
0 ~7 F2 c' j2 X4 `" FJACK R. VINSON7 a: ~# {8 @$ ^' O' a
H. Fletcher Brown Porfessor of Mechanical & Aerospace Engineering,2 @1 |& y+ k7 j, Q5 \) w# l
The Center for Composite Materials and The College of Marine Studies,
x- H5 a& @0 I( u% B: fDepartment of Mechanical Engineering,7 K+ }" h" G; e# `0 [
University of Delaware,. g" v" i r- \, {% x; K
Newark, Delaware, U.S.A.8 N, D0 n; w/ I/ B# V& d7 [$ h5 Y
and, p& m- S/ s0 I5 Q
ROBERT L. SIERAKOWSKI, E( i+ b4 @* c
Chief Scientist,
( `2 a) c+ _( ?7 E( l" `2 {AFRL/MN Eglin AFB,
/ \& t& _+ {2 AFlorida, U.S.A.
5 T+ x# Q, {- \1 r9 S# F
4 o! v; J4 i( z. a$ e5 A( _) f X4 T2 i7 ?
$ o+ l- U/ U) n5 V# ]% ~
Contents/ r k, q9 y+ P$ @5 ]; e) y. W
0 e1 N! M4 \ d; |. F3 V- h1. Introduction to Composite Materials 1' C+ G0 O v) k4 {/ z6 W
q2 c2 S+ x* @, w) G. uGeneral History
8 G+ K9 o1 D% {+ XComposite Material Description* K5 ~6 N8 \& ?: D* V
Types of Composite Materials7 S# C0 F6 R% P9 J
Constituent Properties
2 W( t( V& j* oComposite Manufacturing, Fabrication and Processing/ R9 h! i& U' {
Uses of Composite Materials. v3 @0 q1 g* Y5 h
Design and Analyses with Composite Materials
; ?! i$ y7 ]5 r4 U4 z; u: gReferences3 j; H5 h1 @& x5 f ]
Journals7 L3 ^5 }) N6 U) Y
Problems& x; ?' H2 P7 x( Q; P- U
6 r9 M1 ^; P2 C/ p9 g2. Anisotropic Elasticity and Composite Laminate Theory: }1 z3 R& T! A w- C! _
7 G, ?* g. w9 sIntroduction P/ E% I& } W2 a
Derivation of the Anisotropic Elastic Stiffness and Compliance Matrices4 h6 R- v: k# a) P2 t( t
The Physical Meaning of the Components of the Orthotropic Elasticity, P. D. Z9 J- a2 K
Tensor
$ q, D0 r8 X) X- F' F0 I8 \' ]$ ?Methods to Obtain Composite Elastic Properties from Fiber and Matrix6 y$ i' o% D1 o. n( S
Properties/ L2 x7 O8 P" j
Thermal and Hygrothermal Considerations0 @5 G+ {7 l& O$ W
Time-Temperature Effects on Composite Materials7 z6 p! }. X$ N# _
High Strain Rate Effects on Material Properties7 ^8 x! s& u5 B, z
Laminae of Composite Materials
$ }( {5 r7 C T, `3 X" ELaminate Analyses
6 H/ N! b7 U' M9 s" ^7 gPiezoelectric Effects
& C4 I5 I& p/ d* z A% ZReferences
- M$ l" b$ o- a Y D- @Problems
% w3 Q6 W7 ^, w6 E& y
' O" p8 r. B* _4 s3. Plates and Panels of Composite Materials1 l2 q* w( j" m
. o& B: U2 u, u I! [Introduction
3 o' L/ k, M% p: T3 r0 A; `/ b' N9 HPlate Equilibrium Equations- P; }3 } w& t: `
The Bending of Composite Material Laminated Plates: Classical Theory
) _, M7 s( k; X" mClassical Plate Theory Boundary Conditions( ]5 b; O! N V3 [! d, f& r
Navier Solutions for Rectangular Composite Material Plates
$ J! a( M/ E5 ^8 f# pNavier Solution for a Uniformly Loaded Simply Supported Plate – An
q5 E% l. h9 t* f$ cExample Problem* c1 t( T4 E7 T: g
Levy Solution for Plates of Composite Materials
0 g2 u3 V- |: X& C& V! q. d; B/ J+ x3 Q' \
Perturbation Solutions for the Bending of a Composite Material Plate With
, ?5 c" K7 P8 y/ |: l: _) g2 J2 r1 HMid-Plane Symmetry and No Bending-Twisting Coupling
' I: L! {4 q3 @, _! NQuasi-Isotropic Composite Panels Subjected to a Uniform Lateral Load8 N! B& J+ ? z4 k: r9 v5 I5 D
A Static Analysis of Composite Material Panels Including Transverse* J* |; i& ] R9 D" v8 b; M1 |; h
Shear Deformation Effects
% c1 i2 r: W3 }7 D8 C5 L/ y aBoundary Conditions for a Plate Using the Refined Plate Theory Which9 w& t8 e& f4 t- E+ ^; Z' z7 ]
Includes Transverse Shear Deformation+ ^6 X* g# @& }! r& h
Composite Plates on an Elastic Foundation- k) I, D% g* A8 M. T
Solutions for Plates of Composite Materials Including Transverse-Shear
! j& O+ P1 h& }7 }& Y% ?Deformation Effects, Simply Supported on All Four Edges
* O7 f3 H9 H9 C/ H0 C* q0 h+ L' {, `Dynamic Effects on Panels of Composite Materials: t0 S* g; d0 k; ]
Natural Flexural Vibrations of Rectangular Plates: Classical Theory P) n* R/ P- \8 T, A" v
Natural Flexural Vibrations of Composite Material Plate Including
) ?1 {' p1 X/ `$ xTransverse-Shear Deformation Effects
3 I# o6 G( V2 `! b+ q' @Forced-Vibration Response of a Composite Material Plate Subjected to a
: C: w% `! k" M# A+ O5 T l; qDynamic Lateral Load3 N M) ~) x0 u% a2 |( N. o1 e
Buckling of a Rectangular Composite Material Plate – Classical Theory$ B6 o0 F+ @4 |$ l9 {
Buckling of a Composite Material Plate Including Transverse-Shear z( y) _1 P0 n- [$ J
Deformation Effects
5 S* @' w1 E1 {# J$ B- C7 _5 ~9 NSome Remarks on Composite Structures9 x! a1 N3 u3 s5 R1 w9 p" ]
Methods of Analysis for Sandwich Panels With Composite Material
* D* Y+ T3 t" zFaces, and Their Structural Optimization3 R3 B, \9 s' y% }8 }
Governing Equations for a Composite Material Plate With Mid-Plane6 m# Z/ ]% k8 M# a: J& \
Asymmetry3 u, s: c- c4 H2 F' }9 Y& x/ w4 R
Governing Equations for a Composite Material Plate With Bending-( Y" x' D% \7 b7 }: A0 x% |2 k; g( D
Twisting Coupling/ A5 X6 Z: g! o- j {
Concluding Remarks; a; Z$ ^* L0 w* l D
References- X4 h. G( z: [* X. |( A7 x! K5 {% x
Problems and Exercises8 H7 _" m& F7 E5 \
: U* Z8 s n$ A7 ~$ E: d. B7 E) _
4. Beams, Columns and Rods of Composite Materials6 I6 X |3 e. `: @8 Z8 Y
* R# F$ f% Q1 S2 DDevelopment of Classical Beam Theory
^+ F, p# M/ }$ _ kSome Composite Beam Solutions
$ w6 R. i* Q5 J o2 jComposite Beams With Abrupt Changes in Geometry or Load3 d8 w1 G( ]9 i: W5 F
Solutions by Green’s Functions/ ]( B: T4 P! b& K
Composite Beams of Continuously Varying Cross-Section
" a" Y' J, }1 x+ ~; pRods, D* E7 ]" [! o( B4 {
Vibration of Composite Beams
5 z- M% g1 V) mBeams With Mid-Plane Asymmetry
* O9 R; X7 H0 ?3 @6 }; YAdvanced Beam Theory for Dynamic Loading Including Mid-Plane. P4 M) v6 @5 _* _" }! p
Asymmetry9 d) ?4 s+ x" P4 |( f3 t3 z
Advanced Beam Theory Including Transverse Shear Deformation Effects! V+ {; b3 Z" d/ \* z4 q4 C
Buckling of Composite Columns
5 W- ]0 {, V9 i( h* g* D4 E; E/ W9 MReferences1 N# z Q2 O8 ^
Problems
9 h" D( f0 w+ [4 m, w# Q- T; x
3 e% V0 y1 M+ M% {5 o, L& l* k" f" a- e+ P% v9 p) G* C+ d
5. Composite Material Shells
7 Q E+ h1 L6 `+ ~+ H. N9 S4 j
8 R" a/ d9 x: g* j" y6 ?Introduction& ?. r1 }; { r4 M$ M& g7 L
Analysis of Composite Material Circular Cylindrical Shells
: q; E2 S- ^( C1 E% S+ aSome Edge Load and Particular Solutions
- Z5 X4 e- v. L( v1 a, a3 IA General Solution for Composite Cylindrical Shells Under Axially \2 `9 B3 \/ w
Symmetric Loads4 I6 J! t! |) A5 I" _, u2 t3 N! T
Response of a Long Axi-Symmetric Laminated Composite Shell to an8 ?1 t( @1 J, O* g* s+ S4 ^# ~% m
Edge Displacement
4 n/ |5 P# T3 l* WSample Solutions
* y# Y# M7 j4 _" C0 U6 a, |7 O/ _Mid-Plane Asymmetric Circular Cylindrical Shells4 y. `/ h: ~& ?- Z3 w) G
Buckling of Circular Cylindrical Shells of Composite Materials Subjected
, \6 m% L8 M6 v6 e4 g! Wto Various Loads; }4 u [9 A% R: \( m7 k
Vibrations of Composite Shells) P7 `' D3 k$ S
Additional Reading On Composite Shells
7 N) Q0 Z/ P) C8 P6 b+ aReferences
- T' m! |3 }" p0 C9 K0 G- zProblems
! T6 p4 \/ _# D+ I9 N& v1 C6 i% d- v( Y/ x
! h, l0 B2 |' B9 ^. W, l) Z6. Energy Methods For Composite Material Structures
! m' [- _- z9 F" K. T& L2 |( x- c- Y1 M9 k1 o9 {8 i2 k; P
Introduction4 I0 C& S2 e9 J9 ]! Q
Theorem of Minimum Potential Energy. L! N2 z+ n9 h( \3 H0 I1 i
Analysis of a Beam Using the Theorem of Minimum Potential Energy! c N+ ?. E2 } X: ~& z# i8 A
Use of Minimum Potential Energy for Designing a Composite Electrical
- y6 K8 d. F6 h( |: F$ F+ H" ?Transmission Tower
( I2 \, Q* O- q- vMinimum Potential Energy for Rectangular Plates
, N3 t( j8 `: d' F+ CA Rectangular Composite Material Plate Subjected to Lateral and* t9 _, D/ ~( r; j R5 @& N
Hygrothermal Loads; p, h+ _- h( d( n
In-Plane Shear Strength Determination of Composite Materials in4 x" p/ r4 ^( M/ u" U
Laminated Composite Panels$ m5 |, A- y8 |- s: T
Use of the Theorem of Minimum Potential Energy to Determine Buckling: V2 X; ^6 g! \: W0 \' s1 x% E& h( M
Loads in Composite Plates
+ V& g* T8 Z/ B# j2 L. n9 KTrial Functions for Various Boundary Conditions for Composite Material4 G7 } F7 b/ c( ~" C+ g
Rectangular Plates: Y. u$ K9 N. y6 h
Reissner’s Variational Theorem and its Applications+ }9 p% W, S/ y8 P; B2 ~9 P- y6 Q
Static Deformation of Moderately Thick Beams5 B6 w9 S! V2 P% p: @2 B/ c
Flexural Vibrations of Moderately Thick Beams
$ R6 Y" T4 @7 u& F( _Flexural Natural Frequencies of a Simply Supported Beam Including: E. N! R7 B9 ^" K' Z
Transverse Shear Deformation and Rotatory Inertia Effects
+ @9 D- a2 d% l! Z. h) ?# l. tReferences$ S- \6 A5 y+ @5 k$ |6 k
Problems( s+ c: a- \# Z. p- k, S
6 A1 f M, \' u# ~9 f7. Strength and Failure Theories
# Q% t4 J0 w* ^# }% y# j( I/ u& b( L& I1 ?& L2 [: f
Introduction& ^) U' x6 G. l
Failure of Monolithic Isotropic Materials4 v' z, ^* O" k/ n. e4 s! q9 G# V
Anisotropic Strength and Failure Theories
8 n( F0 O5 U: H+ E* H. }Maximum Stress Theory
0 v: r/ f" m' y4 Z9 u5 ^) f# W$ }Maximum Strain Theory
, w& K( f+ i; u& b& GInteractive Failure Theories) D& y8 q- l. u6 h7 Q: N
Lamina Strength Theories
' _% k( X7 x H3 }9 B! JLaminate Strength Analysis
6 [' E3 O* L8 X: }! E1 C5 W1 ~References- g1 {7 d, G! S% n3 {2 r
Problems, p1 d) M5 j7 b; G1 S
( e) S/ V8 V# H8 e/ H& o, u2 U! s$ s/ w+ [
8. Joining of Composite Material Structures
; _& H2 p& v3 g0 q9 ]/ t
! B' l4 e- [5 [) KGeneral Remarks( m; f3 b& c0 d. _4 U0 H7 g
Adhesive Bonding. C. e% }' H1 m/ g4 D2 Z7 p
Mechanical Fastening. z6 x% J8 W" h8 `$ F' x: z4 g
Recommended Reading
: S$ `, ~/ ?, p$ QReferences
% Z; ^+ \$ i. ]7 S; e! y& `Problems* J( Y& G* n8 n T* t4 i
4 b6 E# o0 g+ I3 X" k% @, z$ J6 s# P; O2 r; @! N
9. Introduction to Composite Design: U6 @1 `& l4 h
& X: q- M; R. oIntroduction
( ^8 u4 D! F I) s3 ?4 l9 l4 g' c* RStructural Composite Design Procedures2 k" \/ Z' M- J' W9 n, p4 H
Engineering Analysis* _) Z9 ^: I" @( k! Y1 P
Appendices
9 o9 b+ z- j& {: E/ A6 h
) L2 H* N* `0 O1 k' d2 d5 `- S& S+ S: n) l3 K
Micromechanics2 w' V* n+ P. l( @- R
Test Standards for Polymer Matrix Composites
7 }" `' B+ X2 Y7 {/ c* nProperties of Various Polymer Composites F. I% P# }# y3 [0 G9 Z
Author Index; Z& B# ]2 X6 i
Subject Index1 e: A6 l$ y: a+ J8 e3 h# \
?# r% o p* v' q
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