Opto-structural Analysis

486 Pages·2018·80.888 MB·English

by  John W. Pepi

OPTO-STRUCTURAL ANALYSIS
John Pepi
ADDENDA and CORRIGENDA to First Printing of SPIE Press Vol. PM288

FRONT MATTER
 Page xv: 16.9.3 External stress relaxation

CHAPTER 1 STRESS AND STRAIN
 Page 3, Eq. (1.7a): E should be 
x x
 Page 3, Eq. (1.7b): E should be 
y y
 Page 8, Table 1.1 Simple support uniform load row, Deflection column:
5WL3/38EI should be 5WL3/384EI
 Page 21, Eq. (1.55): t should be T
 Page 22, directly after Eq. (1.55a), add the following text:
“where t is the ring thickness, b is the ring depth, and the subscripts…”

CHAPTER 3 KINEMATIC MOUNTS
 Page 66, Section 3.3.2, First sentence should be:
“Consider, first, the mount of Fig. 3.4(a) and assume that the flexure is
rigidly attached (no radial pivot) to the optic.”
 Page 78, Eq. (3.43): p2 should be 2

CHAPTER 4 SOLID OPTICS PERFORMANCE
 Page 103, Eq. (4.10): D5 should be R5
 Page 109,second paragraph from bottom: 100 K should be –100 ºC (in two
places)
 Page 111, third equation on the page should be:
1 ΔαΔ𝑇
(cid:3404)
𝑅 𝑡
 Pages 113–114: Example 2 and Figure 4.11 are INCORRECT and should be
eliminated. Example 1 is correct as is.
 Page 115, Example 3: “3-in depth” should be “1-in” depth, and “and
deflection” should be removed from the end of the first paragraph.
1
 Page 115, first sentence of Section 4.5.4: eliminate the inadvertent, misplaced
equation “Y …….λ ” to read:
RMS RMS surface error
When a gradient is diametric across an optic…”
 Page 115, Fig. 4.12 result is correct, but last three entries for z should be:
i
–0.25, –0.35, and –0.45.
 Page 119, last equations are a repeat of Eqs. (1.7a) and (1.7b) (the terms in
parentheses should be in numerator, not the denominator):
ε (cid:3404) (cid:4666)(cid:2978)(cid:3299)(cid:2879)(cid:2973)(cid:2978)(cid:3300)(cid:4667), ε (cid:3404) (cid:4666)(cid:2978)(cid:3300)(cid:2879)(cid:2973)(cid:2978)(cid:3299)(cid:4667)
(cid:3051) (cid:3052)
(cid:3006) (cid:3006)
 Page 123, Eq. (4.53): should be 

 Page 130, Example 4.9.1, first sentence should read:
“A beryllium optic 60 in. in diameter and 2.5 in. deep with a radius of
curvature of 240 in. is brought from room temperature (293 K) to a severe
cryogenic temperature of 100 K that is stabilized with no axial thermal
gradient (uniform soak).”

CHAPTER 5 LIGHTWEIGHT OPTICS: OPTIMIZATION
 Page 143, Example 5.6.1, fourth sentence:
“We find that t = 0.23 in. and a = 2.27 in., with a resulting weight of W =
13.2 lbs.”
 Page 149, Example 2, the equation in Solution a) should be:
(cid:2976)(cid:3005)(cid:3118)(cid:4666)(cid:2868).(cid:2868)(cid:2873)(cid:2869)(cid:4667)
𝑊 (cid:3404) (cid:3404) 16 lbs.
(cid:2872)
 Page 149, Example 3, second sentence should be:
“Under an advanced-polishing flexible-lap technique (a/t = 15), determine
for a 20-in. diameter optic”
 Page 151 Example 4, Second sentence should be:
“Under an advanced-polishing flexible-lap technique (a/t = 15), determine
for a 20-in. diameter optic”

CHAPTER 7 LARGE OPTICS
 Page 181, directly after Eq. (7.2), add the following equation and text:
  = Ka2/t, (7.2a)
s
where K and K are dependent on…”
w s

2
CHAPTER 9 ADHESIVES
 Page 248, text directly after Eq. (9.5) should read:
“where Δε is creep strain, and σ is epoxy stress.”
 Page 266, Eq. (9.18) should be:
(cid:4666)α (cid:3398)α(cid:4667)
(cid:2912) (cid:2922)
𝑡 (cid:3404) 𝑅
(cid:2926) (cid:4666)α (cid:3398)α (cid:4667)
(cid:2915)(cid:2916)(cid:2916) (cid:2912)
 Page 267, fourth equation should be:
(cid:4666)α (cid:3398)α(cid:4667)
(cid:2912) (cid:2922)
𝑡 (cid:3404) 𝑅
(cid:2926) (cid:4666)α (cid:3398)α (cid:4667)
(cid:2915)(cid:2916)(cid:2916) (cid:2912)

CHAPTER 13 PERFORMANCE ANALYSIS OF OPTICAL STRUCTURES
 Page 351, second line of text between Eqs. (13.6) and (13.7) should read:
“We now define N as the number of bays and the overall truss length as
h = L/N.”
 Page 353, first line of last paragraph should read:
“With reference to Table 13.3, we see that for N = 3 and n = 4, the…”
 Page 354, second sentence after Eq. (13.12) should read:
“It is seen that for N = 3 and n = 4, we have an effective CTE of 1.09
ppm/K,…”

CHAPTER 14 NUTS AND BOLTS
 Page 377, Eq. (14.7) should read:
T = 0.2DF for a dry nut and dry thread;
T = 0.15DF for a dry nut and lubricated thread; and
T = 0.13DF for a lubricated nut and lubricated thread.
 Page 382, text directly following Eq. (14.19b) should read:
“where A is the bolt stress area, and A is the effective area of the
b m
compression members, which can be computed, although not
conservatively, as the area under the bolt…”

CHAPTER 15 LINEAR ANALYSIS OF NONLINEAR PROPERTIES
 Page 408, Eq. (15.34) should read:
𝐸 (cid:3404) (cid:1516)(cid:3006)(cid:3167)(cid:2961)(cid:3167)(cid:3031)(cid:3021) (cid:3404) (cid:1516)(cid:3006)(cid:3167)(cid:2961)(cid:3167)(cid:3031)(cid:3021). 
(cid:2929)(cid:2915)(cid:2913)
(cid:1516)(cid:2961)(cid:3167)(cid:3031)(cid:3021) (cid:2961)(cid:3177)(cid:3163)(cid:3161)(cid:2940)(cid:3021)
3
CHAPTER 16 MISCELLANEOUS ANALYSIS
 Page 427, line after Eq. (16.29) should read:
“where p = P/L, and D = K.”
 Page 441 Section 16.9.3 title should read:
External stress relaxation

4

Library of Congress Cataloging-in-Publication Data
Names: Pepi, John W., author.
Title: Opto-structural analysis / John W. Pepi.
Description: Bellingham, Washington, USA : SPIE Press, [2018]
Identifiers:LCCN2018001895|ISBN9781510619333(hardcover)|ISBN151061933X
(hard cover) | ISBN 9781510619340 (PDF) | ISBN 1510619348 (PDF) | ISBN
9781510619357 (ePub) | ISBN 1510619356 (ePub) | ISBN 9781510619364 (Kindle/
Mobi) | ISBN 1510619364 (Kindle/Mobi)
Subjects:LCSH:Opticalinstruments–Designandconstruction.|Opticalengineering.
| Structural analysis (Engineering)
Classification: LCC TS513 .P47 2018 | DDC 621.36–dc23 LC record available at
https://lccn.loc.gov/2018001895
Published by
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Copyright © 2018 Society of Photo-Optical Instrumentation Engineers (SPIE)
All rights reserved. No part of this publication may be reproduced or distributed in
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Thecontentofthisbookreflectstheworkandthoughtoftheauthor.Everyefforthas
beenmadetopublishreliableandaccurateinformationherein,butthepublisherisnot
responsible for the validity of the information or for any outcomes resulting from
reliance thereon.
Printed in the United States of America.
First Printing.
For updates to this book, visit http://spie.org and type “PM288” in the search field.
Contents
Preface xvii
Acknowledgments xix
A Note on Units xxi
1 Stress and Strain 1
1.1 Introduction 1
1.2 Hooke’s Law 1
1.3 Beyond Tension, Compression, and Shear 4
1.3.1 Bending stress 4
1.3.1.1 Combined normal stress 6
1.3.2 Bending deflection 6
1.3.3 Shear stress due to bending 7
1.3.4 Shear deflection due to bending (detrusion) 9
1.3.5 Torsion 10
1.3.5.1 Twist rotation 12
1.3.6 Hooke’s law summary 12
1.4 Combining Stresses 12
1.4.1 Brittle and ductile materials 14
1.5 Examples for Consideration 15
1.6 Thermal Strain and Stress 18
1.6.1 Thermal hoop stress 20
1.6.1.1 Solid disk in ring 22
1.6.2 Ring in ring in ring 23
1.6.2.1 Case study 25
1.6.3 Nonuniform cross-section 26
1.7 Buckling 28
References 29
2 Material Properties 31
2.1 Properties and Definitions 31
2.2 Low-Thermal-Expansion Materials 33
2.2.1 Fused silica 38
2.2.2 ULE® fused silica 39
v