Solution Manual for: Solutions Manual Elasticity: Theory, Applications and Numerics Fourth Edition By Martin H. Sadd, Complete All chapters Already Graded A+.

, Solutions Manual
Elasticity: Theory, Applications and Numerics
Fourth Edition
By

Martin H. Sadd
Professor Emeritus
Department of Mechanical Engineering
University of Rhode Island
Kingston, Rhode Island




Foreword

Exercises found at the end of each chapter are an important ingredient of the text as they
provide homework for student engagement, problems for examinations, and can be used
in class to illustrate other features of the subject matter. This Solutions Manual is
intended to aid the instructors in their own particular use of the exercises. Review of the
solutions should help determine which problems would best serve the goals of
homework, exams or be used in class. As a courtesy to instructors who feel that students
should work homework exercises on their own, we ask instructors not to electronically
post or distribute entire solutions.

The author is committed to continual improvement of engineering education and
welcomes feedback from users of the text and solutions manual. Please feel free to send
comments concerning suggested improvements or corrections to .
Such feedback will be shared with the text user community via the publisher’s web site.

Martin H. Sadd
March 2020

,1.1.

(a) aii  a11  a 22  a33  1  4  1  6 (scalar)
aij aij  a11 a11  a12 a12  a13 a13  a 21 a 21  a 22 a 22  a 23 a 23  a31 a31  a32 a32  a33 a33
 1  1  1  0  16  4  0  1  1  25 (scalar)
1 1 1 1 1 1  1 6 4

aij a jk  0 4 2 0 4 2   
0 18 10
 (matrix)

0 1 1 
0 1 1  0 5 3
 
3


4
aij b j  ai1b1  ai 2 b2  ai 3 b3  (vector)

2

aij bi b j  a11b1b1  a12 b1b2  a13 b1b3  a 21b2 b1  a 22 b2 b2  a 23 b2 b3  a31b3 b1  a32 b3 b2  a33 b3 b3
 1  0  2  0  0  0  0  0  4  7 (scalar)
b1b1
 b1b2 b1b3   1 0 2

bi b j  
b2 b1 b2 b2  
b2 b3   0 0 0 (matrix)

b3 b1
 b3 b2 b3 b3    2 0 4 
bi bi  b1b1  b2 b2  b3 b3  1  0  4  5 (scalar)

(b) aii  a11  a22  a33  1  2  2  5 (scalar)
aij aij  a11a11  a12 a12  a13 a13  a21a21  a22 a22  a23 a23  a31a31  a32 a32  a33 a33
 1  4  0  0  4  1  0  16  4  30 (scalar)
1 2 0 1 2 0 
 1 6 2

aij a jk  0 2 1  
0 2 1    0 8 4
 (matrix)

0 4 2  
0 4 2
  
0 16 8

4


3
aij b j  ai1b1  ai 2 b2  ai 3b3  (vector)

6

aij bi b j  a11b1b1  a12 b1b2  a13b1b3  a21b2 b1  a22 b2 b2  a23b2 b3  a31b3b1  a32 b3b2  a33b3b3
 4  4  0  0  2  1  0  4  2  17 (scalar)
b1b1 b1b2
 b1b3   4 2 2

bi b j  
b2 b1 b2 b2  
b2 b3  2 1 1 (matrix)

b3b1 b3b2
 b3b3  2 1 1 
bi bi  b1b1  b2 b2  b3b3  4  1  1  6 (scalar)

, (c) aii  a11  a 22  a33  1  0  4  5 (scalar)
aij aij  a11a11  a12 a12  a13 a13  a 21a 21  a 22 a 22  a 23 a 23  a31a31  a32 a32  a33 a33
 1  1  1  1  0  4  0  1  16  25 (scalar)
1 1 1 1 1 1  2 2 7
aij a jk  1 0 2 1 0 2   1 3 9
 (matrix)

0 1 4 
0 1 4  1 4 18 
2


1
aij b j  ai1b1  ai 2 b2  ai 3b3  (vector)

1

aij bi b j  a11b1b1  a12 b1b2  a13b1b3  a 21b2 b1  a 22 b2 b2  a 23b2 b3  a31b3b1  a32 b3b2  a33b3b3
 1  1  0  1  0  0  0  0  0  3 (scalar)
b1b1 b1b2
 b1b3   1 1 0

bi b j  
b2 b1 b2 b2  
b2 b3  1 1 0 (matrix)

b3b1 b3b2
 b3b3  0 0 0 
bi bi  b1b1  b2 b2  b3b3  1  1  0  2 (scalar)


(d) aii  a11  a 22  a33  1  2  0  3 (scalar)
aij aij  a11a11  a12 a12  a13 a13  a 21a 21  a 22 a 22  a 23 a 23  a31a31  a32 a32  a33 a33
 1  0  0  0  4  1  0  9  0  15 (scalar)
1 0 0 1 0 0  1 0 0
aij a jk  0 2 1 0 2 1   0 7 3
 (matrix)

0 3 1 
0 3 1  0 9 4 
1


0
aij b j  ai1b1  ai 2 b2  ai 3b3  (vector)

0

aij bi b j  a11b1b1  a12 b1b2  a13b1b3  a 21b2 b1  a 22 b2 b2  a 23b2 b3  a31b3b1  a32 b3b2  a33b3b3
 1  0  0  0  0  0  0  0  0  1 (scalar)
b1b1 b1b2
 b1b3   1 0 1

bi b j  
b2 b1 b2 b2  
b2 b3  0 0 0 (matrix)

b3b1 b3b2
 b3b3  1 0 1 
bi bi  b1b1  b2 b2  b3b3  1  0  1  2 (scalar)