Elasticity: Theory, Applications, and Numerics – Solution Manual (5th Edition) by Sadd | Complete Worked Solutions for Engineering Elasticity

ALL 16 CHAPTERS COVERED




SOLUTIONS MANUAL

,Table of contents
Part 1: Foundations and elementary applications

1. Mathematical Preliminaries

2. Deformation: Displacements and Strains

3. Stress and Equilibrium

4. Material Behavior – Linear Elastic Solids

5. Formulation and Solution Strategies

6. Strain Energy and Related Principles

7. Two-Dimensional Formulation

8. Two-Dimensional Problem Solution

9. Extension, Torsion, and Flexure of Elastic Cylinders

Part 2: Advanced applications

10. Complex Variable Methods

11. Anisotropic Elasticity

12. Thermoelasticity

13. Displacement Potentials and Stress Functions: Applications to Three-Dimensional Problems

14. Nonhomogeneous Elasticity

15. Micromechanics Applications

16. Numerical Finite and Boundary Element Methods

,1


1-1.

(a) aii = a11 + a22 + a33 = 1 + 4 + 1 = 6 (scalar)
aij aij = a11a11 + a12 a12 + a13 a13 + a21a21 + a22 a22 + a23 a23 + a31a31 + a32 a32 + a33 a33
= 1 + 1 + 1 + 0 + 16 + 4 + 0 + 1 + 1 = 25 (scalar)
1 1 11 1 1 1 6 4 
a a = 0 4 20 4 2 = 0 18 10 (matrix)
ij jk     
0 1 10 1 1 0 5 3 
3
a b = a b + a b + a b = 4 (vector)
ij j i1 1 i2 2 i3 3  
2
aij bib j = a11b1b1 + a12b1b2 + a13b1b3 + a21b2b1 + a22b2b2 + a23b2b3 + a31b3b1 + a32b3b2 + a33b3b3
= 1+ 0 + 2 + 0 + 0 + 0 + 0 + 0 + 4 = 7 (scalar)
b1b1 b1b2 b1b3  1 0 2
b b = b b b b b b  = 0 0 0 (matrix)
2 3  
i j  2 1 2 2

b3b1 b3b2 b3b3  2 0 4
bibi = b1b1 + b2b2 + b3b3 = 1 + 0 + 4 = 5 (scalar)

(b) aii = a11 + a22 + a33 = 1 + 2 + 2 = 5 (scalar)
aij aij = a11a11 + a12 a12 + a13a13 + a21a21 + a22 a22 + a23a23 + a31a31 + a32 a32 + a33a33
= 1+ 4 + 0 + 0 + 4 +1+ 0 +16 + 4 = 30 (scalar)
1 2 01 2 0 1 6 2
a a = 0 2 10 2 1 = 0 8 4 (matrix)
ij jk     
0 4 20 4 2 0 16 8
4
a b = a b + a b + a b = 3 (vector)
ij j i1 1 i2 2 i3 3  
6
aijbib j = a11b1b1 + a12b1b2 + a13b1b3 + a21b2b1 + a22b2b2 + a23b2b3 + a31b3b1 + a32b3b2 + a33b3b3
= 4 + 4 + 0 + 0 + 2 +1+ 0 + 4 + 2 = 17 (scalar)
b1b1 b1b2 b1b3  4 2 2
b b = b b b b b b  = 2 1 1 (matrix)
2 3  
i j  2 1 2 2
b3b1 b3b2 b3b3  2 1 1
bibi = b1b1 + b2b2 + b3b3 = 4 +1+1 = 6 (scalar)




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, 2


(c) aii b = ba11 b + ba22 b + ba33 b = b1b+ b0 b+ b4 b= b5 b(scalar)
aij baij b = ba11a11 b + ba12 ba12 b + ba13a13 b + ba21a21 b + ba22 ba22 b + ba23a23 b + ba31a31 b + ba32 ba32 b + ba33a33
= b1+1+1+1+ b0 b+ b4 b+ b0 b+1+16 b= b25 b(scalar)
1 1 11 1 1 2 2 7 b
a b a = b1 0 21 0 2 b= b1 3 9 b b (matrix)
ij b     
b jk
0 1 40 1 4 1 4 b b 18
2
a b b b = ba b b b + ba b b b + ba b b b = b1 b (vector)
ij i1 i b2 i3 b 3  b 
b b1 b 2
bj
1
aijbibbj b = ba11b1b1 b+ ba12b1b2 b + ba13b1b3 b + ba21b2b1 b + ba22b2b2 b + ba23b2b3 b + ba31b3b1 b + ba32b3b2 b + ba33b3b3
= b1+1+ b0 b+1+ b0 b+ b0 b+ b0 b+ b0 b+ b0 b= b3 b(scalar)
b1b1 b1b2 b1b3 b 1 1 0  b 
b bb b = bb b b b bb b bb b = b 1 1 0 b (matrix)
i b b j b 2 b 1 2 2 b 3 b  
b 2
b3b1 b3b2 b3b3 b 0 0 0
bibi b = bb1b1 b + bb2b2 b + bb3b3 b = b1+1+ b0 b= b2 b(scalar)



1-2.
1 1
(a) aij b = b (aij b + ba bji b) b+ b (aij b − ba bji b)
2b 2b
2 1 1  b0 1 1
= b 1 8 3 b+ b −1 0 1
1b 1b

2 b  2 b 
1 3 2 −1 −1 0
clearlya(ij b) b and b a[ij b] b satisfy bthe bappropriate bconditions

1 1
=b + a ) b+ b − a bji b)
(b) aij b
(a bji b(a

2 ij 2 ij
1b2 2 0 1bb 0 2 0 b 
= b 2 4 5 b+ b − b2 0 − b3
2 b  2 b 
0 5 4  3 0 b 
b 0
clearlya(ij b) b and b a[ij b] b satisfy bthe bappropriate bconditions




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