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 Elasticitẙ
12. Thermoelasticitẙ
13. . Displacement Potentials and Stress Functions: Applications to Three-Dimensional Problems
14. Nonhomogeneous Elasticitẙ
15. . Micromechanics Applications
16. Numerical Finite and Boundarẙ Element Methods
,1
1-1.
(a) aii a11 a22 a33 1 4 1 6 (scalar)
aij a ij a11a11 a12 a12 a13 a13 a21a21 a22 a22 a23 a23 a31a31 a32 a32 a33 a3
1 1 1 0 16 4 0 1 1 25 (scalar)
⎡1 1 1⎤⎡1 1 1 ⎤ ⎡1 6 4 ⎤
⎢ ⎥⎢ ⎥ ⎢ ⎥
aij a jk 4 4 18 10⎥ (matrix)
⎢0 2⎥⎢ 2⎥
0 ⎢0
⎢⎣0 1 1⎥⎦ ⎢⎣0 1⎥ ⎢⎣0 3 ⎥⎦
⎦
1 5
⎡ 3⎤
⎢ ⎥
aij b j ai1b1 ai 2 b 2 ai3 b3 ⎢4⎥ (vector)
⎢⎣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 b1b b1b3 ⎤ ⎡1 0 2⎤
⎢ 2 ⎥ ⎢ ⎥
bi b j b2b b2 b3 0 0⎥ (matrix)
⎢b2 b1
2
⎥
⎢0
⎢⎣b3 b1 b3b b3b3 ⎢⎣2 4⎥⎦
2 ⎥⎦
0
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⎤⎡ 2 0⎤ ⎡1 6 2⎤
⎢ 1 ⎥ ⎢ ⎥
⎥⎢
a ij a jk 2 2 1⎥ 4⎥ (matrix)
⎢0 1⎥⎢ ⎢0 8
0
⎢⎣0 4 4 2⎥⎦ ⎢⎣0 8⎥⎦
2⎥⎦ ⎢ ⎡ 4⎤ 16
⎣0 ⎢ ⎥
a ij b j ai1b1 ai 2b2 ai3b3 ⎢3 ⎥ (vector)
, 2
⎢⎣6⎥⎦
aijbib j a11b1b1 a12b1b2 a13b1b3 a21b2b1 a22b2b2 a23b2b3 a31b3b1 a32b3b2
a33b3b3
4 4 0 0 2 1 0 4 2 17 (scalar)
⎡b1b1 b1b b1b3 ⎤ ⎡4 2 2⎤
⎢ 2 ⎥ ⎢ ⎥
bibj b2b b2b3 ⎥ 1⎥ (matrix)
⎢b2b1 ⎢2
2
1
⎢⎣b3 b1 b3b b3b3 ⎢⎣2 1⎥⎦
2 ⎥⎦
1
bibi b1b1 b2b2 b3b3 4 1 1 6 (scalar)
Copyright © 2009, Elsevier Inc. All rights reserved.
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 Elasticitẙ
12. Thermoelasticitẙ
13. . Displacement Potentials and Stress Functions: Applications to Three-Dimensional Problems
14. Nonhomogeneous Elasticitẙ
15. . Micromechanics Applications
16. Numerical Finite and Boundarẙ Element Methods
,1
1-1.
(a) aii a11 a22 a33 1 4 1 6 (scalar)
aij a ij a11a11 a12 a12 a13 a13 a21a21 a22 a22 a23 a23 a31a31 a32 a32 a33 a3
1 1 1 0 16 4 0 1 1 25 (scalar)
⎡1 1 1⎤⎡1 1 1 ⎤ ⎡1 6 4 ⎤
⎢ ⎥⎢ ⎥ ⎢ ⎥
aij a jk 4 4 18 10⎥ (matrix)
⎢0 2⎥⎢ 2⎥
0 ⎢0
⎢⎣0 1 1⎥⎦ ⎢⎣0 1⎥ ⎢⎣0 3 ⎥⎦
⎦
1 5
⎡ 3⎤
⎢ ⎥
aij b j ai1b1 ai 2 b 2 ai3 b3 ⎢4⎥ (vector)
⎢⎣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 b1b b1b3 ⎤ ⎡1 0 2⎤
⎢ 2 ⎥ ⎢ ⎥
bi b j b2b b2 b3 0 0⎥ (matrix)
⎢b2 b1
2
⎥
⎢0
⎢⎣b3 b1 b3b b3b3 ⎢⎣2 4⎥⎦
2 ⎥⎦
0
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⎤⎡ 2 0⎤ ⎡1 6 2⎤
⎢ 1 ⎥ ⎢ ⎥
⎥⎢
a ij a jk 2 2 1⎥ 4⎥ (matrix)
⎢0 1⎥⎢ ⎢0 8
0
⎢⎣0 4 4 2⎥⎦ ⎢⎣0 8⎥⎦
2⎥⎦ ⎢ ⎡ 4⎤ 16
⎣0 ⎢ ⎥
a ij b j ai1b1 ai 2b2 ai3b3 ⎢3 ⎥ (vector)
, 2
⎢⎣6⎥⎦
aijbib j a11b1b1 a12b1b2 a13b1b3 a21b2b1 a22b2b2 a23b2b3 a31b3b1 a32b3b2
a33b3b3
4 4 0 0 2 1 0 4 2 17 (scalar)
⎡b1b1 b1b b1b3 ⎤ ⎡4 2 2⎤
⎢ 2 ⎥ ⎢ ⎥
bibj b2b b2b3 ⎥ 1⎥ (matrix)
⎢b2b1 ⎢2
2
1
⎢⎣b3 b1 b3b b3b3 ⎢⎣2 1⎥⎦
2 ⎥⎦
1
bibi b1b1 b2b2 b3b3 4 1 1 6 (scalar)
Copyright © 2009, Elsevier Inc. All rights reserved.
