ALL 16 CHAPTERS COVERED
nh nh nh
SOLUTIONS MANUAL
nh
,Table of contents nh nh
Part 1: Foundations and elementary applications
nh nh nh nh nh
1. Mathematical Preliminaries nh
2. Deformation: Displacements and Strains nh nh nh
3. Stress and Equilibrium
nh nh
4. Material Behavior – Linear Elastic Solids
nh nh nh nh nh
5. Formulation and Solution Strategies
nh nh nh
6. Strain Energy and Related Principles
nh nh nh nh
7. Two-Dimensional Formulation nh
8. Two-Dimensional Problem Solution nh nh
9. Extension, Torsion, and Flexure of Elastic Cylinders
nh nh nh nh nh nh
Part 2: Advanced applications
nh nh nh
10. Complex Variable Methods nh nh
11. Anisotropic Elasticity nh
12. Thermoelasticity
13. Displacement Potentials and Stress Functions: Applications to Three-Dimensional Problems
nh nh nh nh nh nh nh nh
14. Nonhomogeneous Elasticity nh
15. Micromechanics Applications nh
16. Numerical Finite and Boundary Element Methods
nh nh nh nh nh
,1
1-1.
(a) aii a11 a22 a33 1 4 1 6 (scalar)
n h
nh
n h
nh
n h
nh
n h
nh nh nh nh nh nh nh nh
aij aij a11a11 a12 a12 a13 a13 a21a21 a22 a22 a23 a23 a31a31 a32 a32 a33 a33
nh n h
nh
n h
nh
nh n h
nh
nh n h
nh
n h
nh
nh n h
nh
nh n h
nh
n h
nh
nh n h
nh
nh
1 1 1 0 16 4 0 1 1 25 (scalar)
nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh
1 1 11 1 1 1 6 4
a a 0 4 20 4 2 0 18 10 (matrix)
nh
nh nh
n h nh nh n h n h n h n h
ij
n h
jk
0 1 10 1 1 0 5 3
n h
nh
3
aa bb a b a
n h n h 4 (vector)
nh n h n h nh n h nh
nh
n h b
ij i1
n h 1 i2 2 i3 3 n h nh n h n h
n h
j
n h
2
aij bib a11b1b1 a12b1b2 a13b1b3 a21b2b1 a22b2b2 a23b2b3 a31b3b1 a32b3b2 a33b3b3
nh
nh nh
n h
nh
n h
nh
n h
nh
n h
nh
n h
nh
n h
nh
n h
nh
n h
nh
j
1 0 2 0 0 0 0 0 4 7 (scalar)
nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh
b1b1 b1b2 b1b3 1 0 2
b b b b b b b b 0 0 0 (matrix)
nh
nh n h
nh n h nh nh nh nh n h nh
i j 2
n h n h 1 2 3 n h
n h nh
n h
2n h 2
b3b1 b3b2 b3b3 2 0 4 nh
bibi b1b1 b2b2 b3b3 1 0 4 5 (scalar)
n h
nh
nh
nh
n h
nh
n h
nh nh nh nh nh nh nh nh
(b) aii a11 a22 a33 1 2 2 5 (scalar)
n h
nh
nh
nh
n h
nh
n h
nh nh nh nh nh nh nh nh
aij aij a11a11 a12 a12 a13a13 a21a21 a22 a22 a23a23 a31a31 a32 a32 a33a33
nh n h
nh
nh
nh
nh n h
nh
n h
nh
nh
nh
nh n h
nh
n h
nh
nh
nh
nh n h
nh
1 4 0 0 4 1 0 16 4 30 (scalar)
nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh
1 2 01 2 0 1 6 2
a a 0 2 10 2 1 0 8 4 (matrix)
n h nh
nh
nh
nh
ij
n h n
jk
0 4 20 4 2 0 1 8
h
n h
46
a b a b a b a b 3 (vector)
n h n h nh n h n h nh n h n h nh n h n h nh
nh
ij i1
n h i2 i3 3 n nh n n h
n h
j
n h 1 2 h h
6
aijbibj a11b1b1 a12b1b2 a13b1b3 a21b2b1 a22b2b2 a23b2b3 a31b3b1 a32b3b2 a33b3b3
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
n h
nh
4 4 0 0 2 1 0 4 2 17
nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh (scalar)
b1b1 b1b2 b1b3 4 2 2
b b b b b b b b 2 1 1 (matrix)
nh
nh nh
nh n h nh nh nh nh n h nh
i j 2
n h n h 1 2 3 n h
n h nh
n h
2n h 2
b3b1 b3b2
b3b3 2 1 1 nh
bibi b1b1 b2b2 b3b3 4 11 6 (scalar)
nh
nh
nh
nh
nh
nh
n h
nh nh nh nh nh
Copyrightnh©n h2009,n h ElseviernhInc.nh Alln h rightsnhreser
ved.
, 2
(c) aii a11 a22 a33 1 0 4 5 (scalar)
n h
nh
nh
nh
n h
nh
n h
nh nh nh nh nh nh nh nh
aij aij a11a11 a12 a12 a13a13 a21a21 a22 a22 a23a23 a31a31 a32 a32 a33a33
nh n h
nh
nh
nh
nh n h
nh
n h
nh
nh
nh
nh n h
nh
nh
nh
nh
nh
nh n h
nh
1 111 0 4 0 116 25 (scalar)
nh nh nh nh nh nh nh nh nh nh
1 1 11 1 1 2 2 7
a a 1 0 21 0 2 1 3 9 (matrix)
nh
nh nh
n h nh nh nh
ij
n h n
jk
0 1 40 1 4 1 4 18
h
n h n h
2
a b a b a b a b 1 (vector)
n h n h nh n h n h nh n h n h nh n h n h nh
nh
ij i1
n h i2 i3 3 n nh n n h
n h
n h j 1 2 h h
1
aijbibj a11b1b1 a12b1b2 a13b1b3 a21b2b1 a22b2b2 a23b2b3 a31b3b1 a32b3b2 a33b3b3
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
n h
nh
1 1 0 1 0 0 0 0 0 3 (scalar)
nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh
b1b1 b1b2 b1b3 1 1 0
b b b b b b b b 1 1 0 (matrix)
nh
nh nh
nh n h nh nh nh nh n h nh
i j 2
n h n h 1 2 3 n h
n h nh
n h
2n h 2
b3b1 b3b2
b3b3 0 0 0 nh
bibi b1b1 b2b2 b3b3 1 1 0 2 (scalar)
nh
nh
nh
nh
nh
nh
n h
nh nh nh nh nh
1-2.
1 1
(a) aij (aij a ji ) (aij a ji )
n h
nh
n h
nh nh
nh
nh nh
n h
nh nh
nh
2 2 nh nh
12 1 1 0 1 1
1 8 3 1 0 1
1 nh
nh nh nh
nh nh
2 nh
2 nh
1 3 2 1 1 0
clearlya(ij ) and a[ij ] satisfy the appropriate conditions
nh n h
n h
nh n h
nh nh nh
1 1
(a a )
nh nh
(a a )
(b) aij
nh nh nh
nh nh
ij ji ij ji nh
2 2
1 2 2 0 1 0 2 0
2 4 5 2 0 3
n h nh
nh nh nh
nh nh nh nh
2 nh
2 nh
0 5 4 3 0 n h
nh
0
clearlya(ij ) and a[ij ] satisfy the appropriate conditions
nh n h
n h
nh n h
nh nh nh
Copyrightnh©n h2009,n h ElseviernhInc.nh Alln h rightsnhreser
ved.
nh nh nh
SOLUTIONS MANUAL
nh
,Table of contents nh nh
Part 1: Foundations and elementary applications
nh nh nh nh nh
1. Mathematical Preliminaries nh
2. Deformation: Displacements and Strains nh nh nh
3. Stress and Equilibrium
nh nh
4. Material Behavior – Linear Elastic Solids
nh nh nh nh nh
5. Formulation and Solution Strategies
nh nh nh
6. Strain Energy and Related Principles
nh nh nh nh
7. Two-Dimensional Formulation nh
8. Two-Dimensional Problem Solution nh nh
9. Extension, Torsion, and Flexure of Elastic Cylinders
nh nh nh nh nh nh
Part 2: Advanced applications
nh nh nh
10. Complex Variable Methods nh nh
11. Anisotropic Elasticity nh
12. Thermoelasticity
13. Displacement Potentials and Stress Functions: Applications to Three-Dimensional Problems
nh nh nh nh nh nh nh nh
14. Nonhomogeneous Elasticity nh
15. Micromechanics Applications nh
16. Numerical Finite and Boundary Element Methods
nh nh nh nh nh
,1
1-1.
(a) aii a11 a22 a33 1 4 1 6 (scalar)
n h
nh
n h
nh
n h
nh
n h
nh nh nh nh nh nh nh nh
aij aij a11a11 a12 a12 a13 a13 a21a21 a22 a22 a23 a23 a31a31 a32 a32 a33 a33
nh n h
nh
n h
nh
nh n h
nh
nh n h
nh
n h
nh
nh n h
nh
nh n h
nh
n h
nh
nh n h
nh
nh
1 1 1 0 16 4 0 1 1 25 (scalar)
nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh
1 1 11 1 1 1 6 4
a a 0 4 20 4 2 0 18 10 (matrix)
nh
nh nh
n h nh nh n h n h n h n h
ij
n h
jk
0 1 10 1 1 0 5 3
n h
nh
3
aa bb a b a
n h n h 4 (vector)
nh n h n h nh n h nh
nh
n h b
ij i1
n h 1 i2 2 i3 3 n h nh n h n h
n h
j
n h
2
aij bib a11b1b1 a12b1b2 a13b1b3 a21b2b1 a22b2b2 a23b2b3 a31b3b1 a32b3b2 a33b3b3
nh
nh nh
n h
nh
n h
nh
n h
nh
n h
nh
n h
nh
n h
nh
n h
nh
n h
nh
j
1 0 2 0 0 0 0 0 4 7 (scalar)
nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh
b1b1 b1b2 b1b3 1 0 2
b b b b b b b b 0 0 0 (matrix)
nh
nh n h
nh n h nh nh nh nh n h nh
i j 2
n h n h 1 2 3 n h
n h nh
n h
2n h 2
b3b1 b3b2 b3b3 2 0 4 nh
bibi b1b1 b2b2 b3b3 1 0 4 5 (scalar)
n h
nh
nh
nh
n h
nh
n h
nh nh nh nh nh nh nh nh
(b) aii a11 a22 a33 1 2 2 5 (scalar)
n h
nh
nh
nh
n h
nh
n h
nh nh nh nh nh nh nh nh
aij aij a11a11 a12 a12 a13a13 a21a21 a22 a22 a23a23 a31a31 a32 a32 a33a33
nh n h
nh
nh
nh
nh n h
nh
n h
nh
nh
nh
nh n h
nh
n h
nh
nh
nh
nh n h
nh
1 4 0 0 4 1 0 16 4 30 (scalar)
nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh
1 2 01 2 0 1 6 2
a a 0 2 10 2 1 0 8 4 (matrix)
n h nh
nh
nh
nh
ij
n h n
jk
0 4 20 4 2 0 1 8
h
n h
46
a b a b a b a b 3 (vector)
n h n h nh n h n h nh n h n h nh n h n h nh
nh
ij i1
n h i2 i3 3 n nh n n h
n h
j
n h 1 2 h h
6
aijbibj a11b1b1 a12b1b2 a13b1b3 a21b2b1 a22b2b2 a23b2b3 a31b3b1 a32b3b2 a33b3b3
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
n h
nh
4 4 0 0 2 1 0 4 2 17
nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh (scalar)
b1b1 b1b2 b1b3 4 2 2
b b b b b b b b 2 1 1 (matrix)
nh
nh nh
nh n h nh nh nh nh n h nh
i j 2
n h n h 1 2 3 n h
n h nh
n h
2n h 2
b3b1 b3b2
b3b3 2 1 1 nh
bibi b1b1 b2b2 b3b3 4 11 6 (scalar)
nh
nh
nh
nh
nh
nh
n h
nh nh nh nh nh
Copyrightnh©n h2009,n h ElseviernhInc.nh Alln h rightsnhreser
ved.
, 2
(c) aii a11 a22 a33 1 0 4 5 (scalar)
n h
nh
nh
nh
n h
nh
n h
nh nh nh nh nh nh nh nh
aij aij a11a11 a12 a12 a13a13 a21a21 a22 a22 a23a23 a31a31 a32 a32 a33a33
nh n h
nh
nh
nh
nh n h
nh
n h
nh
nh
nh
nh n h
nh
nh
nh
nh
nh
nh n h
nh
1 111 0 4 0 116 25 (scalar)
nh nh nh nh nh nh nh nh nh nh
1 1 11 1 1 2 2 7
a a 1 0 21 0 2 1 3 9 (matrix)
nh
nh nh
n h nh nh nh
ij
n h n
jk
0 1 40 1 4 1 4 18
h
n h n h
2
a b a b a b a b 1 (vector)
n h n h nh n h n h nh n h n h nh n h n h nh
nh
ij i1
n h i2 i3 3 n nh n n h
n h
n h j 1 2 h h
1
aijbibj a11b1b1 a12b1b2 a13b1b3 a21b2b1 a22b2b2 a23b2b3 a31b3b1 a32b3b2 a33b3b3
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
nh
n h
nh
1 1 0 1 0 0 0 0 0 3 (scalar)
nh nh nh nh nh nh nh nh nh nh nh nh nh nh nh
b1b1 b1b2 b1b3 1 1 0
b b b b b b b b 1 1 0 (matrix)
nh
nh nh
nh n h nh nh nh nh n h nh
i j 2
n h n h 1 2 3 n h
n h nh
n h
2n h 2
b3b1 b3b2
b3b3 0 0 0 nh
bibi b1b1 b2b2 b3b3 1 1 0 2 (scalar)
nh
nh
nh
nh
nh
nh
n h
nh nh nh nh nh
1-2.
1 1
(a) aij (aij a ji ) (aij a ji )
n h
nh
n h
nh nh
nh
nh nh
n h
nh nh
nh
2 2 nh nh
12 1 1 0 1 1
1 8 3 1 0 1
1 nh
nh nh nh
nh nh
2 nh
2 nh
1 3 2 1 1 0
clearlya(ij ) and a[ij ] satisfy the appropriate conditions
nh n h
n h
nh n h
nh nh nh
1 1
(a a )
nh nh
(a a )
(b) aij
nh nh nh
nh nh
ij ji ij ji nh
2 2
1 2 2 0 1 0 2 0
2 4 5 2 0 3
n h nh
nh nh nh
nh nh nh nh
2 nh
2 nh
0 5 4 3 0 n h
nh
0
clearlya(ij ) and a[ij ] satisfy the appropriate conditions
nh n h
n h
nh n h
nh nh nh
Copyrightnh©n h2009,n h ElseviernhInc.nh Alln h rightsnhreser
ved.