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TABLE 2.6
Interrelationships Between the Basic Equations
σ =
D 1 ψ (Chapter 1, Eq. 1.56a)
R
=
D 1
(Chapter 1, Eq. 1.29)
Stress Functions
Compatibility
φ = φ
σ =
D φ
D T R
+ η V =
η = η
(Chapter 1, Eq. 1.56b)
0
on S P
in V
in V
on S u
(Chapter 1, Eq. 1.34)
=
E
s
E 1 s
=
(Chapter 1, Eq. 1.32)
Static
Strain
Displacement
A B
Boundary
A
Equilibrium
B
Displacement
B B
Boundary
Conditio ns
Relations hip
C onditio ns
p
=
p
(
D T s
+
p V ) =
0
=
Du
u
=
u
on S p
in V
in V
on S u
(Chapter 1, Eq. 1.60)
(Chapter 1, Eq. 1.53)
(Chapter 1, Eq. 1.20)
(Chapter 1, Eq. 1.61)
C
Virtual Work
(Eq. 2.54)
D
Complementary Virtual Work
(Eq. 2.78)
V δ
V δ T s dV
u T p V dV
u T p dS
s T dV
p T u dS
S p δ
=
0
V δ
+
S u δ
=
0
References
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