W ext external work
m C
configuration m, m ¼ 0; 1; 2
M uu mass matrix
C uu
damping matrix
K uu
stiffness matrix
K u/ piezoelectric coupled stiffness matrix
K /u piezoelectric coupled capacity matrix
K // piezoelectric capacity matrix
K ug
geometrically induced stiffness due to mechanically induced stresses
K /g geometrically induced stiffness due to electrically induced stresses
S uu
mechanically induced resultant stresses
S u/
electrically induced resultant stresses
F ue
total external force vector
F ub
element body force vector
F us
element surface force vector
F uc
element concentrated force vector
f b
body force vector of an arbitrary point in the shell space
f s
surface force vector of an arbitrary point at the mid-surface
f c
concentrated force vector of an arbitrary point at the mid-surface
F ui
total in-balance force vector
F ut
inertial in-balance force vector
F uu
mechanically induced in-balance force vector
F u/
electrically induced in-balance force vector
G /e
total external charge vector
G /s
surface charge vector
G /c
concentrated charge vector
G /i
total in-balance charge vector
F /u
mechanically induced in-balance charge vector
F // electrically induced in-balance charge vector
q
nodal displacement vector
/ a
actuation voltage vector applied on piezoelectric layer
/ s
sensor voltage vector output from piezoelectric layer
Abbreviations
AEH
Asymptotic expansion homogenization
AFC
Active fiber composite
ANS
Assumed natural strain
CLT
Classical lamination theory
CNT
Carbon nanotube
DOF(s) Degree(s) of ereedom
Acronyms
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