List of notations
Notation Meaning
f(x) Function of one variable
f(x, y),F(x, y) Function of two variables
r Radius of curvature
g Acceleration of gravity
r
Vector in Cartesian coordinates
r
x
First partial derivative with respect to x
r
y
First partial derivative with respect to y
˙r
First parametric derivative
¨r
Second parametric derivative
p Pressure
s Arc length
s(t) One-dimensional spline function
s(u, v) Two-dimensional spline function
y
(x),f
(x)Firstderivative
y

(x),f

(x) Second derivative
n
Normal vector
t
Tangent vector
b
Bi-normal vector
Gradient operator
Δ Laplace operator
κ Curvature
κ
g
Geodesic curvature
κ
n
Normal curvature
κ
m
Mean curvature
δI Variation of integral functional
Γ
k
ij
Christoffel symbols
σ Stress
Strain
ν Poisson’s ratio
λ Eigenvalue
ρ Material density
[B] Shape function derivative matrix
xix
xx Contents
B
i,k
(t) B-spline basis function
E,F,G First fundamental quantities
E Young’s modulus
[D] Elasticity matrix
F Active force
G Green’s function
E
s
Strain energy
E
k
Kinetic energy
E
p
Potential energy
I() Integral functional
I Moment of inertia
[J] Jacobian matrix
M Momentum
[K]Stinessmatrix
[M] Mass matrix
[N] Shape function matrix
Q Heat source
S Surface area
T Surface (traction) force
[T ] Temperature matrix
V Volume
W
e
External work

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