Valid Symbols
You can use the following symbols when defining a symbolic function:
Functions
Supported in Native or FEM mode
Definitions
sin(x)
Native, FEM
standard trigonometric function.
cos(x)
Native, FEM
standard trigonometric function.
tan(x)
Native, FEM
standard trigonometric function.
sinh(x)
Native, FEM
hyperbolic trigonometric function.
cosh(x)
Native, FEM
hyperbolic trigonometric function.
tanh(x)
Native, FEM
hyperbolic trigonometric function.
asin(x)
Native, FEM
arc sine in range –/2 to /2.
acos(x)
Native, FEM
arc cosine in range 0 to .
atan(x)
Native, FEM
arc tangent in range –/2 to /2.
atan2(y,x)
Native, FEM
arc tangent of y/x in range – to .
exp(x)
Native, FEM
exponential function ex.
ln(x)
Native, FEM
natural (base e) logarithm.
log(x)
Native, FEM
base 10 logarithm.
abs(x)
Native, FEM
absolute value. If x>=0 returns x, otherwise –x.
sqrt(x)
Native, FEM
square root.
min(x,y)
Native, FEM
returns the minimum of x and y. If x<y returns x, otherwise y.
max(x,y)
Native, FEM
returns the maximum of x and y. If x>y, returns x, otherwise y.
sign(x,y)
Native, FEM
sign transfer of y to x. If y<0 returns–abs(x), otherwise abs(x).
mod(x,y)
Native, FEM
remainder function, that is x–int(x/y)*y where int() means "integer part of". The sign of the result is always the same as the sign of x.
if(c,x,y)
Native, FEM
"if" test, or switching function. If expression c (the "condition") returns non-zero (true) then the if function returns x, otherwise (if c=0.0) it returns y. Read like this: if c then x else y.
bound(x,lo,hi)
Native, FEM
limits x to be between bounds lo and hi. If x<lo returns lo, if x>hi returns hi, otherwise, returns x. lo must be <=hi.
dead(x,lo,hi)
Native, FEM
provides a "dead zone" when x is between lo and hi. If x<lo returns x–lo, if x>hi, returns x–hi, otherwise returns 0.
ceil(x)
Native, FEM
"ceiling" function, rounds toward positive infinity
floor(x)
Native, FEM
rounds toward negative infinity
near(x,y,delta)
Native, FEM
"nearness" test. Returns 1.0 (true) if x is within delta of y. If abs(x–y)<=delta returns 1.0, otherwise returns 0.0.
pow(x,y)
FEM
exponentiation function x y. The base is x and exponent is y.
Constants:
pi
Native, FEM
= 3.14159...
e
Native
= 2.71828...
Arithmetic Operators:
+
Native, FEM
add
Native, FEM
subtract, unary minus, negate
*
Native, FEM
multiply
/
Native, FEM
divide
^
Native, FEM
exponentiate
Logical Operators (these operators return 1.0 for true, 0.0 for false):
!
Native, FEM
unary "not"
==
Native, FEM
equal
!=
Native, FEM
not equal
<
Native, FEM
less than
>
Native, FEM
greater than
<=
Native, FEM
less than or equal to
>=
Native, FEM
greater than or equal to
&& in Native mode
& in FEM mode
Native, FEM
logical AND
|| in Native mode
| in FEM mode
Native, FEM
logical OR
Grouping Operators:
( )
Native, FEM
parentheses, grouping
* 
The arguments of trigonometric functions, values returned by inverse trigonometric functions and angle coordinates are interpreted as radians in Native mode and as degrees in FEM mode. For example, if a load is defined as a function of cylindrical coordinates (r, theta, z) with the symbolic function "5 * theta * z", the load will be evaluated differently in FEM mode compared to Native mode. Symbolic functions that use trigonometric expressions such as cos(theta) are evaluated consistently and accurately in both modes. However, trigonometric functions that have linear dimensions as arguments, for example cos(x/L), where x is a coordinate and L is a linear dimension, are evaluated differently.