The term “expression” has more than one use when defining user defined results. An expression is:
Primarily, the combination of mathematical values, based on syntax rules and the available math operations.
A column displayed on the Solution Worksheet that indicates the result type.
An entry field in the Details view of a user defined result where you enter mathematical values, such as
UX+UY+UZ.
Note: You can use user defined result expressions across multiple combinations of environments with limited functionality by using a Design Assessment system. However, you can not use it within standard Solution Combinations.
The example of the Solution Worksheet shown below highlights the Expression column.
When a User Defined Result is applied, the content of the above column populates the Expression field of the user defined result's Detail View. In this case, UX.
The content of the Expression field can be modified using mathematical operators to further define the expression. As shown below, you can combine the X, Y, and Z components and then retrieve a new customized result.
Expression Syntax
Expressions support the following syntax:
Operands: ( ‘+’, ‘-‘,’*’, ‘/’, ‘^’)
Functions: (sqrt(), min()…) - always use lower case
Numbers: (scalar quantities such as 1.0, 25, -314.23, or 2.5e12)
Identifiers: unique user defined names
Supported Mathematical Operations
The following is a list of the mathematical operations currently supported for user defined results. The shorthand notation "s" defines a single-valued quantity (constant values such as 1.34) and "a" defines an array. An array is distinguished by its dimension which includes the length, based on the number of rows (that is, number of nodes or elements), and the width, consisting of 1, 3, or 6 columns depending on the type of result stored.
Addition (+): s1+s2, a1+a2, a+s (s+a is not supported)
Subtraction (-): s1-s2, a1-a2, a-s (s-a is not supported)
Multiplication (*): s1*s2, a1*a2, a*s, s*a
Division (/): s1/s2, a1/a2, a/s (s/a is not supported)
Power (^): s1^s2, a1^a2, a^s, s^a, (undefined if s1 = 0 and s2 < 0 or if s1<0 and s2 is a non-integer)
Log base ten (log10): log10(s), log10(a), (s and a > 0.0)
Square root (sqrt): sqrt(s), sqrt(a), (s and a should be >= 0.0)
Dot product (dot): dot(a1,a2) (results in a single-column array consisting of the inner products, one for each row of a1 and a2; thus, a1, a2 should have the same dimensions)
Cross product (cross): cross(a1,a2) (a1, a2 must have 3 columns)
Add Comp (addcomp): addcomp(uvectors) = ux + uy + uz (If the argument uvectors has 3 columns, they are added to produce a single-column array. If the argument is a single-column array, the result will be a scalar summing all the array entries.)
Maximum (max): s = max(s1,s2), a = max(a1,a2)
Minimum (min): s = min(s1,s2), a = min(a1,a2)
Absolute Value (abs): s = abs(s1), a=abs(a1)
Trigonometric Functions (sin, cos, tan): sin(s), cos(s), tan(s), sin(a), cos(a), tan(a) (s and a are both in radians)
Inverse Trigonometric Functions (asin, acos, atan): asin(s), acos(s), atan(s), asin(a), acos(a), atan(a) (return values are in radians; where -1 <= s <= 1 and -1 <= a <=1 for asin and acos)
atan2: atan2(s1,s2), atan2(a1,a2) (return values are in radians; calculates the arctangent of s1/s2 or a1/a2 and uses the sign of the arguments to determine the quadrant of the returned angle)
Note:
The current expression list does not allow input parameters from the Parameter Workspace. Only output parameters are allowed for Min and Max values of a user defined result.
All operations involving two vector arrays must have the same dimensionality.
Any result whose expression contains the addcomp function needs to be scoped to exactly one body.
You cannot perform mathematical operations directly within the Design Assessment system. However, the Design Assessment system provides the ability to use python scripts to combine results from various environment using highly complex, user defined mathematical functions.