/DEQATN

Format

Definitions

Example

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/DRESP1/1
u_in
### RTYPE=5: Displacement
### PTYPE=1: Node
### ATTA=1 : Translational displacement in X-direction 
### ATTI=103 : 103 is node group identifier is due to PTYPE = 1
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#    RTYPE     PTYPE    REGION      ATTA      ATTB      ATTI
         5         1                   1                 103
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/DRESP1/2
u_out
### RTYPE=5: Displacement
### PTYPE=1: Node
### ATTA=1 : Translational displacement in X-direction 
### ATTI=104 : 104 is node group identifier is due to PTYPE = 1
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#    RTYPE     PTYPE    REGION      ATTA      ATTB      ATTI
         5         1                   1                 104
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/DRESP2/4
dresp2
### EQID=1: /DEQATN identifier is 1
### VARTYPE1=3: Indicates the type of variables is 3 (DRESP1)
### ID1=1: first Variable(x) is ID1=1 in DRESP1 (dx in node group 103)
### ID2=2: second Variable(y) is ID2=2 in DRESP1 (dx in node group 104)
#     FUNC      EQID    REGION
         1
# VARTYPE1       ID1       ID2       ID1       ID2       ID1       ID2       ID1       ID2       ID1
         3         1         2
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/DEQATN/1
deqatn
# EQUATIONS
dm(x,y)=(x+y)/2.
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

1. Blank characters in the equation have no effect, even within a constant, variable or function name. Lower and upper case letters are equivalent.
2. There must be only one variable at the left-hand side of each equation in any equation card. The variable of the first equation must be followed by an argument listed in the following format:

   v1(x1,x2,…,xn) = expression(x1,x2,…,xn);
   v2 = expression(x1,x2,…,xn,v1);
   …
   vi = expression(x1,x2,…,xn,v1,v2,…,vi-1);
   …
   vn = expression(x1,x2,…,xn,v1,v2,…,vn-1);

   Where, vi is the variable of equation i. (x1, x2, ..., xn) is the argument list for variable v1. (v1,v2,...,vi-1) is the variable list which corresponds to the result of equation 1 through equation I-1.

3. Constants can be specified in a format of either integer or floating point. A floating point number can be in a format of either normal decimal-point format (3.90) or scientific notation (-2.0E-3), which means -2x10^-3.
   The list of supported mathematical functions is:

   One-argument Functions

   abs(x)

   Absolute value

   acos(x)

   Arccosine

   acosh(x)

   Hyperbolic arccosine

   asin(x)

   Arcsine

   asinh(x)

   Hyperbolic arcsine

   atan(x)

   Arctangent

   atanh(x)

   Hyperbolic arctangent

   cos(x)

   Cosine

   cosh(x)

   Hyperbolic cosine

   exp(x)

   Exponential

   log(x)

   Natural logarithm

   log10(x)

   Common logarithm

   pi(x)

   Multiples of π

   sin(x)

   Sine

   sinh(x)

   Hyperbolic sine

   int (x)

   Real to integer conversion

   sqrt(x)

   Square root

   Two-argument functions:

   
   
   

   Multi-argument functions:

   
   
   

4. The supported operators are:

   Symbol	Meaning	Example
   +	binary +	x + y
   -	binary -	x - y
   *	multiplication	x * y
   /	division	x / y
   **	power	x ** y
   +	unary +	+1.0
   -	unary -	-1.0

5. The precedence of mathematical calculations follows the rules of Fortran language. Parenthesis has a higher priority in the order of precedence than the operators listed above. Two consecutive operators are acceptable only if the second one is unary, plus or minus.
   Examples of operator precedence:

   Expression

   Result

   2**-3

   0.128

   1 / 2 + 3

   3.5

   2*3-4

   2.0

   -2**3**2

   -512.0

   2 + -5

   -3.0

   2 * -5

   -10.0

   2 - -5

   7.0

   2/3/4

   0.16666666....

   2/(3/4)

   2.6666666...

6. Functions can be defined in a layered format, for example, min(sin(x1), x2), with no limit on the number of layers.
7. The /DEQATN entry is referenced by /DRESP2 entry.