/DEQATN

Optimization Keyword

/DEQATN – Design Equation Definition

Description

Specifies one or more equations for use in optimization.

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
/DEQATN/eqn_ID
title
EQN(1); EQN(2); ...
...
EQN(n-1); EQN(n)

Field	Contents	SI Unit Example
eqn_ID	Design equation identifier (Integer > 0)
title	Title (Character, maximum 100 characters)
EQN(i)	i-th equation (Character string)

#---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

# 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----|

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 as follows:

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

sin(x)

sine

sinh(x)

hyperbolic sine

int (x)

real to integer conversion

sqrt(x)

square root

Two-argument functions

2_arg_funct

Multi-argument functions

deqatn_multi

4.	The supported operators are listed below:

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
-232	-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.