Users:Structural Optimization/Variable Bounds
General Treatment of Variable Bounds
Variable bounds are a fast and efficient but crude way to limit the design space. They can be used within constrained and unconstrained optimization, as the bounds are independent of the optimization algorithm. Variable bounds are directly linked to design variables and define a space the design variable has to stay in. If the design variable intends to move out of this space due to a design update, it is projected back onto the boundary of the space defined by the variable bound.
Variable bounds should not be mixed up with real constraints, as the bounds are not defined as response functions producing gradients which are considered by the optimization algorithm.
Variable bounds are connected design variables the following way:
OPT-VAR 1 TYPE=ND-SET 1 SUBTYPE=VEC D1=0.0 D2=0.0 D3=1.0 BOUND=OPT-BOUND 1
List of Offered Variable Bounds
Bound name | Short description | Input sequence |
---|---|---|
RELATIVE_SPHERE | Each design variable defines a sphere of radius R arround its initial position and is forced to remain inside this sphere REMARK: this bound only works for design variables with a fixed direction. |
OPT-BOUND 1 : RELATIVE_SPHERE RADIUS = 1 |
SCALAR_BOUND | An interval is defined by a LOWER and an UPPER bound. The scalar design variable is forced to remain in this interval. REMARK: This bound can't be used for design variables of type NODE_COOR |
OPT-BOUND 1 : SCALAR_BOUND LOWER = 1 UPPER = 10 |
ABSOLUTE_SCALAR | An interval is defined by a LOWER and an UPPER bound. The design variable is forced to remain in this interval. REMARK: this bound only works for design variables with a fixed direction. |
OPT-BOUND 1 : ABSOLUTE_SCALAR LOWER = 1 UPPER = 10 |
ABSOLUTE_CYLINDER | A cylinder is defined by an axis (point 1 to point 2) and a radius. The parameter 'VALID_SPACE' defines if the feasible design is inside or outside of the cylinder. |
OPT-BOUND 1 : ABSOLUTE_CYLINDER P1_X = 0 P1_Y = 0 P1_Z = 0 P2_X = 0 P2_Y = 0 P2_Z = 10 RADIUS = 5 VALID_SPACE = INSIDE ! or OUTSIDE |
ABSOLUTE_BOX | The valid space is defined by a cube-like box defined by a corner node and the dimensions parallel to global coordinate axes. Rotations arround global coordinate axes can be applied. |
OPT-BOUND 1 : ABSOLUTE_BOX CEN_X = 0 CEN_Y = 0 CEN_Z = 0 ! Coordinates of corner node DIM_X = 5 DIM_Y = 5 DIM_Z = 10 ! Dimensions parallel to coordinate axes ROT_X = 45 ROT_Y = 0 ROT_Z = 0 ! Rotates the box defined by the parameters above ! around global axes, values are defined in degrees. |
ABSOLUTE_PLANE | A plane is defined by a node and a normal vector. The design variables have to stay either inside the negative or positive halfspace (positive halfspace: the halfspace the normal is pointing into). |
OPT-BOUND 1 : ABSOLUTE_PLANE P_X = 10 P_Y = 10 P_Z = 0 NORMAL_X = 0 NORMAL_Y = 0 NORMAL_Z = 1 HALFSPACE = POSITIVE ! choose : POSITIVE NEGATIVE |
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