Users:Structural Optimization/Design Variables/Nodal Coordinates

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	[[Category: Users:Structural Optimization]]		[[Category: Users:Structural Optimization]]
−	info will be added soon	+
		+	== General Description ==
		+
		+	=== Short Info ===
		+	With this design variable, the nodal coordinates (shape of the structure) can be optimized.
		+
		+	There are different modes to define how the shape is allowed to change -> SUBTYPES
		+
		+	=== Parameters in the Input File ===
		+
		+	{| border="1" cellpadding="3" cellspacing="0"
		+	|colspan="3" style="background:#efefef;"| Compulsory Parameters
		+	|-
		+	!Parameter
		+	!Values, Default(*)
		+	!Description
		+	|-
		+	!TYPE
		+	|NODE ''ID'', ND-SET ''ID''
		+	|Linking to previously defined nodes or node sets
		+	|-
		+	!SUBTYPE
		+	|VEC D1=''X'' D2=''Y'' D3=''Z''
		+	|change of coordinate in defined direction
		+	|-
		+	!SUBTYPE
		+	|DIR
		+	|change of coordinate in direction of nodal director (changing during optimization)
		+	|-
		+	!SUBTYPE
		+	|FIXED_DIR
		+	|change of coordinate in direction of initial nodal director (constant during optimization)
		+	|-
		+	!SUBTYPE
		+	|XYZ
		+	|change of coordinate in x,y and z direction (3 individual variables per node)
		+	|-
		+	!SUBTYPE
		+	|PLANE
		+	|change of coordinate in plane of initial configuration (constant during optimization)
		+	|-
		+	|colspan="3" style="background:#efefef;"| Optional Parameters
		+	|-
		+	!Parameter
		+	!Values, Default(*)
		+	!Description
		+	|-
		+	!BOUND
		+	|OPT-BOUND ''ID''
		+	|Linking to a bound defined in BOUND block.
		+	Remark: only SCALAR_BOUND is valid.
		+	|-
		+	|}
		+
		+
		+	=== Example of a Complete Input Block ===
		+
		+	This design variable can be defined for one node of for a nodal set. It is good practice to add a bound to the thickness design variables to avoid unrealistic values. In general, it is obvious to choose an upper and lower limit. Since the thickness is a scalar design variable, only SCALAR_BOUND is appropriate.
		+
		+	<pre>
		+	OPT-VAR 1
		+	TYPE=NODE 100 SUBTYPE=THICKNESS BOUND=OPT-BOUND 1
		+	TYPE=ND-SET 2 SUBTYPE=THICKNESS BOUND=OPT-BOUND 1
		+	</pre>
		+
		+	== A complete test example ==
		+
		+
		+	=== Model description ===
		+
		+	This example considers the thickness optimization of the Kresge auditorium. In a first step, the shape of the auditorium was optimized for minimal strain energy under dead load (cfr. PhD M. Firl) with constant thickness. The resulting shape is presented in the figure. In a second step, the thickness of the optimized shape is optimized. Strain energy under dead load is again used as the objective function. The design variables are the thicknesses at every node, constrained between 0.10 and 0.03 m. The shape of the shell is fixed.
		+
		+	[[File:shape.jpg |400px]]
		+
		+	=== Results ===
		+	In the figures, the thickness distribution and the Von Mises stresses in the top plane are shown for 50 optimization steps starting from a constant thickness of 0.05 m. It is clear that the largest part of the shell works very efficient on membrane forces and thus the thickness can be the minimal thickness. Only the support regions are subjected to bending, so the stresses can be reduced significantly by increasing the thickness to the maximal thickness.
		+
		+	[[File:MIT_objSE_thickness.gif| Thickness]]
		+	[[File:MIT_objSE_vmtop.gif | Von Mises top]]
		+
		+	=== Input File ===
		+
		+	to be added

---

Revision as of 11:18, 8 December 2016

Contents 1 General Description 1.1 Short Info 1.2 Parameters in the Input File 1.3 Example of a Complete Input Block 2 A complete test example 2.1 Model description 2.2 Results 2.3 Input File

General Description

Short Info

With this design variable, the nodal coordinates (shape of the structure) can be optimized.

There are different modes to define how the shape is allowed to change -> SUBTYPES

Parameters in the Input File

Compulsory Parameters
Parameter	Values, Default(*)	Description
TYPE	NODE ID, ND-SET ID	Linking to previously defined nodes or node sets
SUBTYPE	VEC D1=X D2=Y D3=Z	change of coordinate in defined direction
SUBTYPE	DIR	change of coordinate in direction of nodal director (changing during optimization)
SUBTYPE	FIXED_DIR	change of coordinate in direction of initial nodal director (constant during optimization)
SUBTYPE	XYZ	change of coordinate in x,y and z direction (3 individual variables per node)
SUBTYPE	PLANE	change of coordinate in plane of initial configuration (constant during optimization)
Optional Parameters
Parameter	Values, Default(*)	Description
BOUND	OPT-BOUND ID	Linking to a bound defined in BOUND block. Remark: only SCALAR_BOUND is valid.

Example of a Complete Input Block

This design variable can be defined for one node of for a nodal set. It is good practice to add a bound to the thickness design variables to avoid unrealistic values. In general, it is obvious to choose an upper and lower limit. Since the thickness is a scalar design variable, only SCALAR_BOUND is appropriate.

OPT-VAR 1
 TYPE=NODE 100 SUBTYPE=THICKNESS BOUND=OPT-BOUND 1
 TYPE=ND-SET 2 SUBTYPE=THICKNESS BOUND=OPT-BOUND 1

A complete test example

Model description

This example considers the thickness optimization of the Kresge auditorium. In a first step, the shape of the auditorium was optimized for minimal strain energy under dead load (cfr. PhD M. Firl) with constant thickness. The resulting shape is presented in the figure. In a second step, the thickness of the optimized shape is optimized. Strain energy under dead load is again used as the objective function. The design variables are the thicknesses at every node, constrained between 0.10 and 0.03 m. The shape of the shell is fixed.

Results

In the figures, the thickness distribution and the Von Mises stresses in the top plane are shown for 50 optimization steps starting from a constant thickness of 0.05 m. It is clear that the largest part of the shell works very efficient on membrane forces and thus the thickness can be the minimal thickness. Only the support regions are subjected to bending, so the stresses can be reduced significantly by increasing the thickness to the maximal thickness.

Input File

to be added

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