In finite elements, the behavior of structural elements (as opposed to continuum elements), such as shells, beams, rods, springs, and concentrated masses, are defined by input parameters, such as shell thickness, cross-sectional properties, and stiffness. Those parameters are modified in a size optimization. Some structural elements have several parameters depending on each other; like beams in which the area, moments of inertia, and torsional constants depend on the geometry of the cross-section.
The property itself is not the design variable in size optimization, but the property is defined as a function of design variables. The simplest definition, as defined by the design-variable-to-property relationship DVPREL1, is a linear combination of design variables defined on a DESVAR statement such that
where 
is the property to be optimized, and 
are linear factors associated to the design variable 
.
Using the equation utility DEQATN, more complicated functional dependencies using even trigonometric functions can be established. Such design-variable-to-property relations are then defined using the DVPREL2 statement.
For a simple gage optimization of a shell structure, the design-variable-to-property relationship turns into
where the gage thickness t is identical to the design variable.
If a discrete design variable is desired, a DDVAL bulk data entry needs to be referenced on the DESVAR bulk data entry for the design variable values.
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