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Keyword type: step
This procedure is used to calculate a feasible direction for an optimization calculation. It must be preceded by one or more *SENSITIVITY steps and the design variables must be of type coordinate. The sensitivities calculated in the sensitivity steps can be used as an objective or as constraints. The feasible direction step calculates how the steepest descent direction of the objective function (*OBJECTIVE) has to be modified to avoid the violation of nonlinear constrains (*CONSTRAINT) or geometric constraints (*GEOMETRIC CONSTRAINT. To calculate this modified descent direction two methods are available selected by the optional parameter METHOD. It can take the value GRADIENT DESCENT or GRADIENT PROJECTION. For details the user is referred to Section 6.9.24.
Default is the GRADIENT DESCENT method. It is an interior point method which means that the starting point for an optimization has to lie in the feasible domain. The influence of the constraints on the feasible direction is always taken into account independent of the distance to the constraint bound. This methods aims to stay away from the constraint boundaries as long as possible on the way to the local optimum.
In contrast to that, the GRADIENT PROJECTION method is based on an active set strategy which means that the steepest descent direction is chosen as long as no constraint boundary is reached. As soon as a constraint boundary is active the fasible direction is calculated by projection the objective gradient on the subspace tangent of all active constraints.
The feasible direction procedure yields values for the motion of the design variables normal to the surface which is needed to reach the objective subject to the constraints. These values are normed to 1 (i.e. the maximum absolute value is 1) and they can be used for a subsequent mesh modification by applying them as boundary conditions to the mesh in a linear elastic calculation. The input deck for this calculation is automatically generated in the feasible direction step and gets the name jobname.equ. Before creating this input deck, the values are scaled by the mesh modification factor, which the user specifies on the line underneath *FEASIBLE DIRECTION.
First line:
Second line:
Example: *FEASIBLE DIRECTION,METHOD=GRADIENT PROJECTION .1
defines a feasible direction step with the gradient method for the treatment of the constraints. The maximum modification of the mesh is 0.1.
Example files: opt1, opt3.