Design Optimization

Beside the pure FE modeling, PERMAS also allows the definition of a design model and its automatic optimization as fully integrated functionality designed for large and complex problems.

The objective function of an optimization may be the weight or any other specified constraint. Multi objective optimization is possible, too.

Dependent nodes are also allowed for shape modifications. This allows the use of incompatible meshes to realize larger modifications without the need to remesh a structure.

Different optimization parameters, such as topology and shape may be combined as multimodal optimization.

Sizing:

areas of cross section, inertia moments and general functions between these properties e.g. for beam elements,
all parameters of standard beam cross sections,
thicknesses/offsets/nonstructural mass of membrane and shell elements,
stiffness and mass of spring elements,
mass of mass elements,
damping parameter of damping elements,
parameters of control elements,
convection film coefficients,
material parameters.

Parametric shape optimization:

node coordinates for shape optimization,
use of incompatible meshes (for positioning) without remeshing,
use of design elements,
bead design.

Freeform optimization (Non-parametric/free-shape optimization):

Thickness change on surfaces with complex geometry,
For stress homogenization under weight constraints or for weight optimization under stress limits,
Combination with parametric constraints like static or dynamic displacement limits,
Release directions may also be spcified as constraint.

Design variable linking

E.g. for symmetry conditions or cyclic repetitions

Design constraints and design objective

In each optimization constraints shall limit the value range for design variables as well as for the response quantities like:

Displacements, velocities, accelerations,
Element forces,
Reaction forces,
Stresses,
Compliance,
Weight,
Contact gap widths,
Contact pressure,
Contact forces,
Eigenfrequencies,
Buckling load scale factors,
Sound radiation power density,
Temperatures,
Heat fluxes,
General constraints as combination or arbitrary function of the above mentioned quantities. Such functions include global criteria like max/min, absmax/absmin, or RMS.
Element quality, where the PERMAS element test is mapped to a continuous variable with values between 0. (i.e. perfect element) and 1. (i.e. erroneous element). This design contraint will help to avoid the failure during optimization due to collapsing elements Each design constraint can also be used as objective function. Design constraint functions can be used to build more complex constraints out of the above listed basic constraints.
A general objective function facility can be used to set up an objective function dependent on multiple constraint values (like max/min, absmax/absmin, RMS).

Each design constraint can also be used as objective function. Design constraint functions can be used to build more complex constraints out of the above listed basic constraints.
A general objective function facility can be used to set up an objective function dependent on multiple constraint values (like max/min, absmax/absmin, RMS).

The following analysis types are available for design optimization:

For frequency response optimization amplitudes, phases, real, and imaginary values of the above listed results are available for constraint or objective definition. The limits for the constraints can be made dependent on frequency.

The design optimization allows taking into account several loading cases as well as different boundary conditions using the variant analysis. In addition, dynamic mode frequencies can also be optimized, where a mode tracking during the structural changes is performed automatically.

If a small part of a structure is optimized, substructuring can be used to reduce run time by separating the desgin space in the top component. So, the reduction of the unmodified parts has to be done only once.

Different solvers can be combined in one optimization task as well as sizing and shape parameters.

Shape optimization to minimize temperatures where the fingers hold the mug

Optimization results

The results of an optimization are the history of the objective function and an overview on the validity of the design after each iteration. In addition, the values of the design variables and the constraints are available as a function of the iterations performed. These functions may easily be viewed as xy-plots. The export of sensitivities is also possible.

Moreover, element properties may be prepared for result processing (i.e. thickness distribution) and exported for post-processing.

The results of a shape optimization can be exported as displacements for post-processing with the original model or as new model with identical topology and modified coordinates.

Optimization for a robust design is achieved by additional reliability constraints. Then, the design fulfills all of the above mentioned constraints and it is also reliable regarding uncertain model parameters.

Bead design of a tank to maximze first eigenfrequencies

Optimum bolt positions to achieve identical bolt forces

Parametric shape optimization of spokes to survive wheel impact test

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Design Optimization