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PERMAS-OPT Design Optimization

Positioning

Beside the pure FE modeling, PERMAS also allows the definition of a design model and its automatic optimization.

The following design variables are provided:

  • 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.
  • Non-parametric 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
Bead design of a tank to maximze first eigenfrequencies

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,
  • 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

The objective function of an optimization may be the weight or any other specified constraint.

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.

The following solvers are available for optimization:

  • Linear statics,
  • Inertia relief,
  • Eigenvalue analysis,
  • Modal frequency response analysis,
  • Steady-state heat transfer analysis.

With the aid of module AOS additional solvers are available for Optimization:

  • contact analysis,
  • Nonlinear material behaviour

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.

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

The 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.

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.