Optimizing monotonically increasing load curves

In cases where a monotonically increasing curve such as pressure_vs_leakage in *AIRBAG or effective_stress_vs_effective_strain in plasticity models in *MAT are to be parametrically identified by an optimization software such as LS-OPT to match against a physical test, it is important to ensure that the points identified by LS-OPT satisfy the non-negative slope. To satisfy this, it is common to place constraints on the points such that the f(Xi+1) is greater than or equal to the f(Xi). This method is less desired as LS-OPT has inherent difficulties in removing points that do not satisfy the constraint.

An alternative method suggested in this post eliminates the need to have constraints by using *PARAMETER_EXPRESSION keyword such that LS-OPT only computes an incremental value of the function whose lower bound is ZERO to yield a minimum slope of zero that is permitted by LS-DYNA.

The method is illustrated here.

  • Carlos Lois says:

    Hello Suri,

    Up to now I was doing the following instead of what you propose:

    composite ‘constraint_P2_P1’ {P2-P1}

    constraint ‘constraint_P2_P1’
    lower bound constraint ‘constraint_P2_P1’ 1e-006

    Is this also better or you still recomend generating a delta parameter which must be larger than 0?

    Thanks for the clarification.


  • Suri Bala says:

    Hello Carlos,

    With the DELTA method, there is no need to use a constraint since the lower limit is 0.
    This overcomes the problem of having to moving design points. I like this method since it guarantees monotonicity at every experiment point. Constraints based should also work but I encountered difficulties in certain situations where the points violated the constraints but this may be fixed in newer versions with the “strict” and “move” options.

    Hope this helps.
    Suri Bala

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