Stress Constraints

The LATSTR field on the LATTICE continuation line in the DTPL entry can be used to define the stress constraint for the second phase. The stress constraint method can be selected using LATPRM, STRMETH. The stress upper bound value (LATSTR) is not applied for the first phase; instead, it is passed through to the second phase. For the CBEAM elements in the second phase corresponding DRESP1 response(s) is (are) created based on the defined stress constraint. If LATPRM, STRMETH, PNORM (default) is specified, the Stress NORM method is used to calculate the maximum stress value that is constrained for a given set of CBEAM elements. It is important to use the Stress NORM for stress constraints in the second phase due to the large number of beam elements. If stress constraints for all beams are considered as individual constraints in the optimization problem, the size of the optimization problem would be too large. The application of Stress NORM in the second phase, Euler buckling constraints, and the Lattice Sizing+ process are controlled by the internally generated parameter LATPRM, LATTICE, YES. Further modification of this parameter is not recommended. If this parameter is reset to NO, the stress NORM method is not applied in the handling of stress constraints in the second phase. This can possibly lead to a slow optimization run or maybe even termination of the program with an "Optimization problem is too large" error. The usage of Stress NORM improves efficiency of the handling of stress constraints in the second phase so it is recommended to retain the LATTICE parameter set to YES (Additionally, the LATPRM, LATTICE, YES parameter activates Euler Buckling constraints in phase 2). The Stress NORM feature creates two responses for a model, one stress NORM response for the elements with highest 10% of the stresses and a second stress NORM response for the rest of the model. Therefore, there may be two Stress Responses in the Retained Responses table of the OUT file.

The STRESS field on the DTPL entry can be used to specify stress constraints for the first phase topology optimization. This stress constraint is not passed through to the second phase.

DRESP1 stress responses are not allowed in the first phase (topology) of the lattice optimization.

Stress NORM Method

The Stress NORM method is used to approximately calculate the maximum value of the stresses of all the elements included in a particular response. This is also scaled with the stress bounds specified for each element. Therefore, to minimize the maximum stresses in a particular element set, the resulting stress NORM value (

σ_{N O R M}

) is internally constrained to a value lower than 1.0.(1)

σ_{N O R M} = {(\frac{1}{n} \sum_{i = 1}^{n} {(\frac{σ_{i}}{σ_{b o u n d}})}^{p})}^{\frac{1}{p}}

Where,

$σ_{N O R M}$: Stress NORM value
$n$: Number of elements
$σ_{i}$: Individual stress value of each element $i$
$σ_{b o u n d}$: Stress bound for each element
$p$: Penalty (power) value (default = 6.0)

The Penalty or Power value ( $p$ ) can be modified using the parameter DOPTPRM, PNORM.

The value $p$ = 6.0 is the default and higher values of ( $p$ → $\infty$ ) increases the accuracy of the stress norm function ( $σ_{N O R M}$ → $(\frac{σ_{\max}}{σ_{b o u n d}})$ ), which can lead to instability of the optimization run. Values lower than 6 ( $p$ → 1) moves the stress norm function closer to the average ratio ( $σ_{N O R M}$ → $\frac{1}{n} \sum_{i = 1}^{n} (\frac{σ_{i}}{σ_{b o u n d}})$ ). The default value is a reasonable approximation of the maximum ratio value and reduces instability.

The Stress NORM feature creates two responses for a model, one stress NORM response for the elements with highest 10% of the stresses and a second stress NORM response for the rest of the model. Therefore, there may be two Stress Responses in the Retained Responses table of the OUT file.

In addition to the default Stress Norm method, an alternative method can be selected using LATPRM,STRMETH,FSD. The alternative method may be faster for some models.