Bolt Sequence Optimization/Design Exploration using HyperStudy

Garima Singh

The Parameterized File Model type connection is very useful for parametrizing values such as material properties (Young’s Modulus, Hardening Coefficients etc.), load collector values (forces, moments etc.) and in some cases using different material types as design variables or even load cases referenced in the solver file for unique design exploration studies. These are some of the parameters that cannot be imported in HyperStudy using the HyperMesh Model type connection.

This article is specifically about parametrizing the load case ID referenced in the solver file for various load cases which together form a bolting sequence in OptiStruct. Another important aspect is that since the requirement is to study the effect of bolting sequence on the output response/finding optimal bolting sequence for a target output response value, the bolting sequence should be unique in a DOE/Optimization iteration & should not get repeated.

As shown in Figure 1, there is a plate subjected to a bolting sequence as 1,2,3,4,5,6,7 & 8. Thus, a HyperStudy setup needs to be defined to either find the optimal bolting sequence using an Optimization approach (as shown in Figure 2) or to understand the effect of a variety of bolt sequences on the output response using a DOE approach.

Figure 1: Baseline design with bolting sequence as 1,2,3,4,5,6,7 & 8.

Figure 2: Optimized design with optimal bolting sequence as 1,7,2,6,3,4,5 & 8.

Since the bolting sequence has to be unique for a DOE/Optimization iteration, there is a requirement for adding design variable links & constraints in the HyperStudy setup. Without adding these design variable constraints, the bolting sequence would get repeated which is not intended as shown in Figure 3.

Figure 3: Design with repeated bolting sequence as 1,1,3,2,6,6,7 & 7.

Hence, for the HyperStudy setup, the following steps needs to be followed:

1. Defining the design variables: This step requires parameterizing the load case ID i.e. PRETENSION ID of all the eight load cases & setting the eight design variables mode as Discrete type from Continuous type. Since there are in total eight bolt sequences, eight discrete steps with a step size of 1 need to be defined as 1,2,3,4,5,6,7 & 8. By doing so, the intermediate continuous values will not be included for the DOE/Optimization studies.
2. Defining a design variable link: A link should be defined for the design variable 8 i.e. DV_8 using the expression 36-DV_1-DV_2-DV_3-DV_4-DV_5-DV_6-DV_7. Here, 36 is the sum of the eight design variables & DV_1, DV_2 etc. are the design variables name in HyperStudy respectively.
3. Defining the design variable constraints: Three design variable constraints need to be defined as follows:
   • Constraint 1: The product of the design variables subtracted by the product value should be ≤ 0.5.In this setup, the design variable constraint expression is as follows: abs(DV_1*DV_2*DV_3*DV_4*DV_5*DV_6*DV_7*DV_8 - 40320).
   • Constraint 2: The sum of the design variables subtracted by the sum value should be ≤ 0.5. In this setup, the design variable constraint expression is as follows: abs(DV_1+DV_2+DV_3+DV_4+DV_5+DV_6+DV_7+DV_8 - 36).
   • Constraint 3: The length of the design variable vector should be ≥ 7.5. In this setup, the constraint expression is as follows: numpts(remove_succ_dup_indx(sort(0,{DV_1, DV_2, DV_3, DV_4, DV_5, DV_6, DV_7, DV_8}))).

 

Based on the above defined HyperStudy setup, the various Optimization/DOE iterations with unique bolting sequence will be as follows:

Figure 4 : Optimization/DOE iterations with unique bolting sequence with no repeated values.

However, few points to be noted regarding the above mentioned HyperStudy setup:

1. The following HyperStudy setup is applicable when in total there are eight design variables & the setup will vary if the design variables are less or more than eight.
2. If the design variables are less than eight i.e. for example six, then in that scenario, the third design variable constraint will not be required & the first two design variable constraints are sufficient.
3. If the design variables are more than eight, then a unique design variable constraint has to be added to obtain unique values of the bolting sequence.

Hence, with regards to point 3 mentioned above, additional suggestions are as follows:

• If the user is not able to add a working design variable constraint when the design variables are more than eight, it is recommended to use the DOE approach using the ‘Run Matrix’ DOE method instead of a HyperStudy created DOE/Optimization approach.
• Thus, by using this ‘Run Matrix’ DOE method, the user can provide custom DOE iterations to HyperStudy to perform a certain set of evaluations of bolting sequence & interpret the result accordingly.
• However, with this approach, there are a few limitations such as follows: the DOE post-processing features such as Pareto Plot & Linear Effects cannot be used as the result obtained from the user-provided DOE iterations may or may not be sufficient to provide reliable results. However, the Parallel Coordinate plot feature can be used to visualize the data trends & to interpret the effect of the bolting sequence on the output response.