The widespread adoption of tools such as finite element analysis (FEA) has greatly reduced product development cycles. The integration of FEA into CAD software platforms allows the design and analysis to be performed concurrently.
During the design phase, an engineer may evaluate different design options using FEA and iterate—using trial and error—to refine the design for one or two key parameters. The problem with this manual approach is that other design parameters, outside of those the user is setting, can inadvertently be impacted. For example, a part modified to minimize weight by removing portions of the material may result in unacceptable changes in the part’s natural frequency. Optimization tools enable modifying multiple variables for iterative design changes while maintaining certain limits on other design parameters.
Parametric Optimization
Many current FEA software tools include the ability to perform optimization. Essentially, these routines automate the common trial-and-error approach of changing design variables and determining the impact of these changes. The advantage of incorporating these tools into an automated algorithm is that the software can “keep an eye on” other variables that may be impacted by changing the variable of interest.
Parametric optimization involves the following concepts:
- Variables: These are the values that the user wants to modify from the part design.
- Constraints: These are the limits that are placed on various parameters.
- Goals: This is generally the parameter optimized. For example, minimizing weight on a part would be a common goal.
Parametric Optimization Example
Consider the simple cantilever section shown in Figure 1. It is loaded with 500 lbs., which are evenly distributed along the top and fixed on the right end.
Figure 1
The goal of the optimization is to minimize the volume (and therefore weight) of this component while maintaining stresses below a certain level. The parameters are summarized in Table 1 below.
Parameter | Type | Initial Value | |
Left edge | variable | 4.00 | in |
Web thickness | variable | 1.00 | in |
Cutout width | variable | 8.00 | in |
Volume | goal | 14.52 | in^{3} |
Weight | goal | 4.10 | lb |
Table 1.
The power of the parametric optimization method is that the algorithm can modify multiple variables until an optimum can be achieved. However, the optimization routine must be given guidance on what the allowable ranges would be for the variables. Additionally, the constraints must be defined. These are summarized in Table 2 for our example model.
Variables | Range | ||
Min | Max | ||
Left edge | 2.75 | 4.25 | in. |
Web thickness | 0.50 | 1.00 | in. |
Cutout width | 8.00 | 9.00 | in. |
Constraints | |||
von Mises stress | <20,000 | psi | |
Goal | |||
Minimize volume | TBD | in.^{3} |
Table 2.
A baseline study is required as a starting point. Error! Reference source not found. gives the results of the baseline study for the dimensions of Figure 1 above and a 500-lb. uniform load as shown.
Figure 2
The maximum von Mises stress is 12,200 psi.* Because we have an allowable stress of 20,000 psi, there is an opportunity to remove material to lighten the component. Our optimization goal can be expressed as “take away as much material as possible from this part while keeping stresses and deflections below a certain threshold.” Typically, the user would manually change dimensions, rerun the analysis, check stresses and repeat the cycle until some target is reached. We will look at how that optimization workflow can be automated.
Parametric Optimization Using SOLIDWORKS Simulation
Optimization in SOLIDWORKS Simulation is performed by first running an initial study (“Baseline Study” for our example) to ensure there is a solvable base simulation. In the simulation interface, right clicking this study tab presents the menu in Figure 3.
Figure 3
The user initiates an optimization study by selecting “Create New Design Study.” The dialog box shown in Figure 4 is then presented. The split screen allows interactive selection, from the graphics window, of the variables involved in the optimization. Clicking on the dimension in the graphics window populates the corresponding variable in the optimization variables section.
Figure 4
Figure 5 is a screenshot of the SOLIDWORKS Simulation populated dialog for our current optimization design study.
Figure 5
These values correspond to the values presented previously in Table 2. The optimization is now ready to run with the “Optimization” checkbox active.
SOLIDWORKS Simulation performs several iterations of the linear static “Baseline Study,” intelligently modifying the variables that were defined in the setup. This is an automated trial and error with normalized equations (response functions) being formed at each iteration to estimate the next-best dimension values so as to get closer to the goal of minimizing the weight.
The results of the optimization are given below in Table 3. The weight is reduced by 25 percent compared with the original configuration. Figure 6 shows the component with the optimized dimensions.
Variables | Initial | Optimum Found | |
Left edge | 4.0 | 2.76 | in. |
Web thickness | 1.0 | 0.55 | in. |
Cutout width | 8.0 | 8.97 | in. |
Constraints | |||
von Mises stress <20,000 | 12,200 | 19,777 | psi |
Goal | |||
Minimize volume | 14.52 | 11.06 | in.^{3} |
Weight | 4.10 | 3.12 | lb. |
Table 3
Figure 6
Optimization Solve Efficiency
For our example, 13 iterations of the “Baseline Study” were required to find the optimal solution for the three variables. The number of iterations required to achieve the optimal is related to the number of variables. For example, three, four, five or six variables require 13, 25, 41 or 49 iterations, respectively.
For large models with long solution times for a given study, the cumulative optimization solve time can be prohibitive. However, SOLIDWORKS Simulation offers an alternative “Fast Results” setting. This can reduce the solution time up to 50 percent for four to 10 variables. However, not every model can take advantage of this speed increase. Studies with nonlinear boundary conditions or frequency analysis may require smaller steps and thus more iterations
to find a true optimum. Also, there is no difference in the high-quality and fast algorithms for less than four variables.
It is important to note that the optimization schemes are simply mathematical methods to rapidly cycle through different scenarios of a given study. A less-than-optimal solution is not considered “incorrect” from a stress/strain perspective—it is just not the theoretical optimum.
Shape Optimization
Other technologies for optimizing structures include shape optimization. This approach takes a defined design space and volume and determines the optimal design within that envelope. These methods address the topology, or shape, of a structure and can strategically carve away material that does not carry significant load. By contrast, SOLIDWORKS Simulation optimization works with dimensional criteria.
However, there is an opportunity for a hybrid approach with SOLIDWORKS Simulation. A results feature called “Design Insight” gives the user an indication of load path and regions that are not carrying significant load and also highlights where material may be removed.
Figure 7 shows how this feature indicates results. The user can evaluate the feasibility of removing material in the lightly loaded translucent portions of the model. This requires manually reshaping the part contours. Depending on the ultimate design goal, this may or may not be worth pursuing.
Figure 7. Although SOLIDWORKS Optimization does not does not do freeform shape change, “Design Insight” hints at where material may be removed.
Conclusion
CAD-native analysis and optimization offer powerful methods for streamlining part design. In this article, we looked at the parametric optimization tools in SOLIDWORKS Simulation. In this case a part’s weight was optimized without the lengthy manual trial and error approach.
Also, the part’s load path can be viewed through the SOLIDWORKS Simulation “Design Insight” option. This can provide further material reduction by identifying regions of a component that are lightly loaded.
*von Mises stress relates to a commonly used failure theory applied to metal parts.
About the Author
Attilio Colangelo has more than 25 years of experience in engineering and project management in the chemical, process, ceramic and advanced-materials industries. His specialties include CAE, with an emphasis on FEA, high-temperature and heavy industrial design. His software skills include SOLIDWORKS Simulation, NASTRAN, Caesar II, ANSYS and iOS programming.