Engineering Optimization

Transcription

1 Engineering Optimization Most engineering design involves using optimization software which minimizes or maximizes a merit or objective function while satisfying functional constraints (such as stress levels) and regional constraints (such as a part size). The user must define the Design Variables (DV), the Objective or Merit Function (MF) and the design constraints. The Design Variables are a sub set of all of the Analysis Variables (such as all part dimensions) that define the design. The Analysis Variables are used to compute Analysis Functions (AF), such as area, mass, deflections, stresses, etc., from which the Merit Function is constructed. The optimization is subject to two types of limits or constraints. One type of limit is known as the Regional Constraints and they are simply upper and/or lower bounds on a Design Variable. In SolidWorks these are identified as Bounds in the window where you select the Design Variables. The other type is the Functional Constraints that place limits on some item that is calculated from the Design Variables. In SolidWorks they are simply called Constraints in the optimization study window. There are at least three user friendly engineering optimization software tools on campus: SolidWorks Simulation (for deflections, frequencies, thermal and stress), the ANSYS finite element system (for multi physics), and the TK Solver system (for user defined applications). ANSYS is by far the most powerful, but quite difficult to learn. ANSYS has an internal design optimization ability that lets the user define almost any multi physics objective function. SolidWorks is the easiest to learn, but has only a few pre defined merit functions from which to select. [The Rice CAAM department is world known for advanced software for extremely large optimization applications, such as scheduling the daily flights of an airline so as to minimize costs.] SolidWorks Press Frame Assembly Optimization Example A press frame assembly consists of a top plate, two side plates, and a back plate (see Figure 1). You would like to reduce its weight (and thus cost) while placing limits on its deflection and peak stress value. Its bottom feet are welded to a very stiff member, and the underside of the top plate is subjected to a load of 5,000 pounds (see Figure 2). It is made of alloy steel. The bottom arch width, top overhang thickness, and the side plate thickness are to be varied as the Design Variables (DV). The first two DV parametric dimensions are seen in the Figure 1. Often, the parametric dimensions selected as Design Variables are re named by the user to make the documentation easier to follow. If you do not see any part dimension names, use Options System Options General and turn on Show dimension names. Figure 1 The press frame assembly dimensions J.E. Akin, Rice University, Page 1 of 9

2 Figure 2 Press frame assembly dimension names, loads, and supports For example, the side plate part can be opened with its thickness dimension (D11) displayed (Figure 3). You can double click on the Primary Value name in the Dimension frame and change the dimension name. For example, here the default name is changed to Thick (see Figure 4). Changing the names is not required, but it can help you better understand the results. Figure 3 Identify a part design variable dimension J.E. Akin, Rice University, Page 2 of 9

3 Figure 4 Renaming a part dimension used as a design variable After changing the names of any parametric dimensions in individual parts, open the assembly and use Simulation New Study Static to create a study that will serve as the beginning of the optimization study. The initial mesh and deflection results are shown in Figures 5 and 6. They will be used as the starting point for the optimization search. Figure 5 Initial assembly static mesh and resultant displacements J.E. Akin, Rice University, Page 3 of 9

4 Figure 6 Initial design displacement vectors The initial deflections are small and the final deflections are allowed to be larger, but will be to be limited to 0.04 inches. Likewise, the initial von Mises effective stress value is recovered (in Figure 7), since alloy steel is a ductile material. It will be constrained not to exceed a relative low level of 15,000 psi (to create a high Factor of Safety). Figure 7 Low initial stresses imply excess material is used The goal is to reduce the amount (mass) of material used. The initial mass properties of this assembly are listed in Figure 8 (where weight is incorrectly called mass for these units): J.E. Akin, Rice University, Page 4 of 9

5 Figure 8 Initial mass properties data After the initial static study is complete, use Simulation New Study Optimize to create a study called opt_press. Right click on Objective and choose the Merit Function which is to minimize the mass (weight), based on the prior static study. Then, right click on Design Variables and select Add. Figure 9 The objective study windows J.E. Akin, Rice University, Page 5 of 9

6 Click on the top arm depth as the first Design Variable (DV1), and define its upper and lower regional constraint values. Repeat the process for the arch width (DV2), and the side plate thickness (DV3): Figure 10 Setting the Regional Constraints J.E. Akin, Rice University, Page 6 of 9

7 Now you are ready to add your Functional Constraints. Right click on Constraints and pick Add. Figure 11 Consider the computed functional constraints Impose a functional limit on the equivalent von Mises stress and the deflection anywhere in the assembly: Figure 12 Define multiple computed functional constraints Right click on the Study Name and select Run. You will see the default number of parametric changes executed. Each will require a new mesh generation for the current parametric dimensions. If you set conflicting sizes, that can cause a negative volume, then the mesh generation may fail and abort the optimization study. The results show the original (static) model and the final iteration result. Here, the final (of 15 iterations) Design Variable values are circled in red, and the assembly is displayed with those parametric dimensions. In this case, the final iteration violated a constraint, so it does not represent a feasible design. J.E. Akin, Rice University, Page 7 of 9

8 Figure 13 Optimization after 15 iterations You can check the results for any design iteration. For the last iteration you see that the von Mises effective stress had a peak value of 16,160 psi, which is greater than the design goal value. However, the displacement is about half the maximum allowed value. Therefore, you could manually begin with these Design Variable values and manually change them, or the fillet radius where the peak stress occurs, to get a new design that meets all the design requirements. This result suggests that the fillet radius should be considered as a Design Variable. Figure 14 Design Variables and Functional Constraints after 15 iterations J.E. Akin, Rice University, Page 8 of 9

9 You can graph the value of any Design Variable at each iteration (Figure 15). Figure 15 The Design Variable iteration history You can also see how the objective (mass) varied during the iterations (Figure 16) Figure 16 The Merit Function iteration history You can also select any of the created parametric design sets to study the corresponding assembly results. Almost any real world design problem will require the use of some optimization study. So, look for that ability in the design software available to you. J.E. Akin, Rice University, Page 9 of 9