## An explanation of the simulation process ...

The methods used by Nonlinear Engineering typically involve the use of computers to simulate products and/or processes in an effort to reduce the cost, time, and effort required to produce an end product. The best way to explain is to go through an example.

Note that the following shows a very simple part created for this explanation.

### Step 1: The Question

The customer will typically have a simple question:

Will the bracket in this drawing (Fig. 1) support a 4800 Newton force?

### Step 2: Refine the Question

Frequently, the initial question is too general, and it is almost always necessary to get more detail in order to model the part or process:

How will this part be used?

It will be attached to a rigid surface with two bolts. The force will act vertically downward on the hook.

What issues concern you most?

Can the diagonal support be reduced to save weight? Is the section near the hook thick enough to carry the load?

### Step 3: Define Modeling Objectives

• An elastic material model will be sufficient for this case. It is not the designer's intention that the bracket should permanently deform under the given load.
• Solve for the equivalent stresses and determine the high stress areas.
• Recommend design improvements. Areas that are too highly stressed should be thickened. Areas that are not stressed can be thinned to reduce the material required.

### Step 4: Formulate the Model

Use basic engineering principles to establish boundary conditions, such as which portions of the bracket should be fixed. Loading conditions must also be determined.

Fig. 2 shows the 4800 N force acting downward. The bolt holes should be constrained since the bolts will be rigidly connected to the wall. The back side of the bracket between the holes will be pressed against the wall by the action of the force, so that area should also be fixed. Note that for a more sophisticated analysis, the actual contact condition between the wall and bracket could be simulated.

### Step 5: Create Geometry

Using various tools, a three dimensional representation of the part is created (See Fig. 3). A two dimensional drawing was provided by the customer. If he can provide an electronic version of the design, such as an AutoCad drawing, DXF file, or an IGES file, it will speed up the process.

### Step 6: Create Finite Element Mesh

The finite element method involves breaking an object into small (finite sized) pieces (elements), called a mesh. The solution for each individual element is relatively easy to determine, but each one depends upon all, or many, of the others. This is why a computer is required. There is an equation for each element, and each equation has as many terms as there are elements.

Fig. 4 shows the mesh for the part in question. There are 2221 elements in this model, they have parabolic interpolating functions, and a tetrahedral shape (four corners).

### Step 7: Computer Solution

From the analyst's point of view, this is often the easiest step. The computer solution can run anywhere from a few seconds to many days or even weeks, though that is seldom practical. In this case the solution completed in 4 minutes and 14 seconds.

### Step 8: Examine Results

There is a region of high stress near the hook, shown as red in Fig. 5. The diagonal brace and rear, vertical portion of the bracket are stressed very little as indicated by their blue color.

### Step 9: Recommendations

Due to low stresses, the diagonal brace and vertical portions of the bracket could be reduced in size to save weight.

The thickness near the hook should be increased, the length of the hook extension decreased, or the diagonal moved outward to reduce stresses in the horizontal portion of the bracket.

These recommendations would be discussed with the customer. Most likely, further modeling would be performed to prove out the design changes.