Using Mathcad Prime 9 to solve complex engineering problems

This PTC talk featured guest speaker Jan Claeys, CAD Consultant at 9altitudes, who discussed solving a practical engineering problem with Mathcad Prime 9 while demonstrating his model to analyze a beam's performance.

PTC Mathcad is an engineering calculation solution that helps you design better products faster. With PTC Mathcad, you have the power to do highly accurate engineering calculations and then easily share this critical IP. The powerful math engine and intuitive documentation front-end of
PTC Mathcad can handle the simplest equations or the most complex multi-step engineering analysis.

It is a vital first step in your product's digital design definition. It allows engineers to document their calculations in an engineering notebook with natural mathematical notation and unit intelligence. Show your work using rich formatting options alongside plots, text, and images in a single, professionally formatted document. Mathcad is intuitive, making verifying the work that goes into large projects easy. Streamline revisions and reuse between projects, integrate external materials, and drive precise and accurate calculations downstream.

With Mathcad, you can open up a worksheet and perform engineering calculations using the math notation you are familiar with and add images, write some text, and put in graphs or plots. The worksheet is more than just engineering calculation software or a professionally formatted document; it is where the design intent lives.

How does the Mathcad model assist engineers?

Claeys developed his Mathcad model six years ago. His demonstration in the PTC talk centered on applying a known deflection at several nodes along a beam. There are a given number of nodes, and at every node, he applied a vertical deflection; the problem he sought to solve was what load needed to be applied to realize such a deformation. What are the vertical reaction forces, and what is the resulting bending stress? The advantage of this model In Mathcad prime was that it allowed the engineer to choose the number of nodes and inter-distance of these nodes. By doing that in a virtual way, it was possible to decrease the number of tests in the lab quite significantly.

What is the advantage of singularity functions?

To do this, he used singularity functions, not something he had developed himself but a mathematical function that has been around for more than 40 years. A singularity function is an expression for x written as, where n is any integer (positive or negative) including zero, and x0 is a constant equal to the value of x at the initial boundary of a specific interval along the beam.

The advantage of using such functions is that it allows you to describe loads with the same type of function. The only thing that differs is the position along the beam where the load is acting and the exponent meaning that you can make distinctions between different types of loads. This is a massive advantage of using such a type of function.

What is new in the latest version of Mathcad?

The latest version of the product, Mathcad Prime 9, uses the same ribbon interface that will be familiar to users of other PTC products. In the latest incarnation, you can use the new text functions. For example, if there are several chapters in the calculation, every chapter can use a distinct text style to clearly distinguish between the different steps in the calculation. You can also add internal hyperlinks, meaning that if you control-click the link, it will allow you to continue working on the corresponding chapter. This is handy when making a calculation that you want to communicate with colleagues; it would be nice to present a clearer picture to my colleagues.

Internal links and Go-to pages make it easy to navigate through lengthy documents. Internal links add the benefit of connecting your notes and calculations across the worksheet for effective referencing. All color selection menus are enhanced to include a custom color picker allowing you to highlight sections of your document or make certain equations or plots stand out in the colors you want. You can now press the spacebar when typing a new region to convert it from the default math region to a textbox.

PTC also continues to deliver on the power of the new symbolic engine, and valuable enhancements have been made to the numeric engine to give users access to more mathematical operations and functionality than ever before.

Performing the calculation in Mathcad?

To start the calculation, Mathcad needs the input data. In this case, it is a very basic beam with a rectangular section and a given length. The dimensions come from the model in Creo Parametric. A significant advantage of Mathcad as a concept, contrary to Microsoft Excel, is that it works with units, meaning that the user can apply units to values. Everything you do can be annotated with texts; hyperlinks can be added to show sources of information.

Also, because this is a design document, it is possible to distinguish between the materials used. This is achieved through the so-called combo box, meaning that you have a given material's density and yield strength. The combo box allows you to make a distinction between these materials. Because of this, you can choose and, while designing, see what difference it makes switching from steel to titanium or aluminum, for example.

To see a complete run-through of how the model Claeys developed works within Mathcad, watch the full Talk here.