While most of our readers are familiar with parametric modeling using 3D CAD tools, I'm going to venture a guess that probably a smaller number have experienced parametric modeling using a mathematical tool for computing physical models and simulations.

In the world of parametric mathematical modeling, the tandem combination of flagship products from Maplesoft – Maple 15 and MapleSim 5 – create a bellwether environment for learning and applying this important engineering technology set. While we'll touch on the Maple 15 math engine, the majority of our discussion will focus on MapleSim 5 for using mathematical methods for exploring physical models and simulation.

**Mathematical Modeling Similarities and Differences**

Before we delve into Maple 15 and MapleSim 5 from Maplesoft, we'll briefly cover what parametric mathematical modeling is and how it differs from parametric CAD modeling. A parametric CAD model is a geometric representation of a physical model, where parameters are a subset of the CAD application's parameters and are used to define the geometry in a CAD system.

**MapleSim 5 is a parametric physical modeling and simulation tool built on a foundation of symbolic computation technology. It efficiently handles all of the complex mathematics involved in the development of engineering models, including multi-domain systems, plant modeling, and control design.**

On the other hand, a parametric mathematical model is a description of a physical system using mathematical concepts, where parameters are expressed as variables in mathematical expressions used to describe conditions affecting a physical system.

In its most rudimentary form, mathematical models represent physical systems using mathematical concepts, such as equations and functions. A mathematical model begins by stating a real world problem, moving to abstraction as the model is built, solving the model using mathematical techniques, and returning to the real world with solutions and results based on the calculations performed in the mathematical modeling tool.

Keep in mind that mathematical models are not just used to mimic real world problems, but actually solve real world problems using mathematical techniques with results that can be applied to physical systems. Generally, the success of a mathematical model is judged on how accurate its predictions are, as well to what degree it can be applied.

**Starting the Math Engine: Maple 15**

Maple 15 is Maplesoft's primary technical computing product and the math engine that supplies the computing horsepower to MapleSim 5 through a direct connection. It can handle math problems from simple algebra to advanced number theory with myriad expressions and everything in between. Maplesoft says it can also compute symbolic solutions to differential equations that no other system can handle, as well as solve 96% of the standard benchmark standard for differential equations (Differentialgleichungen by Kamke). Differential equations are especially important when using MapleSim 5 because the behavior of a mathematical model is typically defined with ordinary differential equations (ODEs).

**Using the smart document environment provided by Maple, you can automatically capture all of your technical knowledge in an electronic form that combines calculations, explanatory text and math, graphics, images, sound, and diagrams.**

Like an increasing number of computationally intensive CAD applications, Maple 15 takes advantage of a computer's CPU by automatically detecting and using all available cores for performing computations in parallel. Memory management and allocation is also improved in Maple 15.

CAD users are familiar with parametric design, and on the mathematical side Maple 15 provides parametric solving. For example, you can get complete solutions to parametric polynomial equations showing all of the different solutions in terms of the properties of the unknown parameters. Sort of a mathematical equivalent of “what-if” scenarios in CAD simulation.

I found one of the best ways for getting up to speed with Maple 15 were the Clickable Math tools that include demonstrations for exploring and learning common mathematical concepts, such as methods of integration and derivatives.

A word of advice – time spent brushing up on some basic math concepts in Maple 15 will help flatten your learning curve with MapleSim 5, so plan on setting aside a least a little time to do so. All in all, Maple 15 is an excellent tool for learning math at many different levels.

**Physical Modeling and Simulation**

MapleSim 5 is a multi-domain (mechanical, electrical, etc.) modeling and simulation tool for physical systems, including complex electromechanical (mechatronic) systems. In MapleSim vernacular, physical modeling, (or better described as physics-based modeling), involves using mathematics and physical laws to describe the behavior of a single engineering component or a system of interconnected components.

Unlike competing mathematical modeling products that use a signal-flow approach and require explicit definition of system inputs and outputs, MapleSim employs a unique topological representation for connecting components with no need for considering how signals flow between them. A big advantage to topological representation is that it translates to its mathematical representation, and this ability allows MapleSim to automatically generate system equations. The system equations are then simplified (redundant equations are removed, expressions are combined and reduced without fidelity loss, etc.), solved, and results are displayed.

Because it’s different than familiar CAD tools, before we get started, let's take a quick tour of the MapleSim 5 user interface.

**The MapleSim 5 User Interface**

- Main Toolbar – Tools for running a simulation.
- Navigation Toolbar – Tools for browsing models and changing model views.
- Model Workspace Toolbar – Tools for laying out and selecting objects, and adding elements.
- Model Workspace – The area where model block diagrams are created and edited.
- Palettes Pane – Tools for creating MapleSim models and managing projects with two tabs:

- Libraries – Sample models and domain-specific components that can be added to models.
- Project – Tools for creating and browsing models, managing simulation results, probes, and documents that can be attached to models.

- Console – Contains panes for Help, progress messages, and diagnostic debugging messages.
- 3D Workspace (Visualization Area) – The area in the window where models being created or edited are displayed.
- Parameters Pane – Provides viewing and changing of parameter values and component names in physical models, specifies simulation values, and configures display options for simulation results graphs/plots. The contents of the parameters pane change depending on the component or subsystem selected in the Model Workspace. This portion of the user interface forms the basis and essence of MapleSim's parametric mathematical modeling capabilities. All engineering parameters can be edited, with the exception of constants (such as pi), where modifications would not make sense.

The MapleSim 5 interface includes many new and improved features to reduce model development time and help manage complex models. For example, enhanced diagnostic tools provide early feedback related to the definition of the model itself, such as identifying inconsistent initial conditions. MapleSim then provides assistance in resolving the problem, so corrections can be made before running the simulation. Other additions include increased control over parameters and initial conditions, easy export of 3D animation simulation results, and streamlined design environments for building both model diagrams and 3D model representations. The improved simulation engine in MapleSim can now generate highly optimized C code for MapleSim models.

The basic steps for creating and simulating a physical model using MapleSim follow. Be mindful that the simulation process described below is greatly simplified and summarized.

- Add and connect model components into a system. Start by selecting components from the MapleSim component library. They are organized in domain-specific palettes , such as electrical, mechanical, etc. Next, define how components will interact in the model by specifying component property values, such as parameter units and initial conditions. Continue adding components and subsystems and specifying values. Annotate the model with lines, math notation, etc. As you build a model, view components and subsystems in the Model Tree browser.
- Simulate and visualize a model. All components in models contain algebraic and/or differential equations that describe behavior. Components may define events which, in turn, can change component behavior. Connections between components generate additional equations that describe how the components interact with each other. All of the equations are collected into one large system and parameters are substituted in. MapleSim then takes this potentially large system of hybrid equations and simplifies for solving, while ensuring that no information is lost and full accuracy of the results are preserved. The equation is integrated and solved. Lastly, the results are generated and displayed with graphs showing quantities of pre-defined interest. For multi-body mechanical systems, 3D animations can be displayed.
- Analyze a model. Because MapleSim is integrated into the Maple environment, if required, you can use Maple commands, embedded components, plotting tools, and other features to analyze and manipulate behavior of MapleSim models or subsystems. For example, you can use Maple to retrieve and work with MapleSim model equations, test input and output values, as well as perform other advanced analysis tasks.

Maplesoft provides excellent documentation and tutorials for MapleSim 5, along with recommended best practices that include:

- To begin building a model, drag components from palettes to the workspace, then position, orient, and connect them.
- Create subsystems for component groups that can be reused and analyzed.
- Use the debugging console to identify unintended subsystem copies and unconnected components.
- When building electrical models, include ground components in electrical circuits and verify connections of current and voltage sources.
- When building 1D translational models, verify that all force arrows are pointed in the same direction.

These are just a few best practices, but these and others will ensure that models work as intended the first time.

**What's New in MapleSim 5**

Since it been a while since I had last taken a close look at MapleSim, I was interested in what was new in MapleSim 5. Some of the highlights I discovered included:

- Over 150 new components in MapleSim 5 that expand the modeling capabilities of MapleSim, so you can use it to model a wider range of systems. A new Magnetic Library has components that can be used to model electromagnetic solenoids, saturating transformers, motors, and other devices.
- A new thermal fluids library adds thermal fluids components, so you can model heat loss in pipes and valves in MapleSim. Additional electrical components include multiphase switches, analog switches and semiconductors, three-phase transformers, and digital converters. Mechanical components have been expanded and provide 1D translational and rotational motion and force drivers, and sensors.

MapleSim 5 includes over 150 new additional components, including new libraries for magnetics and thermal fluids.

MapleSim 5 includes over 150 new additional components, including new libraries for magnetics and thermal fluids.

- MapleSim 5 includes enhanced diagnostics to assist you in testing, building, and troubleshooting your model. In addition to construction diagnostics, MapleSim 5 now provides early feedback related to the definition of the model itself, such as identifying inconsistent initial conditions, so that you can make corrections before running a simulation. MapleSim shows the location of the problem within the model by highlighting the affected components. In many cases, MapleSim provides guidance to help you resolve the problem, such as telling you which variables may need to change. With these enhanced diagnostics, simulation problems are avoided or resolved quickly, reducing model development time.
- You can quickly experiment with your model by changing parameter and initial conditions values directly, without having to first navigate to the subsystem or component where the parameter is defined in the model diagram. You can also temporarily override system variables, such as modifying a single instance of a shared library component or subsystem. Once you are satisfied with the results, you can choose to maintain different values or promote the new value so it is shared by all copies.
- The model design environment now includes smart automatic rerouting of diagrams to simpler, cleaner forms, scalable port labels, and automatic labeling of subsystem ports. As a result, it is faster to construct the diagram, and the results are easier to interpret.
- Numerous improvements to the 3D modeling environment make it easier to construct and explore 3D models. MapleSim 5 lets you zoom in on a selection or the position of the cursor. You can select a specific component from a list of all components that share the same position in the 3-D diagram.

**MapleSim’s multi-domain modeling environment lets you combine elements from different domains into a single model. This electro-hydraulic clutch actuator includes components from the new magnetics library in MapleSim 5, as well as electrical, mechanical, and hydraulic components.**

**Final Thoughts**

Maple 15 and MapleSim 5 form a combination of software products that work extremely well together for solving general mathematical problems, but really excel at creating and solving parametric problems involving physical models and simulation.

Each succeeding release of Maple and MapleSim get significantly better and as mathematical learning, modeling, and simulation tools, continue to be in class by themselves.

**Evaluation**

**MapleSim5/Maple 15**

**Mathematical tools for parametric physical modeling and simulation**

**Pluses:**Wide range of math modeling capabilities; product support (documentation, tutorials, etc.); result outputs; appeal and usefulness to broad range of prospective technical users.

**Minuses:**None significant.

**Overall Grade: A+**

**Price: Maple 15 – $2,275 (USD)**

**MapleSim 5 – $5,515 (USD)**

*Discounted pricing available for academic and government users.*

**For More Information: www.maplesoft.com**

**The Week’s Top 5**At MCADCafé we track many things, including the stories that have attracted the most interest from our subscribers. Below are the news items that were the most viewed during last week.

**New Software With Integrated NVIDIA iray Simplifies 3D Rendering and Animation**Bunkspeed, a developer of 3D rendering and animation technology introduced the Bunkspeed PRO Suite 2012 that builds on Bunkspeed SHOT and Bunkspeed MOVE with new features and work flow capabilities that are suited for industrial designers, engineers, marketers, architects, and any 3D creative professionals who want to take their images and animations to a new level. With this release, the company merged its previous software Bunkspeed SHOT PRO and Bunkspeed Move PRO, and integrated NVIDIA iray version 2, into a single “PRO Suite,” simplifying its offering. The entire product line is now based on the same core technology, user interface, and the NVIDIA iray engine, allowing users to move seamlessly from Bunkspeed SHOT, to Bunkspeed MOVE to the Bunkspeed PRO Suite as skills and requirements increase. Bunkspeed Pro Suite 2012 features include all the functionality of Bunkspeed SHOT 2012 and Bunkspeed MOVE 2012 plus:

- Advanced image processing and camera manipulation tools
- Single click “render pass” output for post production
- All new configuration and model set capability for creation of variants
- Photometric lights including spot, point and directional
- Bunkspeed QUEUE - Simple yet powerful “visual” render queue allowing the user to see jobs in process and render offline
- Bunkspeed BOOST - Allows a Bunkspeed PRO user to connect to another Bunkspeed PRO users machine to boost offline render power.

**
CIMdata Releases 2011 PLM Market and Solution Supplier Analysis Report**

CIMdata, Inc. announced the release of the CIMdata 2011 PLM Market and Solution Supplier Analysis Report, the third of five modules of the CIMdata PLM Market Analysis Report Series. This report focuses on the PLM market, its main segments, and the financial results for PLM solution suppliers. It is important to note that all data and revenue information presented in this report are based on CIMdata’s estimates of the PLM market and the revenue performance of the PLM solution suppliers. The CIMdata PLM Market Analysis Report Series is packaged as five modules:

- The CIMdata 2011 Executive PLM Market Report provides an overview of CIMdata’s complete global analysis.
- The CIMdata 2011 PLM Industry Review and Trends Report is mainly qualitative in nature, and focuses on key issues facing the global PLM ecosystem of solution providers and end user organizations.
- The CIMdata 2011 PLM Market and Solution Supplier Analysis Report details measures of and forecasts for the overall PLM market and key segments, including Tools, cPDm, and Digital Manufacturing.
- The CIMdata 2011 PLM Market Geographic Analysis Report provides an additional view of the 2010 market results, by major geography.
- The CIMdata 2011 PLM Market Industry Analysis Report provides an industry segmentation view of the 2010 market results.

**
Rapidform Updates 3D Scan Data Processing Tool**

INUS Technology released its turnkey Software Development Kit (SDK) for 3D scanning application development. The updated version of Rapidform.dll enables developers to rapidly deploy industry-proven point, mesh and surfacing functions into their own software products with minimal effort. The latest version of Rapidform.dll focuses on making mesh operations easier and more powerful. The SDK now includes Rapidform’s advanced rewrap, adaptive remeshing and curvature flow improvement algorithms, making mesh optimization easier. INUS Technology has spent more than a decade creating and refining point cloud and mesh processing tools to deliver great results from any type of 3D scanner. With Rapidform.dll, third party developers can take advantage of this expertise and integrate the technology into their own apps. New features in the SDK include:

- Mesh topology improvement tools
- Mesh editing capabilities, such as mesh Boolean operations and mesh cutting
- Advanced triangle normal repair (to fix common issues with mesh direction)
- User interface APIs for large point cloud and mesh display and selection tools

**
Altair Releases Student Edition of Its Popular HyperWorks Computer-Aided Engineering Software Suite**

Altair Engineering, Inc. announced the release of the HyperWorks 11.0 Student Edition, a personal academic version of the popular suite of computer-aided engineering (CAE) software used by manufacturers around the world. The Student Edition offers affordable opportunities for engineering and design students to gain experience in computer simulation with the same software that engineering professionals use to design and develop everything from aircraft and automobiles to computer chips and golf clubs. As part of the program's global roll-out, the first 200 students in each country to register at the Altair Online Store will receive the HyperWorks 11.0 Student Edition for free. The HyperWorks Student Edition is available for purchase now through Altair's Online Store (
https://secure.altair.com/onlinestore) and includes access to core HyperWorks commercial technologies that support the complete CAE workflow process for various solution types and applications.

** Jeffrey Rowe** is the editor of MCADCafé and MCAD Weekly Review. He can be reached at
Email Contact or 719.221.1867.

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