1. Finite Element Primer for Engineers: Part 4 Mike Barton & S. D. Rajan

2. ©, 2000, Barton & Rajan  Contents

3. ©, 2000, Barton & Rajan  Technologies That Compete With the FEM Other numerical solution methods: – Finite differences » Approximates the derivatives in the differential equation using difference equations. » Useful for solving heat transfer and fluid mechanics problems. » Works well for two-dimensional regions with boundaries parallel to the coordinate axes. » Cumbersome when regions have curved boundaries. – Weighted residual methods (not confined to a small subdomain): » Collocation » Subdomain » Least squares* » Galerkin’s method* – Variational Methods* (not confined to a small subdomain) * Denotes a method that has been used to formulate finite element solutions.

4. ©, 2000, Barton & Rajan  Technologies that Compete With the FEM (cont.) Prototype Testing » Reliable. Well-understood. » Trusted by regulatory agencies (FAA, DOT, etc.) » Results are essential for calibration of simulation software. » Results are essential to verify modeled results from simulation. » Non destructive testing (NDT) is lowering costs of testing in general. » Expensive, compared to simulation. » Time consuming. » Development programs that rely too much on testing are increasingly less competitive in today’s market. » Faster product development schedules are pressuring the quality of development test efforts. » Data integrity is more difficult to maintain, compared to simulation.

5. ©, 2000, Barton & Rajan  Contents

6. ©, 2000, Barton & Rajan  Future Trends in the FEM and Simulation The FEM in particular, and simulation in general, are becoming integrated with the entire product development process (rather than just another task in the product development process): – FEM cannot become the bottleneck. A broader range of people are using the FEM: – Not just hard-core analysts. Increased data sharing between analysis data sources (CAD, testing, FEM software, ERM software.) FEM software is becoming easier to use: – Improved GUIs, automeshers. – Increased use of sophisticated shellscripts and “wizards.”

7. ©, 2000, Barton & Rajan  Future Trends in the FEM and Simulation (cont.) Enhanced multiphysics capabilities are coming: – Coupling between numerous physical phenomena. » Ex: Fluid-structural interaction is the most common example. » Ex: Semiconductor circuits, EMI and thermal buildup vary with current densities. Improved life predictors, improved service estimations. Increasing use of non-deterministic analysis and design methods: – Statistical modeling of material properties, tolerances, and anticipated loads. – Sensitivity analyses. Faster and more powerful computer hardware. Massively parallel processing. Decreasing reliance on testing. FEM and simulation software available via Internet subscription.

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9. ©, 2000, Barton & Rajan  Selected FEM Resources on the Internet The internet offers virtually unlimited resources to persons interested in the FEM. The following links are a small sample of FEM sites on the Internet which the author has found useful. Thousands more (at least!) are readily available. Most commercial FEM developers have extensive presence on the Internet, with web pages that include company histories, descriptions of software products, and example FEM solutions. Other good FEM resources on the web originate with academia, government, and discussion and user groups.

10. ©, 2000, Barton & Rajan  Selected FEM Resources on the Internet (cont.) http://www.engineeringzones.com - A website created to educate people in the latest engineering technologies, manufacturing techniques and software tools. Exellent FEM links, including links to all commercial providers of FEM software. http://www.comco.com/feaworld/feaworld.html - Extensive FEM links, categorized by analysis type (mechanical, fluids, electromagnetic, etc.) http://femur.wpi.edu - Extensive collection of elementary and advanced material relating to the FEM. http://www.engr.usask.ca/%7Emacphed/finite/fe_resources/fe_resources.html - Lists many public domain and shareware programs. http://sog1.me.qub.ac.uk/dermot/ferg/ferg.html#Finite - Home page of the the Finite Element Research Group at The Queen's University of Belfast. Excellent set of FEM links. http://www.tenlinks.com/cae/ - Hundreds of links to useful and interesting CAE cited, including FEM, CAE, free software, and career information. http://www.geocities.com/SiliconValley/5978/fea.html - Extensive FEM links. http://www.nafems.org/ - National Agency for Finite Element Methods and Standards (NAFEMS).

11. ©, 2000, Barton & Rajan  Contents

12. ©, 2000, Barton & Rajan  References Cashman, J., 2000. “Future of Engineering Simulation,” ANSYS Solutions, Vol. 2, No. 1, pp. 3-4. Chandrupatla, T. R. and Ashok D. Belegundu, 1997. Introduction to Finite Elements in Engineering, Prentice Hall, Upper Saddle River, New Jersey. Kardestuncer, H., 1987. Finite Element Handbook, McGraw-Hill, New York. Krouse, J., 2000. “Physical Testing Gets a Bum Rap,” ANSYS Solutions, Vol. 2, No. 2, p. 2. Lentz, J., 1994. Finite Element Analysis Cross Training, unpublished lecture notes, Honeywell Engines and Systems, Phoenix, AZ. Nikishkov, G.V., 1998. Introduction to the Finite Element Method, unpublished lecture notes, University of Arizona, Tucson, AZ. Rajan, S.D., 1998. Finite Elements for Engineers, unpublished lecture notes, Arizona State University, Tempe, AZ. Segerlind, L. J., 1984. Applied Finite Element Analysis, John Wiley and Sons, New York.