Finite Element Primer for Engineers: Part 3 Mike Barton & S. D. Rajan

Finite Element Primer for Engineers: Part 3 Mike Barton & S. D. Rajan

Introduction to the Finite Element Method (FEM) Steps in Using the FEM (an Example from Solid Mechanics) Examples Commercial FEM Software Competing Technologies Future Trends Internet Resources References Contents

Static analysis Deflection Stresses Strains Forces Energies Dynamic analysis Frequencies Deflection (mode shape) Stresses Strains Forces Energies Information Available from Various Types of FEM Analysis • Heat transfer analysis • Temperature • Heat fluxes • Thermal gradients • Heat flow from convection faces • Fluid analysis • Pressures • Gas temperatures • Convection coefficients • Velocities

Automotive industry Static analyses Modal analyses Transient dynamics Heat transfer Mechanisms Fracture mechanics Metal forming Crashworthiness Example FEM Application Areas • Aerospace industry • Static analyses • Modal analyses • Aerodynamics • Transient dynamics • Heat transfer • Fracture mechanics • Creep and plasticity analyses • Composite materials • Aeroelasticity • Metal forming • Crashworthiness • Architectural • Soil mechanics • Rock mechanics • Hydraulics • Fracture mechanics • Hydroelasticity

The FEM has been applied to a richly diverse array of scientific and technological problems. The next few slides present some examples of the FEM applied to a variety of real-world design and analysis problems. Variety of FEM Solutions is Wide and Growing Wider

This example shows an intravenous pump modeled using hexahedral elements.

Car tires require sophisticated analysis because of their complex geometry, large deformations, nonlinear material behavior, and varying contact conditions. Brick elements are used to represent the tread and steel bead, while shell elements are used in the wall area. Membrane elements are used to represent the tire cords.

This guitar features two strips of graphite running the length of the neck. This FEM model was used to study how much the neck moved when string forces were applied and moisture content changed. Using the FEM calculations, designers could try different reinforcement scenarios to increase neck stability.

Dynamic analysis of a tuning fork, to find it's first eight modes of vibration. 5 1 6 2 7 3 8 4

Commercially Available FEM Software Suites • Here we present a survey of some of the better-known integrated FEM software packages. These integrated systems allow users to perform all facets of FEM analysis, including modeling, meshing, solution and post-processing. • The Internet provides a vast new resource for individuals interested in the FEM. See the Reference section of this paper for interesting FEM links to start your Internet research. • In addition to the integrated FEM packages listed below, many vendors offer dedicated software for solid modeling, mesh generation, FE equation generation and solution, and post-processing.

Commercially Available FEM Software Suites (cont.)(partial list)

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.

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.

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.”

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.

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. Selected FEM Resources on the Internet

Selected FEM Resources on the Internet (cont.) • http://www.ansys.net • 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://www.engr.usask.ca/%7Emacphed/finite/fe_resources/fe_resources.html - Lists many public domain and shareware programs. • http://sog1.me.qub.ac.uk/ - 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.gorni.eng.br/ - Extensive FEM links. • http://www.nafems.org/ - National Agency for Finite Element Methods and Standards (NAFEMS). • http://www.6dof.com/

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.

Finite Element Primer for Engineers: Part 3 Mike Barton & S. D. Rajan