Lying by Approximation: The Truth about Finite Element Analysis

– The widespread availability of commercial FEA software in the academic institutions and pressure from industry to include it in the modern undergraduate curriculum has resulted in unique challenges in teaching the topic to undergraduate students who may or may not be adequately prepared to handle the subject. The present expository paper shares the author's experiences in delivering the FEA subject to university students both at the undergraduate and the graduate levels. The most common pitfalls for the understanding of the tool, particularly by the undergraduate students are highlighted.

Journal of Computer Science

Computer simulations and computational methods, such as the Finite Element Analysis (FEA) have become essential methodologies in science and engineering during the last decades, in a wide variety of academic fields. Six decades after the invention of the digital computer, advanced FE simulations are used to enhance and leapfrog theoretical and experimental progress, at different levels of complexity. Particularly in Civil and Structural Engineering, significant research work has been made lately on the development of FE simulation codes, methodologies and validation techniques for understanding the behavior of large and complex structures such as buildings, bridges, dams, offshore structures and others. These efforts are aimed at designing structures that are resilient to natural excitations (wind loads, earthquakes, floods) as well as human-made threats (impact, fire, explosion and others). The skill set required to master advanced FEA is inherently interdisciplinary, requiring in-depth knowledge of advanced mathematics, numerical methods and their computational implementation, as well as engineering sciences. In this paper, we focus on the importance of sound and profound engineering education and knowledge about the theory behind the Finite Element Method to obtain correct and reliable analysis results for designing real-world structures. We highlight common mistakes made by structural engineers while simulating complex structures and the risk of structural damage because of humanmade mistakes or errors in the model assumptions. The event of the collapse and eventual sinking of a concrete offshore platform in the North Sea is presented as a case study where a serious error in the finite element analysis played a crucial role leading to structural failure and collapse.

undamentals of Finite Element Analysis is intended to be the text for a senior-level finite element course in engineering programs. The most appropriate major programs are civil engineering, engineering mechanics, and mechanical engineering. The finite element method is such a widely used analysis-and-design technique that it is essential that undergraduate engineering students have a basic knowledge of the theory and applications of the technique. Toward that objective, I developed and taught an undergraduate "special topics" course on the finite element method at Washington State University in the summer of 1992. The course was composed of approximately two-thirds theory and one-third use of commercial software in solving finite element problems. Since that time, the course has become a regularly offered technical elective in the mechanical engineering program and is generally in high demand. During the developmental process for the course, I was never satisfied with any text that was used, and we tried many. I found the available texts to be at one extreme or the other; namely, essentially no theory and all software application, or all theory and no software application. The former approach, in my opinion, represents training in using computer programs, while the latter represents graduate-level study. I have written this text to seek a middle ground. Pedagogically, I believe that training undergraduate engineering students to use a particular software package without providing knowledge of the underlying theory is a disservice to the student and can be dangerous for their future employers. While I am acutely aware that most engineering programs have a specific finite element software package available for student use, I do not believe that the text the students use should be tied only to that software. Therefore, I have written this text to be software-independent. I emphasize the basic theory of the finite element method, in a context that can be understood by undergraduate engineering students, and leave the software-specific portions to the instructor. As the text is intended for an undergraduate course, the prerequisites required are statics, dynamics, mechanics of materials, and calculus through ordinary differential equations. Of necessity, partial differential equations are introduced but in a manner that should be understood based on the stated prerequisites. Applications of the finite element method to heat transfer and fluid mechanics are included, but the necessary derivations are such that previous coursework in those topics is not required. Many students will have taken heat transfer and fluid mechanics courses, and the instructor can expand the topics based on the students' background. Chapter 1 is a general introduction to the finite element method and includes a description of the basic concept of dividing a domain into finite-size subdomains. The finite difference method is introduced for comparison to the

The Mechanical Engineering Department at California State University, Northridge uses SolidWorks and related analysis applications such as CosmosWorks and FloWorks as the computational tools of choice for solid modeling (CAD) and finite element analysis (FEA). Originally the use of these tools was concentrated in the senior design capstone course, but one of the Department's goals is to integrate the use of this software throughout the curriculum. While the addition of new freshman and sophomore design courses have helped to fulfill this mission, some engineering courses have been slow to adopt the use of FEA for solving practical design problems. Barriers for adopting FEA in traditional engineering courses include time constraints related to covering the necessary breadth of material and the learning curve for faculty who are not especially proficient with creating complex assemblies in SolidWorks. An approach for lowering these barriers is to create SolidWorks model files for a number of engineering case studies in a variety of mechanical engineering disciplines. These files and associated documentation are made available to faculty and students to facilitate the assignment of design problems which require the use of FEA for their solution. Use of a Design vary key geometric dimensions by referencing SolidWorks objects via the Applications Programming Interface allows a student to easily create modified parts and analyze the effect of the changes with the appropriate FEA package. This paper describes models that have been created for courses in fluid mechanics and machine design. Emphasis is placed on a specific assignment created for a fluid mechanics course, including a comparison of the results from FloWorks with one-dimensional flow models. A preliminary assessment of the effectiveness of this assignment for demonstrating the role of FEA in analysis and design is also given.

2004 Annual Conference Proceedings

Finite element analysis (FEA) has become an essential tool in the product design process of many companies. A course in FEA is required in a large number of mechanical engineering and mechanical engineering technology curricula. Most FEA courses necessarily include some balance of theory and practical use of a commercial FEA program. In a course recently developed at Milwaukee School of Engineering, another element has been added to the FEA class in the Mechanical Engineering Technology Program: a mechanics of materials laboratory in which physical experiments are conducted to support the analysis exercises. In this paper, the course content will be discussed, with emphasis on the specific lab exercises that allow measured results to be compared to FEA results.

Scott Kiefer has spent the past ten years teaching mostly undergraduate courses in mechanics and mechatronics. He started his career at the University of Puerto Rico-Mayaguez, moved to Tri-State University, and is currently at Michigan State University. His BS is in Mechanical Engineering from the University of Wisconsin-Platteville, and his MS and PhD are also in Mechanical Engineering from North Carolina State University. Abstract Research has indicated that a good percentage of students who are dropping out of engineering are doing so because they have either lost interest or actually come to dislike studying it. This paper describes an effort to better connect students to engineering by incorporating lecture materials into a Solid Mechanics course that use example problems that students encounter in their every day lives. For example, rather than drawing a picture of an axial load being applied to a steel bar to talk about axial stress and strain, a pair of iPod headphones is shown and a discussion moderated about what kind of load would be needed to break them and how much would they stretch. The real life examples adopted in this course were first created by Eann Patterson as part of a National Science Foundation sponsored project to change the undergraduate mechanical engineering curriculum and make it more attractive to a diverse group of students. Specifically, this paper critiques the adaptation of five real life examples taken from the original project. Student response to the lecture material was measured by specific survey questions about the real life examples, survey questions about the course as a whole, interviews, and standard student course evaluation forms.