Continuum Mechanics As The First Mechanics Course

This paper describes an introductory course in continuum mechanics. Taught within Harvey Mudd College’s broad, unspecialized curriculum, the course is designed for second-semester sophomores or juniors who have not had any of the standard engineering courses in mechanics (i.e., statics, dynamics, or strength of materials). We describe in this paper the course’s development and its contents, including its many illustrative real-world case studies. We also show how it is uniquely positioned to demonstrate the connections between solid and fluid mechanics, as well as the larger mathematical issues shared by both fields, to students who have not yet taken courses in fluid mechanics and/or strength of materials. We also discuss our success in introducing continuum mechanics at such an early point in the curriculum, as we detail the course’s implementation over eight semesters, its assessment during that time, and the response of some 300 students who have taken the course. Introduction Continuum mechanics is a course taken routinely by graduate students or, less frequently, by advanced undergraduates who are likely to go on to graduate work in mechanics. As a result of changes made within Harvey Mudd College’s broad, unspecialized engineering curriculum, we have developed an introduction to continuum mechanics for second-semester sophomores or juniors who have not had any of the standard engineering courses in mechanics (i.e., statics, dynamics, or strength of materials). The essence of continuum mechanics, the internal response of materials to external loading, is often obscured by the complex mathematics of its formulation. By building gradually from onedimensional to twoand three-dimensional formulations, we are able to make the essence of the subject more accessible to undergraduate students. From this gradual development of ideas, with many illustrative real-world case studies interspersed, students develop both physical intuition for how solids and fluids behave, and the mathematical techniques needed to begin to describe P ge 941.1 Proceedings of the 2004 American Society for Engineering Education Annual Conference & Exhibition Copyright © 200, American Society for Engineering Education this behavior. At the same time they gain a unique appreciation for the connections between solid and fluid mechanics. This course is well positioned to demonstrate the connections between solid and fluid mechanics, as well as the larger mathematical issues shared by both fields, to students who have not yet taken courses in fluid mechanics and/or strength of materials. The context and foundation provided by this course are available to students as they specialize (by choosing electives, by selecting career paths, or by going to graduate school) in either solid or fluid mechanics, or specialize in the connections themselves by returning to a deeper study of the overarching field of continuum mechanics. Over four academic years, we have had success in introducing this subject at such an early point in the curriculum. Such a course could replace statics and first courses in strength of materials and in fluid mechanics in many curricula. We anticipate that such a course will become more common in unspecialized curricula such as ours, as well as in new curricula, and in traditional curricula, many of which feel dual pressures to become broader and to reduce the number of credit hours. In most engineering curricula, students take a year of mechanics in their introductory physics courses. Then, in civil and mechanical engineering programs, they will more than likely take onesemester introductory courses called statics, dynamics, and strength of materials—and there is a great deal of repetition involved. Depending on one’s point of view and rhetorical preferences, one might regard this aspect of curricular structure as useful reinforcement, or as repetition that consumes far too much of an increasingly scarce resource, curricular time. Indeed, one might argue—and this is certainly the stance implied by Harvey Mudd’s unspecialized program—that such repetitious reinforcement mistakenly substitutes topical content in the curriculum for a more holistic emphasis on engineering as a process that may be better learned by applying the principles of and approaches to engineering modeling and problem solving across a broader range of topics. There is certainly an attendant risk of making topical coverage too superficial, but there is perhaps an equally great risk of obscuring the power and generality of a processbased approach by too much repetition of the same topic(s) in ever greater detail. In our later discussion of student reaction to this course, we will also note that students were engaged by our devoting a significant portion of the course to a series of case studies. This approach, too, bears something of the “cost” of substituting meaningful discussions of both technical and social aspects of events such as the 1981 collapse of the Kansas City Hyatt Regency Hotel and the construction of the Three Gorges Dam in central China for further “depth” in the analysis of one-dimensional bars or of the hydrostatics of dams. It seemed to us that such case studies would offer conceptual reinforcement, real-world application, and an extension and expansion of course material whose benefits far outweighed this cost. Indeed, students have responded very well to the case studies: their interests have been piqued by realworld aspects of engineering, and they have been inspired to delve further into the underlying technical issues.