Structural Analysis

Course Contents

Structural Analysis is a method of description on how structures will mechanically behave under theoretically assumed conditions. Study on structural analysis is that of systematics composed of the fundamentals of physical science and applied mechanics.

The goals of this course are to teach students the fundamentals of computational methods and, through both lecture and student presentations, for students to gain the fundamentals of structural analysis methods. Additionally, while being exposed to cutting edge theory and sophisticated knowledge backed up by the instructor's experience in career as well as research activities in the related field.

This course will provide students with the knowledge and skills indispensible to implementing structural design and structural planning which will be required in the future internships.

Key Features

0. Basic thoughts for Graduate Courses (Master's Courses)

There are 4 approaches in education: 1) educational, 2) theoretical, 3) historical, and 4) heuristic approaches.

Educational approach 1) is that begins with easy-to-understanding concept and gradually proceeds to harder-to-understanding one. This method is frequently used for beginners. Theoretical approach 2) assumes that students already have basic understandings on the concept and naturally proceeds showing how more complex concepts are deduced. It is exactly this method which is used in the process of finding corollaries and theorems deduced from the presumed axioms of geometry. Historical approach 3) is teaching method based upon the historical order of development or discovery of the matters. In this approach, possible lack in the logical consistency or in easiness-to-understanding might be inevitable.

And the final approach, heuristic approach 4), is that in which, in the beginning stage of learning, all foregoing three approaches are evenly combined aiming to raise the level of learning followed by prompting students to find the clues to solve the problem.

What I am trying to say is that in actual classes all methods from 1) to 4) are used properly in accordance of cases, but in graduate school, method 4) should be mainly adopted. In other words, students in the class are expected to think and experiment for themselves, and carefully investigate the validity of the obtained results.

Several tips are adopted to design the class in its construction and how to carry out the lecture as well as the practice as shown in the followings.

1.Class Tips

The objective of this course is for students to completely grasp the fundamental parts of the theories and methods necessary for the structural analysis and design, particularly architectural design. In architectural construction, framed structures using beams and columns are mainstream, whereas continuous structures such as plates and shells are very rare. That is why one tends to think that learning only the knowledge of frame structures is generally sufficient for structural analysis and design.

However, the mechanics of architectural frames is based on the theory of three-dimensional elasticity as an academic framework, and the mechanics of architectural frames is obtained through several assumptions by which three-dimensional problem can be reduced into the fundamental theories with lower dimension. Therefore, students should start their study with an understanding of three-dimensional mechanics, through which they can straightly reach the fundamental principles.

However, in reality, many buildings are constructed using construction materials with standardized widths and thicknesses and, therefore, understanding of the two- or one-dimensional approaches are much more important from the viewpoint of actual structural design. For this reason, in this class, shell theory is intensively dealt with, which is basically for the structures consisted of curved lines and surfaces and, however, can cover all the related field of actual structural analysis.

On the other hand, in order to grasp the concepts detailed above, students will need some knowledge on a few mathematical methods. This class is consist of several fundamentals such as 1) matrix theory, 2) variational methods and principle, and 3) the theory of curved lines for the first half of the course, being followed by the shell theory and the finite element method(FEM) in the latter half.

2.Seminar tips

It is impossible to grasp highly complex and multilayered theories simply by thinking. Like a mountain climbing, you can only achieve a full understanding little by little, one step at a time. That is why honest hard work is imperative and students need check their own progress along the way. A steady effort is needed for students by fixing their theoretical progress through writing it down, and this is one and only way for letting them to smoothly move to the next theoretical process.

To attain the goals outlined above, in each class, a set of practice problems relating to topics just learned must be completed before the beginning of the next class. Many students might find seemingly unnecessary suffering in this process, but the state of having mastered cannot be found through such difficulty.

3.Tips on how this class will proceed

In this course, the textbook written by myself is distributed to each student. However, this is not only for professor but also for students who are to be assigned the portion in it, which each student lectures according to the predicted schedule. Each student is required to study in advance the preliminarily assigned portion of the textbook ahead of their class, prepare a summary and distribute its copy among the students in the class as well as the professor at the beginning of the class. Then, based on this summary, the student will be in charge of the class as an instructor, where he or she is expected to clearly explain the contents of the assigned section. The students listening will deepen their understanding of the textbook through the explanation. According to the explanation contents, professor adds some supplementary explanations with an additional lecture.

As mentioned above, students will be also assigned the practice problems each class. All students should prepare their answers as a report and the student who was in charge of the lecture of the foregoing week should give a presentation of the practice problem by distributing a copy of the answers. Students are expected to make copies of their homework ahead of the beginning of the class. All students (not just the student who presented their answers) will present their homework at the end of class. In this way, each student both presents a lecture and explains the homework answers at least once.

The course contents have been designed so that students learn the shell theory and fully grasp the course contents by placing a certain amount of burden on all students.

I have to mention here that in the class surveys of the foregoing years, many have stated, as was expected, "it was so hard," "it was a lot of work," but many have also stated "it was really worth of such hard work." It is true that studying is very hard. But one student stated, "I have realized that it is necessary to overcome the hardship in order to truly grasp a concept." For us teachers, such success to have let them state so is the greatest pleasure among the other all things.

The Aims of This Course

Structural Analysis is a method of prediction on how structures will mechanically behave under predicted conditions. The fundamental of the structural analysis is based upon physical science and applied mechanics. The goal of this course is to teach students the fundamentals of structural and computational mechanics and, through both lectures and presentations, to let them gain a mastery of structural analysis methods. Additionally, through touching the cutting edge theory and the sophisticated knowledge of the professor in charge in the related field, students are expected to obtain the ability for investigation and analysis of the structures, which is required for effective and rational structural design.

Contents of This Course

1	Fundamentals and Application of Matrix Method
	1	Matrix Calculation
	2	Application to Structural Engineering
2	Variational Method
	1	Variational Method and the Variational Principle
	2	Direct Method
3	Theory of Curved Lines and Curved Surfaces
	1	Geometry of Curved Lines
	2	Geometry of Curved Surfaces
4	Shell Theory
	1	Fundamental equation of Shell Theory
	2	Membrane Theory
5	Field Equation and Energy Principle
6	Finite Element Method

Movie presented at IASS-IACM 2008

IASS-IACM 2008: 6th Conf. on Computation of Shell & Spatial Structures "Computational Morphogenesis:Its Current State and Possibility for the Future"

Handout given at IASS-IACM 2008

Computational Morphogenesis -Its Current State and Possibility for the Future-

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