CEVE-MECH 527-427 MATRIX METHODS IN STRUCTURAL MECHANICS

FALL 2010

Ryon 201, Course MW 11 to 12:15 pm

Office Hours: MW 4:00 to 5:00 pm

Instructor: Professor Satish Nagarajaiah

Department of Civil and Environmental Eng.

Department of Mechanical Eng. and Material Science

213 Ryon Bldg., 713-348-6207

Satish.Nagarajaiah@rice.edu

Course

Outline

427 Introduction to matrix structural analysis of beams, trusses, and frames.

527 Introduction to differential and integral formulations: Minimum Principles, Variational Principles, Weighted Residuals, Energy Principles, and Principal of Virtual Work. Boundary, Initial and Eigenvalue problems. Introduction to finite element and finite difference methods for structural mechanics. Applications to static and dynamic truss, beam and frame problems. Use of computer software. 527 UG/Graduate Version. Graduate Version requires extra work: assignments and project.

Text Book: Detailed course notes will be provided: No textbook required.

Recommended prior courses: CEVE/MECH 311

Grading Policy:

Grading Policy	CEVE/MECH 527	CEVE/MECH 427
HW Assignments	20 %	25 %
Exam 1 (In class: closed book)	20 %	25 %
Exam 2 (In class: closed book)	20 %	25 %
Final Take Home (Computer Based Exam)	20 %	25 %
Final Project/Presentation	20 %	--

Homework Policy:

Homework due date will be announced in class. Homework submitted late will receive partial grade at the discretion of the instructor.

ADA:

If you have a documented disability that will impact your work in this class, please contact me to discuss your needs. Additionally, you will need to register with the Disability Support Services Office in the Ley Student Center. 713/348-5841; www.dss.rice.edu

COURSE TOPICS:

INTRODUCTORY MATHEMATICAL/ENERGY CONCEPTS

• Linear Algebra: Matrices, Determinants, Vector Spaces

• Positive/Negative/Semi Definite/ Indefinite Systems: Minimum Principles

• Energy Principles, Principal of Virtual Work/Complementary Virtual Work

• Stability and Dynamics, Eigen-value Analysis

INTRODUCTORY CONCEPTS IN STRUCTURAL ANALYSIS

• Unit load Method

• Deflection of trusses using complementary virtual work method

• Deflection of beams and frames using complementary virtual work method

• Classical compatibility methods: Method of consistent displacements

STIFFNESS METHOD/FINITE ELEMENT METHOD

• Stiffness Method using weighted residual/Galerkin/principle of virtual work

• Element stiffness matrix

• Coordinate Transformations

• Global stiffness matrix

• Solution, nodal displacements, element forces

• Settlement, initial and thermal strains

• 2D/3D -- truss, beam, frame elements

• Stiffness method for trusses, beams and planar frames

• Plane stress problems

Course Objectives and Outcomes

Course Objectives:

The objective of 427/527 is to learn the fundamental concepts of modern matrix structural mechanics, such as the stiffness method and the finite element method; while, briefly learning the concepts of classical structural analysis such as, energy methods, method of consistent displacement methods, displacement and force methods. The course builds on the fundamental concepts of structural analysis learnt in mechanics of solids and structures course (CEVE 311). The students will:

1. Gain a fundamental understanding of the analysis of statically determinate and indeterminate structures such as trusses, beams, frames and plane stress problems

2. Learn the determination of deflections using energy method

3. Study the classical structural analysis methods, such as energy, compatibility, and equilibrium methods

4. Learn the fundamental concepts of the stiffness method and apply it to a variety of structural problems involving trusses, beams, frames (two and three dimensional), and plane stress

5. Understand the introductory concepts of the finite element methods applied to structural mechanics problems

6. Learn the use of structural analysis software typically used in structural engineering design firms

Course Outcomes:

Students successfully completing 427/527 course will have a clear and thorough understanding of the fundamental concepts of modern structural mechanics and sufficient analysis skills for successful professional practice. The students will have the ability to perform advanced structural analysis by hand and by modern computer software. The students will be able to:

1. Apply the concepts of linear algebra (matrices, determinants) to structural analysis and mechanics problems

2. Calculate the deflection of trusses and beams using energy methods

3. Perform the structural analysis of determinate and indeterminate structures using classical compatibility methods, such as method of consistent displacements, force and equilibrium methods

4. Perform structural analysis using the stiffness method. Solve multiple degree of freedom two and three dimensional problems involving trusses, beams, frames and plane stress

5. Understand basic finite element analysis

6. Analyze complex structures using computer software

7. Document structural analysis results, write detailed project report, and communicate the project findings to the class by making a detailed PowerPoint presentation

Contribution to Meeting the Professional Component:

Engineering Content, 100%, 3 credit hours

Although not a required course, the students are advised to take this course as an essential preparation for professional practice