ME 305 - INTRODUCTION TO FINITE ELEMENTS IN MECHANICAL ENGINEERING

1993 Catalog Data: M.E. 305 Introduction to Finite Elements in Mechanical Engineering. Prerequisite: ME 311. I. (3)

Rod element stiffness matrix. The assembly process. Solution techniques, gaussian elimination. Truss examples. Beam elements. Frame examples. Plate bending. Heat conduction. Triangular and quadrilateral elements. The isoparametric formulation. Plane stress applications. The course is project oriented with a substantial design content. A commercial finite element package is used extensively.

TEXTBOOK:

Course Notes

"Work Book and Study Guide for ME 305, Finite Element

Modeling" by Andrew W. Santangelo (course pack)

COORDINATOR:

Richard A. Scott, Professor, ME

GOALS:

(i) To teach students the basic physical, engineering and computational issues involved in finite element codes. (ii) To familiarize students with a commercial finite element code (currently NASTRAN) and to use it in design projects.

PREREQUISITE BY TOPIC:

1. Elementary matrix analysis

2. Constant coefficient ordinary differential equations

3. Linear, infinitesimal elasticity theory for isotropic materials

4. Euler-Bernoulli beam theory

5. Theory of heat conduction

TOPICS:

1. Introduction and course overview (1 period)

2. Review of one-dimensional elasticity; stresses, strains and deformations in axially loaded members. Classical solutions. (3 periods)

3. Stiffness matrix for an axially loaded rod. (1 period)

4. Assembly processes for axially loaded rods (1 period)

5. Global/local coordinates and global stiffness matrix for trusses. (2 periods)

6. Truss analysis using NASTRAN. (3 periods)

7. Review of matrix theory. LDU decomposition. Gauss elimination. (2 periods)

8. Principle of virtual work for elastic bodies. Beam elements. Equivalent nodal loads.

(3 periods)

9. Plane stress/strain. Area elements. Turner triangle. Area coordinates. (3 periods)

10. Natural coordinates. Quadrilateral elements. Isoparametric formulation. (4 periods)

11. Gauss quadrature. (1 period)

12. Plane stress examples using NASTRAN. (2 periods)

13. Discussion of design projects. Modelling issues. (3 periods)

14. Dynamic problems. Consistent mass matrix. (2 periods)

15. Eigenvalue problems. Inverse power iteration. Use of NASTRAN. (3 periods)

16. Heat conduction. Thermal stiffness matrix. Solutions using NASTRAN. (4 periods)

12. Exams/reviews. (4 periods)

TOTAL: 42

COMPUTER EXPERIENCE:

(i) Students learn to operate NASTRAN (MSC/PAL II) through a series of assigned computer homework problems, (ii) Part of the midterm is an assigned design project, (iii) A final design project is required. Student work in groups of three and the projects are to some degree individual.

ESTIMATED CONTENT: (Engineering Science, Design)

Engineering Science: 67%,

Engineering Design: 33%