ME/AE 6212 Advanced Finite Element Analysis
Introduction to MATLAB
MATLAB (Matrix Laboratory) is an interactive software for doing vector and matrix
manipulations and general numerical computations. A summary of MATLAB commands
are given below with exampl

5.4.4 Direct Integration of Second Order Systems [11, 16., 17]
5.4.4.1 Central Finite Diﬁ’erence Method
Recall the second order equation (5.86):
{MW} + mm + [K]{ U} = {Fm} r> to (5.141)
{U} and being given for I: to
The central finite difference method is

Problem 3.9 in Text
Axial deformation of a stepped bar
Solve using FEM 1D Book Code
d = 4 in
Steel
12 in
d = 2.5 in
d = 2 in
Steel
Aluminum
8 in
200 kips
10 in
Steel, Es=30 x 106 psi
Aluminum, Ea = 10 x 106 psi
500 kips
Input Data
Problem 3.9: Stepped Bar

ME/AE 6212
DYNAMIC ANALYSIS: Transient Response
TRANSIENT RESPONSE PROBLEMS
When a structure has a load that varies with time, its corresponding
response (displacement, stress etc.) will vary with time. The dynamic
loads arise due to gust loads, impact fo

ME/AE 6212
DYNAMIC ANALYSIS: Free Vibration
DYNAMIC ANALYSIS
1. FREE VIBRATION PROBLEMS:
Natural frequencies of vibration and the
corresponding mode shapes
2. TIME DEPENDENT PROBLEMS:
Motion of structures with time under a
prescribed load or impulse.
CL

ME/AE 6212
CHAPTER 9 Part 2
Isoparametric Elements
Isoparametric Element
Use the same interpolation functions (or shape functions) for representing
the dependent variable and geometry.
For example:
s
u ui i
i
1
r
x xi i ,
i
1
r
y yi i
i
1
where i are shap

ME/AE 6212
Advanced Finite Element Analysis
Instructor: Dr. K.(KC) Chandrashekhara
Department of Mechanical and Aerospace Engineering
Missouri University of Science and Technology
Contact and Internet Access Information
Instructor: Dr. K. (KC) Chandrashek

ME/AE 5212
Introduction to Finite Element Analysis
Tutorial
Instructor: Dr. K. Chandrashekhara
Computer Assistants: Z. Huo and X. Wang
Copyright 2015
Department of Mechanical and Aerospace Engineering
Missouri University of Science and Technology
Rolla, M

ME/AE 5212
Axisymmetric Problems
Three-dimensional problems with axisymmetric geometry and
loading can be analyzed as two-dimensional problems
The cross-section revolves about the z-axis to form the threedimensional solid. The z-axis is called the axis

AE/ME 6527 Section A
Homework #00
Spring Semester 2016 January 29, 2016.
Due Wednesday, February 03.
1. Sign a copy of the course syllabus and outline, appending it to the present
homework statement, and save it as a single pdf le using the le name conven