AE 370 Programming assignment #7
Finite difference solution of PDEs
Solution
Problem 1. Implicit solver for dynamic response of a string
Solve the problem of the dynamic response of a membrane (assume infinite in the y direction)
2 w
2 w
w
T 2 = q x, t +

AE370 Programming Assignment #3
Solution
Problem 1. The Gauss quadrature rule with N integration points yields the exact integration of a
polynomial function of order 2N-1. For other types of function, this method can be used to evaluate the
approximate n

AE 370 Homework Assignment #8
Solution
Topics: Rayleigh-Ritz Method and 1D Finite Element Analysis
Problem 1
Consider the beam bending problem shown in Figure 1.
z
po
x
k
Figure 1
The beam is homogeneous and linearly elastic. It has a length L, a moment o

AE370 Programming Assignment #2
Solution
Topic: Polynomial interpolation
Problem 1. One of the standard inspection processes for aerospace vehicle is to monitor the crack
propagation after a certain number of flight cycles. Special non-destructive tests c

AE 470 Programming assignment #6
Finite difference solution of PDE
Solution
Problem 1. Implicit dynamic beam bending solver (Important note: this first part of the assignment is
a pencil-and-paper exercise)
The dynamic response of an elastic double-cantil

AE470 Fall 2009 Final Exam
3 hours Closed notes, closed books, no calculator
Problem 1
The dynamic response of a string of length L, density , damping coefficient under (constant) tension
T and subjected to the effect of a lateral load q (in N/m) and an e

AE370 Programming assignment #6
Solution
Problem 1. Beam Bending Non-constant cross section
Consider a cantilever beam with varying area moment inertia I(x) = Io(1 - x/2L), elastic modulus E, length
L, applied distributed load q, and applied shear force P

Problem 1
Least square fit coefficient associated with each approximation order:
Enter the order of the least square fit, N: 1
least_coeffs =
1.0e+03 *
-1.1820
0.5440
Enter the order of the least square fit, N: 4
least_coeffs =
-66.6667
-74.0559
128.1643

AE470 Programming assignment #6
Friday October 8, 2010
Due Monday October 25, 2010
Topic: Numerical solution of ODE
Problem 1. Nonlinear ODE
This problem is an extension of the second problem of the 4th homework assignment, which was concerned with
the eq

AE470 Programming assignment #5
Wednesday September 29, 2010
Due Friday October 8, 2010
Solution
Topic: Numerical solution of ODE
Problem 1. Nonlinear ODE
a) Study the stability and precision of Heuns scheme. Detail every step of your derivation. Is the s

AE470 Programming assignment #7
Monday, November 1, 2010
Due on Wednesday, November 10, 2010
Topic: Finite difference method
Problem 1. Mode III fracture problem
One class of two-dimensional linearly elastic problems are so-called anti-plane shear problem

Chapter 2 - Survey of basic numerical schemes
Table of contents
2.1. Computational errors
2.1.1 Sources of approximation
2.1.2 Precision and stability
2.1.3 Computer arithmetic
2.2. Interpolation and polynomial approximation
2.2.1 Least square fit
2.2.2 P

AE470 Programming assignment #7
Solution
Topic: Finite difference method
Problem 1. Mode III fracture problem
One class of two-dimensional linearly elastic problems are so-called anti-plane shear problems for which
only one of the three displacement compo

AE470 Programming assignment #9
Monday November 30, 2010
Due on Friday December 10, 2010
Topics: Rayleigh-Ritz and Finite Element Methods
Problem 1. Rayleigh-Ritz method (Taken from 2004 final exam)
The expression of the potential energy for a beam (of le

AE 370 Homework 8
Assigned Monday, 18 April 2011
Due Monday, 25 April 2011
Due Wednesday, 27 April 2011
Topic: Rayleigh-Ritz method
1. Recall the example from class of a clamped-free rod with a linearly varying axial load, governed
by the DE
EAu00 (x) = f

AE 470 Programming assignment #6
Finite difference solution of PDE
Friday November 6, 2009
Due on Friday November 20, 2009
Problem 1. Implicit dynamic beam bending solver (Important note: this first part of the assignment is a
pencil-and-paper exercise)
T

AE 370 Homework 6
Assigned Friday, 4 March 2011
Due Friday, 11 March 2011
Topic: Solution of linear systems
Matlab commands: diag, inv, log10, \ (matrix left division)
1. For the system of equations
5x1 15x2 x3 + 2x4 = 11,
3x1 + 20x2 + 4x3 = 8,
x1 + 6x2 +

AE470 Homework assignment #4
Wednesday September 15, 2010
Due on Wednesday September 22, 2010
Solution
Topic: Numerical methods for root finding
Problem 1. Hybrid bisection/secant method
The classical relation between the pressure ratio ( pt = total press

AE470 Homework assignment #2
Wednesday September 1, 2010
Due on Wednesday September 8, 2010
Solution
Problem 1. Linear least square fit
Show (by hand) that the 1st order polynomial least square fit for two points xa , ya and xb , yb is what
(
)
(
)
we exp

AE 370 Homework 1
Assigned Friday, 21 January 2011
Due Friday, 28 January 2011
Topic: Matlab refresher
As per the syllabus, all programming assignments must be completed individually. To receive
any credit, every program and function must contain the comm

AE 370 Finite Element Project
Friday April 1, 2016
Due Monday April 18, 2016
Topics: Finite Element Method using Commercial Code Abaqus
Practice Problem 1 & 2:
Step by step instructions are given in the practice problem set attached for solving 2D and
3D

AE370 Homework 5
Friday April 10, 2015
Due on Friday April 24, 2015
Topic: Finite element method
Problem 1: Rayleigh Ritz Method
Problem 2: 1D FEM (Done in class)
Problem 3: 2D FEM