Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2012
Homework 8
MAE 4700/5700 (Fall 2012)
2D finite elements: linear elasticity
Due Monday, October 29st, 12:00 midnight
Problem 1 Thermal expansion (hand calculation)
An elastic body subjected to temperature tends to expansion. This expansion is given in
the
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2012
Homework 9
MAE 4700/5700 (Fall 2012)
2D finite elements: linear elasticity
Due Monday, November 5th , 12:00 midnight
Problem 1 Axisymmetric analysis (Matlab)
The problem of stress analysis of solids of revolution (axisymmetric solids) under
axisymmetric l
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2012
Homework 7
MAE 4700/5700 (Fall 2012)
2D finite elements: scalar
Due Monday, October 22th, 12:00 midnight
Problem 1 Confined flow around a rectangular wall
The irrotational flow of an ideal fluid (i.e. a nonviscous fluid) about a rectangular wall
(see the
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2012
MAE 4700/5700 (Fall 2012)
Exam 1
October 16th, 7:309:30 pm
Write in capital letters your full name and ID number on the front of the exam
book.
Closed books & notes.
No electronic devises will be allowed during the exam Violators will be
penalized follow
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2012
MAE 4700/5700 (Fall 2011)
Homework 6
2D finite elements
Due Tuesday, October 17th, 12:00 midnight
Problem 1 Weak form of the steadystate heat flow problem in twodimensions
(hand calculation)
Consider the problem definition in the following figure:
The g
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2011
MAE 4700/5700 (Fall 2011)
Introduction to MATLAB
8/25/11
MATLAB Tutorial
The following tutorial has been compiled from several resources including the online
Help menu of MATLAB. It contains a list of commands that will be directly helpful for
understandi
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2011
Finite Element Analysis for
Mechanical and Aerospace
Design
Prof. Nicholas Zabaras
Materials Process Design and Control Laboratory
Sibley School of Mechanical and Aerospace Engineering
101 Rhodes Hall
Cornell University
Ithaca, NY 148533801
[email protected]
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2011
Finite Element Analysis for
Mechanical and Aerospace Design
Prof. Nicholas Zabaras
Materials Process Design and Control Laboratory
Sibley School of Mechanical and Aerospace Engineering
101 Rhodes Hall
Cornell University
Ithaca, NY 148533801
[email protected]
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2011
Finite Element Analysis for
Mechanical and Aerospace Design
Prof. Nicholas Zabaras
Materials Process Design and Control Laboratory
Sibley School of Mechanical and Aerospace Engineering
101 Frank H. T. Rhodes Hall
Cornell University
Ithaca, NY 148533801
E
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2011
Finite Element Analysis for
Mechanical and Aerospace
Design
Prof. Nicholas Zabaras
Materials Process Design and Control Laboratory
Sibley School of Mechanical and Aerospace Engineering
101 Rhodes Hall
Cornell University
Ithaca, NY 148533801
[email protected]
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2011
MAE4700/5700: Finite Element Analysis for
Mechanical and Aerospace Design
Prof. Nicholas Zabaras
Materials Process Design and Control Laboratory
Sibley School of Mechanical and Aerospace Engineering
101 Frank H. T. Rhodes Hall
Cornell University
Ithaca, N
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2011
Finite Element Analysis for
Mechanical and Aerospace Design
Prof. Nicholas Zabaras
Materials Process Design and Control Laboratory
Sibley School of Mechanical and Aerospace Engineering
101 Frank H. T. Rhodes Hall
Cornell University
Ithaca, NY 148533801
E
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2011
Finite Element Analysis for
Mechanical and Aerospace
Design
Prof. Nicholas Zabaras
Materials Process Design and Control Laboratory
Sibley School of Mechanical and Aerospace Engineering
101 Rhodes Hall
Cornell University
Ithaca, NY 148533801
[email protected]
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Spring 2014
3.
Beams
linear elastic
only transverse loads
plane normal sections remain plane and normal
only plane stress  xx
Beam theory:
d2 u
d2
EI
dx2
dx2
So a solution is predicted to be a quartic polynomial uy (x) = a1 x4 + .
The shape function, however, is onl
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2011
Finite Element Analysis for
Mechanical and Aerospace
Design
Prof. Nicholas Zabaras
Materials Process Design and Control Laboratory
Sibley School of Mechanical and Aerospace Engineering
101 Rhodes Hall
Cornell University
Ithaca, NY 148533801
[email protected]
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2011
Finite Element Analysis for
Mechanical and Aerospace Design
Prof. Nicholas Zabaras
Materials Process Design and Control Laboratory
Sibley School of Mechanical and Aerospace Engineering
101 Frank H. T. Rhodes Hall
Cornell University
Ithaca, NY 148533801
E
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2011
Finite Element Analysis for
Mechanical and Aerospace Design
Prof. Nicholas Zabaras
Materials Process Design and Control Laboratory
Sibley School of Mechanical and Aerospace Engineering
101 Frank H. T. Rhodes Hall
Cornell University
Ithaca, NY 148533801
E
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2011
Finite Element Analysis for
Mechanical and Aerospace Design
Prof. Nicholas Zabaras
Materials Process Design and Control Laboratory
Sibley School of Mechanical and Aerospace Engineering
101 Frank H. T. Rhodes Hall
Cornell University
Ithaca, NY 148533801
E
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2011
Finite Element Analysis for
Mechanical and Aerospace Design
Prof. Nicholas Zabaras
Materials Process Design and Control Laboratory
Sibley School of Mechanical and Aerospace Engineering
101 Frank H. T. Rhodes Hall
Cornell University
Ithaca, NY 148533801
E
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2011
Finite Element Analysis for
Mechanical and Aerospace Design
Prof. Nicholas Zabaras
Materials Process Design and Control Laboratory
Sibley School of Mechanical and Aerospace Engineering
101 Frank H. T. Rhodes Hall
Cornell University
Ithaca, NY 148533801
E
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2011
Finite Element Analysis for
Mechanical and Aerospace Design
Prof. Nicholas Zabaras
Materials Process Design and Control Laboratory
Sibley School of Mechanical and Aerospace Engineering
101 Frank H. T. Rhodes Hall
Cornell University
Ithaca, NY 148533801
E
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2011
Finite Element Analysis for
Mechanical and Aerospace Design
Prof. Nicholas Zabaras
Materials Process Design and Control Laboratory
Sibley School of Mechanical and Aerospace Engineering
101 Frank H. T. Rhodes Hall
Cornell University
Ithaca, NY 148533801
E
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2011
Finite Element Analysis for
Mechanical and Aerospace Design
Prof. Nicholas Zabaras
Materials Process Design and Control Laboratory
Sibley School of Mechanical and Aerospace Engineering
101 Frank H. T. Rhodes Hall
Cornell University
Ithaca, NY 148533801
E
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2011
Finite Element Analysis for
Mechanical and Aerospace
Design
Prof. Nicholas Zabaras
Materials Process Design and Control Laboratory
Sibley School of Mechanical and Aerospace Engineering
101 Rhodes Hall
Cornell University
Ithaca, NY 148533801
[email protected]
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2011
MAE4700/5700: Finite Element Analysis for
Mechanical and Aerospace Design
Prof. Nicholas Zabaras
Materials Process Design and Control Laboratory
Sibley School of Mechanical and Aerospace Engineering
101 Frank H. T. Rhodes Hall
Cornell University
Ithaca, N
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Spring 2014
1.
General
DOF: nodes local DOF
BCs applied to prevent rigid body motion
2.
Trusses
all joints are pins
no moments on/in bars
axial deformation only
small displacements
ux , uy are essential BCs, fx , fy are natural
Local global:
C S 0 0
d1x0
d1x
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Spring 2014
5.
Shape/approximation functions
in general polynomials: u
= 0 + 1 x + 2 x.
lowerorder term cannot be omitted in favor of higherorder term completeness
must be continuous within element
must provide interelement continuity for all DOF (displacement, sl
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2012
MAE 4700/5700 (Fall 2012)
Homework 4
1DBVP
Due Monday, September 24th, 12:00 midnight
All homework problems here refer to the solution of onedimensional boundary value
problems: Weak forms, issues of numerical integration, discretization, boundary
condit
Finite Element Analysis for Mechanical and Aerospace Design
MAE 4700

Fall 2012
MAE 4700/5700 (Fall 2012)
Homework 3
trusses and beams
Due Monday, September 17th, 12:00 midnight
In this homework, we consider the analysis of beams. Problems 2 and 5 require
verification of the MatLab results with the Ansys solutions. Problem 5 combines