AE420/ME471 First programming assignment Solution
Topic: Finite element solution of 1D axi-symmetric problems Consider the simple structural problem of an axi-symmetric membrane (under constant tension T) on an elastic foundation (with distributed stiffne
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5.7 Isoparametric elements
Table of content
5.7.1 Introduction - Terminology
5.7.2 Isoparametric 1-D element
5.7.3 Isoparametric 2-D elements
* Quadrilateral elements
* Triangular elements
5.7.4 Convergence of mapped elements
5. 50
AE 420 / ME
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3. Basic concepts of FEM: solution of 1-D bar problem
Table of contents
3.1 Basic concepts : mesh, nodes, elements, interpolation, .
3.2 FEA of axially loaded bar
3.3 Notes : direct method, higher-order elements,
3.4 Principle of Virtual Work (P
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Chapter 2. Rayleigh-Ritz Method (RRM)
Basic idea: we assume that we know the spatial variation of the displacement field,
except for some unknown coefficients to be determined with the aid of the PMPE
Implementation:
n
u(x, y, z ) qi fi (x, y,
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5.5 Convergence of global elements
3 basic issues:
Convergence: does the numerical solution tend to the exact one (i.e., does the
numerical error tend to zero) as the number of elements tend to infinity (i.e., as the
element size h tend to zer
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Application
The expression of the potential energy for a membrane on an elastic foundation is
=
2
2
1 w w
T + + kw 2d
2 x y
qw d
where
w(x, y ) is the membrane deflection
T is the constant tension
k is the stiffness of the elastic foundatio
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Example 1
1) Use the finite element method (direct and PMPE approaches) to solve the following problem:
Q
1
k1
1
2
k6
k2
2
3
k3
3
6
4
k4
4
P
5
5 k5
AE 420 / ME 471
3. 29
Example 2
AE 420 / ME 471
3. 30
1
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Example 3
AE 420 / ME 471
3. 31
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Group Project
Presentation in class
Oct 30 and Nov 1 2013
AE 420 / ME 471
5. 1
Breakdown of Grade Allocation
Innovativeness of Research Question: 20%
Approach: 20%
Appropriate use of FEM: 30%
Interpretation of FEM Results: 20%
Presentation: 10%
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4. FEA of 2-D truss problems
Definition : a truss element is a 1-D structural element that can transmit efforts only along
its axis.
7
Example : bridge structure
1
4
8
6
2
9
7
3 5
1
8
2
10
3
9
11
12
10 15
16
14
4 13
5
11
18
17
19
6
P
+ own weigh
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AE 420 / ME 471 / CSE 451
Introduction to the Finite Element Method
Instructor: Huck Beng Chew
306H Talbot Lab.
Phone: 217-333-9770
Email: hbchew@Illinois.edu
Teaching Assistant: Marcus Tan
Email: htan8@Illinois.edu
AE 420 / ME 471
1. 1
What is
AE 420 / ME 471 - Second FE Programming Assignment Finite Element Code for 2-D Static Truss Structures Friday, March 12, 2010 Due on Friday, March 19, 2010 Problem description The assignment consists of 2 steps. Step 1) Code development From the course we