ME335A Finite Element Analysis Win 16
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ME335A Winter Quarter 2016 Supplementary Notes #1
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Introduction
In the rst part of the course we will review the mathematical formulation of the nite
element method (FEM). We will see that the FEM can be based on t
ME335A Win 16 Problem Set 8
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ME335A Problem Set #8
Given Th Mar 3
Due in class Th Mar 10
Problem 1.
A 3-node triangular element in plane strain has nodal coordinates,
fxe11 ; xe21 g = f0; 11g
fxe12 ; xe22 g = f0; 0g
fxe13 ; xe23 g = f8; 8g
If,
de11
de21
ME335A Win 16 Problem Set 4
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ME335A Problem Set #4
Given Th Jan 28
Due in class Th Feb 4
Problem #1 (20 points)
Here we consider the location of Barlow points for the piecewise quadratic nite element
space. Assume that node 3 is the element center point
ME335A Win 16 Problem Set 6
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ME335A Problem Set #6
Given Fr Feb 12
Due in class Th Feb. 18
Problem #1
Use 1, 2 and 3-point Gaussian quadrature to integrate the following functions over [ 1; 1]
and express the integration error as a percentage of the exac
ME335A Win 16Solution Problem Set 2
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ME335A
Solution
Problem Set #2
Problem #1
i. (5 points) Galerkin approximation:
a(wh ; uh ) + (wh ; v h ) = (wh ; f ) + wh (0)h
a(wh ; g h )
(wh ; g h ) :
ii. (5 points) Stiness coe cients:
KAB = a(NA ; NB ) + (NA ; N
ME335A Win 16Solution Problem Set 1
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ME335A
Solution
Problem Set #1
Problem #1 (10 points)
Use the denitions of a( ; ) and ( ; ) to verify the properties of symmetry and bilinearity
for the model problem.
Operational symmetry:
Z 1
Z 1
u;x v;x dx =
v;x u;
ME335A Win 16 Problem Set 5
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ME335A Problem Set #5
Given Th Feb. 4
Due in class Th Feb. 11
Problem #1
Hughes, Ex. 8, pp. 107, parts (i), (ii) and (iii).
Problem #2
Hughes, Ex. 3, pp. 159.
Problem #3
Consider the 6-node (Lagrange) element shown.
1. Develo
ME335A Win 16 Problem Set 2
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ME335A Problem Set #2
Given Thu Jan 14
Due in class Thu Jan 21
Problem #1
Hughes, Ex.2, pp. 46, parts (i) (v) only.
Remark 1 Parts (vi) and (vii) will be solved in a later problem set. Note that this problem (string on an ela
ME335A Win 16 Problem Set 3
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ME335A Problem Set #3
Given Th Oct 9
Due in class Th Oct 16
Problem #1
Consider the nite element space of piecewise quadratic functions. The quadratic element
will have three nodes. Assume that local node 3 is located at the
ME335A Win 16 Problem Set 1
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ME335A Problem Set #1
Given Thu Jan 7
Due in class Thu Jan 14
Problem #1
Hughes, Ex.1 , pp. 7.
Problem #2
Consider the dierential equation
u;xx + u + x3 = 0;
x 2 (0; 1)
State the weak form (W ) when the boundary conditions ar
ME335A Win 16 Computing Assignment 1
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ME335A Computing Assignment #1
Given: Th Jan 21
Due: In class Tu Feb 2
Consider the two-point boundary value problem,
u;xx + u = f
u(1) = g
u;x (0) = h
x 2 (0; 1)
(1)
(2)
(3)
with data as follows,
f (x) = 2:0
g = 1:0
ME335A Win 16 Problem Set 7
ME335A Problem Set #7
Given Th Feb 18
Due in class Th Feb 25
Problem
Problem
Problem
Problem
Problem
#1
#2
#3
#4
#5
Ex.1 , pp.
Ex. 5, pp.
Ex. 1, pp.
Ex. 1, pp.
Ex. 2, pp.
81.
83
91
98
188
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