ABSTRACT ZHENG, FEI. Computational Investigation of High Speed Pulsjets. (Under the direction of Dr. William L. Roberts). Pulsejet may be the simplest propulsion system ever. Due to its simplicity, the pulsejet may be an ideal low-cost micro-propulsion sy
MAE 472, Spring 2010 Homework #1 Due 1/28/10
Problem 1 You are asked to design a tension strut for an aircraft which will survive 6,000 flights (using a factor of safety of 1.6). A typical loading on the part during a single flight is given below:
The S-N
Truss Element cont.
o The next step is to assemble elements to form a structure. o The best method to show the process is through an example:
1. Label node numbers 2. Label global displacements
3. Label element numbers and orientation ()
1
4. Construct ta
Work and Energy Principles Strain energy and complementary strain energy (Beam)
To calculate the strain energy, we use the same expressions for ez from before, substitute them into: 1
T U Ee z2 Ee z e z dV 2 V
2
dwo d 2vo d 2uo d 2vo d 2 uo 1 dwo U E y
Truss Element
o The first element we will consider is a 2D truss element. o Supports an axial load only.
o Element Forces
There are 2 element forces, one applied at each node.
1
o Element Displacements
There are 2 element displacements, one at each no
Solution for HW5 Problem 3 (Ansys problem)
Following previous steps in the example Specify geometry
Set keypoint numbers as #1(0,0), #2(60,34.64), #3(60,103.92), and #4(120,0), and create lines from keypoints (The order of the keypoints for a line doesnt
Introduction
o The finite element method (FEM) The complete structure is divided into a finite number of discrete elements.
The deformation of each element is relatively simple.
o The finite element method has 6 steps: 1. 2. 3. 4. 5. 6. o First we need so
MAE 472, Spring 2010 Homework # 5 Due 4/8/10
Problem 1 The truss member shown below has a cross-sectional area that varies linearly from A0 to AL. The modulus of elasticity E is constant throughout the bar. Derive the element stiffness matrix in local coo
Problem 3 The rigid bar system below consists of 2 bars, each with length L: All connections are pinned. The loads P are applied at the center of each bar. Assume small displacements (i.e. each pinned connection moves in the vertical direction only).
Find
Failure theories: Maximum Normal Stress Criterion: 1 St , 1 Sc , 2 St , 2 Sc Maximum Shear Stress (Tresca) Criterion: 1 2 SY , 1 SY , 2 SY
(at failure)
(at failure)
Maximum Distortion Energy (Von-Mises) Criterion 2 2 (at failure) 12 1 2 2 SY Principal Str
Problem A rigid bar of length L is supported by linear springs with spring constants of K1 and K2 respectively. Assume that the deformations are small and motion of the bar is restricted to the vertical plane. Use the vertical displacements at points A an
Failure theories: Maximum Normal Stress Criterion: 1 St , 1 Sc , 2 St , 2 Sc Maximum Shear Stress (Tresca) Criterion: 1 2 SY , 1 SY , 2 SY
(at failure)
(at failure)
Maximum Distortion Energy (Von-Mises) Criterion 2 2 (at failure) 12 1 2 2 SY Fatigue: Good
MAE 472, Spring 2010 Homework #4
Problem 1 Calculate the horizontal deflection at points D and C for the simply supported five-bar truss shown below. Use Castigliano's method to solve the problem.
Due 3/12/10
Problem 2 Solve Allen and Haisler problem 5.1
MAE 472, Spring 2010 Homework # 6 Due 4/29 /10
Problem 1 For the frame (beam) structure below, find the final equilibrium equation for the entire system, including the appropriate boundary conditions. You do not need to solve the final equations. Assume E
Finite Element Method 2D Beam Element
Now we consider the 2D beam element, 6 DOF in local coordinates: u1 x displacement of node 1 u2 - z displacement of node 1 u3 - rotation of node 1 u4 - x displacement of node 2 u5 - z displacement of node 2 u6 - rotat
Failure theories: Maximum Normal Stress Criterion: 1 St , 1 Sc , 2 St , 2 Sc Maximum Shear Stress (Tresca) Criterion: 1 2 SY , 1 SY , 2 SY
(at failure)
(at failure)
Maximum Distortion Energy (Von-Mises) Criterion 2 2 (at failure) 12 1 2 2 SY Principal Str
Required steps for solution of virtual work problems MAE 472
Find relationship between W1 and W 2 when system is in equilibrium.
W1
W2
45 o 60 o
1. Determine # of DOFs.
1 DOF
2. De ne equilibrium position and draw diagram in equilibrium state with all dis
Problem 1
The tapered beam shown below has a rectangular cross-section whose depth varies linearly in x:
w ghw U
. x:
.Yv
g)
Reqmwd: Iticuéizc {hr beam with 1M; {liilitti'lia liiuili}? antiwar section properties db inow:
« ,1]
s W
l
e i
/
rm
Problem Specification Determine the force in each member of the following truss. Indicate if the member is in tension or compression. The cross-sectional area of each member is 0.01 m, the Young's modulus is 200x109 N/m2 and Poisson ratio is 0.3.
2m A
1m
MAE 472, Spring 2010 Homework #2 Due 2/9/10
Problem 1 For the rigid block with mass m on an inclined plane shown below, calculate the virtual work done by gravity for a virtual displacement. a) b) c) d) up the incline down the incline in the horizontal di