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, th
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
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. Lab
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
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 Displaceme
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
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 m
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 th
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
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-Mise
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 vertic
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-Mise
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
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.
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 displace
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-Mise
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 posi
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}? antiw
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 mod
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)