Introduction To Finite Element Analysis And Design
2nd Edition
ISBN: 9781119078722
Author: Kim, Nam H., Sankar, Bhavani V., KUMAR, Ashok V., Author.
Publisher: John Wiley & Sons,
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 2, Problem 3E
Solve the differential equation in problem 2 using (a) two and (b) three finite elements. Use the finite element approximation described in section 2.4. Plot the exact solution and two- and three-element solutions on the same graph. Similarly, plot the derivative
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
(3) For the given boundary value problem, the exact solution is
given as = 3x - 7y. (a) Based on the exact solution, find
the values on all sides, (b) discretize the domain into 16
elements and 15 evenly spaced nodes. Run poisson.m and
check if the finite element approximation and exact solution
matches, (c) plot the D values from step (b) using topo.m.
y
Side 3
Side 1
8.0
(4) The temperature distribution in a flat slab needs to be studied under the conditions shown i
the table. The ? in table indicates insulated boundary and Q is the distributed heat source. I
all cases assume the upper and lower boundaries are insulated. Assume that the units of length
energy, and temperature for the values shown are consistent with a unit value for the coefficier
of thermal conductivity.
Boundary Temperatures
6
Case
A
C
D.
D.
00
LEGION
Side 4
z epis
Use the Lax method to solve the inviscid Burgers' equation using a mesh with
51 points in the x direction. Solve this equation for a right propagating discontinu-
ity with initial data u = 1 on the first 11 mesh points and u = 0 at all other points.
Repeat your calculations for Courant numbers of 1.0, 0.6, and 0.3 and compare
your numerical solutions with the analytical solution at the same time.
3. Using the trial function u¹(x) = a sin(x) and weighting function w¹(x) = b sin(x) find
an approximate solution to the following boundary value problems by determining the value
of coefficient a. For each one, also find the exact solution using Matlab and plot the exact
and approximate solutions. (One point each for: (i) finding a, (ii) finding the exact solution,
and (iii) plotting the solution)
a.
(U₁xx -2 = 0
u(0) = 0
u(1) = 0
b. Modify the trial function and find an approximation for the following boundary value
problem. (Hint: you will need to add an extra term to the function to make it satisfy
the boundary conditions.)
(U₁xx-2 = 0
u(0) = 1
u(1) = 0
Chapter 2 Solutions
Introduction To Finite Element Analysis And Design
Ch. 2 - Answer the following descriptive questions.
a....Ch. 2 - Use the Galerkin method to solve the following...Ch. 2 - Solve the differential equation in problem 2 using...Ch. 2 - Prob. 4ECh. 2 - Using the Galerkin method, solve the following...Ch. 2 - A one-dimensional heat conduction problem can be...Ch. 2 - Solve the one-dimensional heat conduction problem...Ch. 2 - Prob. 8ECh. 2 - Solve the differential equation in problem 8 for...Ch. 2 - Prob. 10E
Ch. 2 - Prob. 11ECh. 2 - Prob. 12ECh. 2 - Using the Galerkin method, calculate the...Ch. 2 - The boundary-value problem for a clamped-clamped...Ch. 2 - The boundary-value problem for a cantilevered beam...Ch. 2 - Prob. 16ECh. 2 - Consider a finite element with three nodes, as...Ch. 2 - A vertical rod of elastic material is fixed at...Ch. 2 - A bar in the figure is under the uniformly...Ch. 2 - Prob. 20ECh. 2 - A tapered bar with circular cross section is fixed...Ch. 2 - The stepped bar shown in the figure is subjected...Ch. 2 - A bar shown in the figure is modeled using three...Ch. 2 - Consider the tapered bar in problem 17. Use the...Ch. 2 - Consider the tapered bar in problem 21. Use the...Ch. 2 - Consider the uniform bar in the figure. Axial load...Ch. 2 - Determine shape functions of a bar element shown...Ch. 2 - Consider a finite element with three nodes, as...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- i need the answer quicklyarrow_forwardQ3) Find the optimal solution by using graphical method:. Max Z = x1 + 2x2 Subject to : 2x1 + x2 < 100 X1 +x2 < 80 X1 < 40 X1, X2 2 0arrow_forwardDIna Sami h.w1: solve the following differential equation numerically using Runge-Kutta Method (4th order). Find y (0.5) when y = 2 x + y, y (0) = 1. Take h = 0.5 boiker 00arrow_forward
- 3. Using the trial function uh(x) = a sin(x) and weighting function wh(x) = b sin(x) find an approximate solution to the following boundary value problems by determining the value of coefficient a. For each one, also find the exact solution using Matlab and plot the exact and approximate solutions. (One point each for: (i) finding a, (ii) finding the exact solution, and (iii) plotting the solution) a. (U₁xx - 2 = 0 u(0) = 0 u(1) = 0 b. Modify the trial function and find an approximation for the following boundary value problem. (Hint: you will need to add an extra term to the function to make it satisfy the boundary conditions.) (U₁xx - 2 = 0 u(0) = 1 u(1) = 0arrow_forwardInsulated Ax h, T» 1 2 3 4 5arrow_forwardPlease be careful with the decimalarrow_forward
- 2. Solve the following ODE in space using finite difference method based on central differences with error O(h). Use a five node grid. 4u" - 25u0 (0)=0 (1)=2 Solve analytically and compare the solution values at the nodes.arrow_forwardUse the graphical method to find the optimal solution for the following LP equations: Min Z=10 X1 + 25 X2 Subject to X1220, X2 ≤40 ,XI +X2 ≥ 50 X1, X2 ≥ 0.arrow_forwardQuestion 2: Air at the temperature of T1 is being heated with the help of a cylindrical cooling fin shown in the figure below. A hot fluid at temperature To passes through the pipe with radius Rc. a) Derive the mathematical model that gives the variation of the temperature inside the fin at the dynamic conditions. b) Determine the initial and boundary conditions to solve the equation derived in (a). air T1 Re Assumptions: 1. Temperature is a function of onlyr direction 2. There is no heat loss from the surface of A 3. Convective heat transfer coefficient is constantarrow_forward
- I need the answer as soon as possiblearrow_forwardThis is a multiple-part question, I just need help with part C, Table 2.2 is provided and you can refer to above parts for equations and boundary equations.arrow_forwardThis question Has multiple parts, i need just the Part B solved, Part A is about driving the equation that is mentioned in part a, Use that equation and the table to solve part b, should be simple.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
Principles of Heat Transfer (Activate Learning wi...
Mechanical Engineering
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Cengage Learning
Heat Transfer – Conduction, Convection and Radiation; Author: NG Science;https://www.youtube.com/watch?v=Me60Ti0E_rY;License: Standard youtube license