
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
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
Assume the Link AO is the input and revolves 360°, determine a. the coordinates of limit positions of point B, b. the angles (AOC) corresponding to the limit positions
oyfr
3. The figure shows a frame under the
influence of an external loading made up
of five forces and two moments. Use the
scalar method to calculate moments.
a. Write the resultant force of the
external loading in Cartesian vector
form.
b. Determine the
& direction
of the resultant moment of the
external loading about A.
15 cm
18 cm
2.2 N-m
B
50 N
45°
10 cm
48 N.m
250 N
60 N
20
21
50 N
25 cm
100 N
A
118,
27cm 5, 4:1
The 2-mass system shown below depicts a disk which rotates about its center and has rotational
moment of inertia Jo and radius r. The angular displacement of the disk is given by 0. The spring
with constant k₂ is attached to the disk at a distance from the center. The mass m has linear
displacement & and is subject to an external force u. When the system is at equilibrium, the spring
forces due to k₁ and k₂ are zero. Neglect gravity and aerodynamic drag in this problem. You may
assume the small angle approximation which implies (i) that the springs and dampers remain in
their horizontal / vertical configurations and (ii) that the linear displacement d of a point on the
edge of the disk can be approximated by d≈re.
Ө
K2
www
m
4
Cz
777777
Jo
Make the following assumptions when analyzing the forces and torques:
тв
2
0>0, 0>0, x> > 0, >0
Derive the differential equations of motion for this dynamic system. Start by sketching
LARGE and carefully drawn free-body-diagrams for the disk and the…
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
- A linear system is one that satisfies the principle of superposition. In other words, if an input u₁ yields the output y₁, and an input u2 yields the output y2, the system is said to be linear if a com- bination of the inputs u = u₁ + u2 yield the sum of the outputs y = y1 + y2. Using this fact, determine the output y(t) of the following linear system: given the input: P(s) = = Y(s) U(s) = s+1 s+10 u(t) = e−2+ sin(t) =earrow_forwardThe manometer fluid in the figure given below is mercury where D = 3 in and h = 1 in. Estimate the volume flow in the tube (ft3/s) if the flowing fluid is gasoline at 20°C and 1 atm. The density of mercury and gasoline are 26.34 slug/ft3 and 1.32 slug/ft3 respectively. The gravitational force is 32.2 ft/s2.arrow_forwardUsing the Bernoulli equation to find the general solution. If an initial condition is given, find the particular solution. y' + xy = xy¯¹, y(0) = 3arrow_forward
- Test for exactness. If exact, solve. If not, use an integrating factor as given or obtained by inspection or by the theorems in the text. a. 2xydx+x²dy = 0 b. (x2+y2)dx-2xydy = 0 c. 6xydx+5(y + x2)dy = 0arrow_forwardNewton's law of cooling. A thermometer, reading 5°C, is brought into a room whose temperature is 22°C. One minute later the thermometer reading is 12°C. How long does it take until the reading is practically 22°C, say, 21.9°C?arrow_forwardSolve a. y' + 2xy = ex-x² b. y' + y sin x = ecosx, y(0) = −1 y(0) = −2.5arrow_forward
- = MMB 241 Tutorial 3.pdf 2/6 90% + + 5. The boat is traveling along the circular path with a speed of v = (0.0625t²) m/s, where t is in seconds. Determine the magnitude of its acceleration when t = 10 s. 40 m v = 0.0625² 6. If the motorcycle has a deceleration of at = (0.001s) m/s² and its speed at position A is 25 m/s, determine the magnitude of its acceleration when it passes point B. .A 90° 300 m n B 2arrow_forward= MMB 241 Tutorial 3.pdf 4/6 67% + 9. The car is traveling along the road with a speed of v = (2 s) m/s, where s is in meters. Determine the magnitude of its acceleration when s = 10 m. v = (2s) m/s 50 m 10. The platform is rotating about the vertical axis such that at any instant its angular position is u = (4t 3/2) rad, where t is in seconds. A ball rolls outward along the radial groove so that its position is r = (0.1+³) m, where t is in seconds. Determine the magnitudes of the velocity and acceleration of the ball when t = 1.5s.arrow_forwardThe population of a certain country is known to increase at a rate proportional to the number of people presently living in the country. If after two years the population has doubled, and after three years the population is 20,000, estimate the number of people initially living in the country.arrow_forward
- = MMB 241 Tutorial 3.pdf 6/6 100% + | 日 13. The slotted link is pinned at O, and as a result of the constant angular velocity *= 3 rad/s it drives the peg P for a short distance along the spiral guide r = (0.40) m, where 0 is in radians. Determine the radial and transverse components of the velocity and acceleration of P at the instant = 1/3 rad. 0.5 m P r = 0.40 =3 rad/sarrow_forward= MMB 241 Tutorial 3.pdf 1/6 90% + DYNAMICS OF PARTICLES (MMB 241) Tutorial 3 Topic: Kinematics of Particles:- Path and Polar coordinate systems and general curvilinear QUESTIONS motion. 1. Determine the acceleration at s = 2 m if v = (2 s) m/s², where s is in meters. At s = 0, v = 1 m/s. 3 m 2. Determine the acceleration when t=1s if v = (4t2+2) m/s, where t is in seconds. v=(4²+2) m/s 6 marrow_forward5.112 A mounting bracket for electronic components is formed from sheet metal with a uniform thickness. Locate the center of gravity of the bracket. 0.75 in. 3 in. ༧ Fig. P5.112 1.25 in. 0.75 in. y r = 0.625 in. 2.5 in. 1 in. 6 in. xarrow_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