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,
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Chapter 2, Problem 19E
A bar in the figure is under the uniformly distributed load q due to gravity. For a linear elastic material with Young’s modulus E and uniform cross-sectional area A, the governing differential equation can be written as
a. Starting from the above differential equation, derive an integral equation using the Galerkin method.
b. Write the expression of boundary conditions at
c. Derive the assembled finite element matrix equation, and solve it after applying boundary conditions.
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For the cantilever plane truss in the figure above, use MATLAB to determine:
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Assuming that both supports are going to be fixed and the values of E = 70 GPa and A = 0.003125
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Question 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 constant
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...
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