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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Textbook Question
Chapter 1, Problem 9E
In the structure shown, rigid blocks are connected by linear springs. Imagine that only horizontal displacements are allowed. Write the global equilibrium equations
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Q: For the spring system shown in the accompanying figure, determine the
displacement of each node. Start by identifying the size of the global matrix.
Write down elemental stiffness matrices, and show the position of each
elemental matrix in the global matrix. Apply the boundary conditions and
loads. Solve the set of linear equations.
Also, compute the reaction forces.
k2 = 9 lb
k1 = 20b
in
20 lb
k,=5 lb
ww
lb
in
kz = 5 lb
in
ks = 9
in
lb
k6 = 9 in
50 lb
k4 = 20 lb
kg = 20 b
in
in
K1
For the spring shown above,
kl=100 N/mm, k2-200N/mm, k3-100N/mm, P-500N, ul-u3-0
Find:
1. The global stiffness matrix
2. Displacements of nodes 2 and 3
The figure below shows a beam supported by a spring while subjected to a horizontal force f.
The spring has a natural unstretched length 7 and stiffness constant k. The total length of the
beam is 3L, the force acts at 2L (see figure). The spring sits on vertical slider, such that it
remains horizontal at all times.
7
2L
(a) Find the equilibrium values of the angle 0 as a function of the parameters: k,L,1, and f.
(b) Let 1 = L and f = 4kL. Determine the stability of the solution at 0 = 0 and interpret the result.
(c) Using the other stationary value for the angle, verify that the moment of the applied force and
the spring about the pivot (bottom left) sum to zero.
Chapter 1 Solutions
Introduction To Finite Element Analysis And Design
Ch. 1 - Answer the following descriptive questions a....Ch. 1 - Calculate the displacement at node 2 and reaction...Ch. 1 - Repeat problem 2 by changing node numbers; that...Ch. 1 - Three rigid bodies, 2,3, and 4, are connected by...Ch. 1 - Three rigid bodies, 2,3, and 4, are connected by...Ch. 1 - Consider the spring-rigid body system described in...Ch. 1 - Four rigid bodies, 1, 2, 3, and 4, are connected...Ch. 1 - Determine the nodal displacements, element forces,...Ch. 1 - In the structure shown, rigid blocks are connected...Ch. 1 - The spring-mass system shown in the figure is in...
Ch. 1 - A structure is composed of two one-dimensional bar...Ch. 1 - Two rigid masses, 1 and 2, are connected by three...Ch. 1 - Use the finite element method to determine the...Ch. 1 - Consider a tapered bar of circular cross section....Ch. 1 - The stepped bar shown in the figure is subjected...Ch. 1 - Using the direct stiffness matrix method, find the...Ch. 1 - A stepped bar is clamped at one end and subjected...Ch. 1 - A stepped bar is clamped at both ends. A force of ...Ch. 1 - Repeat problem 18 for the stepped bar shown in the...Ch. 1 - The finite element equation for the uniaxial bar...Ch. 1 - The truss structure shown in the figure supports a...Ch. 1 - The properties of the two elements of a plane...Ch. 1 - For a two-dimensional truss structure as shown in...Ch. 1 - The 2D truss shown in the figure is assembled to...Ch. 1 - For a two-dimensional truss structure as shown in...Ch. 1 - The truss shown in the figure supports force Fat...Ch. 1 - Prob. 27ECh. 1 - In the finite element model of a plane truss in...Ch. 1 - Use the finite element method to solve the plane...Ch. 1 - The plane truss shown in the figure has two...Ch. 1 - Two bars are connected as shown in the figure....Ch. 1 - The truss structure shown in the figure supports...Ch. 1 - It is desired to use the finite element method to...Ch. 1 - Determine the member force and axial stress in...Ch. 1 - Determine the normal stress in each member of the...Ch. 1 - The space truss shown has four members. Determine...Ch. 1 - The uniaxial bar shown below can be modeled as a...Ch. 1 - In the structure shown below, the temperature of...Ch. 1 - Prob. 39ECh. 1 - The three-bar truss problem in figure 1.23 is...Ch. 1 - Use the finite element method to determine the...Ch. 1 - Repeat problem 41 for the new configuration with...Ch. 1 - Repeat problem 42 with an external force added to...Ch. 1 - The properties of the members of the truss in the...Ch. 1 - Repeat problem 44 for the truss on the right side...Ch. 1 - The truss shown in the figure supports the force ....Ch. 1 - The finite element method as used to solve the...Ch. 1 - Prob. 48E
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