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 6E

Consider the spring-rigid body system described in problem 3. What force

Hint: Impose the boundary condition

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(PSD) A precision milling machine, weighing 4500 N, is supported on a rubber mount. The force-deflection relationship of the rubber mount is given by F = 270x + 0.25(x^3). Determine the equivalent linearized spring constant of the rubber mount at its static equilibrium position.

Dynamics of rigid bodies
Problem 5

PROBLEMFor the plane truss given below, using the Matrix Stiffness Analysis method, determine;• Determine displacements of the joints• Determine the forces in the truss members• Determine the support reactionsNote that the whole system has 4 nodes and hence 8 degrees of freedom. These degrees of freedomsare shown (in their positive directions) on the right hand side of the problem picture (1 to 8). So, thesystem stiffness matrix, K, will be 8x8 in size.Force and displacement units should be consistent (mm’s and N’s for example)

# 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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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

Figure below shows a mass-spring model of the type used to design packaging systems and vehicle suspensions, for example. The springs exert a force that is proportional to their compression, and the proportionality constant is the spring constant k. The two side springs provide additional resistance if the weight W is too heavy for the center spring. When the weight W is gently placed, it moves through a distance x before coming to rest. From statics, the weight force must balance the spring forces at this new position. (if x=d) These relations can be used to generate the plot of x versus W. (a) The following values are given: k1=104 N/m; k2 = 1.5 *104 N/m; d =0.1 m. Create a function that computes the distance x, using the input parameter W; Then, test your function for the following two cases, using the values: W=500 N W=2000 N. (b) Create another script and use your function to plot x versus W for 0 < W < 3000 N for the values of k1, k2, and d given in part a.

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Find the global stiffness matrix, displacement at node 1&2, reaction forces at 1&4, and force in spring for the following figure shown below. k1=90 N/mm, k2=1800 N/mm, k3=80 N/mm, P=600 N and u1=u4=0

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'A model for the elbow joint models the bicep muscle connecting to the horizontal forearm by a vertical tendon 4cm from the elbow joint. A mass m is held in the hand 30cm from the elbow joint. If the maximum tension that can be exerted by the tendon before injury occurs is 2250N, find the maximum mass that can be held in this way.'
Im stuck on this question

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Derive the governing differential equation for each system with the chosen generalized coordinate.
a. The springs both have the coefficient of k. (see figure below).
Solve completely. Answers that will be provided COPIED/PLAGIARIZED from the other sources will be reported.

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Find the stiffness matrices for each element and the large (general) set of equations of the system.
(Start from the left when numbering the node points)
(Start from the left when numbering the elements)

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Find the differential equations for the motion of a pendulum in that its mass m is connected to a flexible helical spring (constant of stiffness K and length l. ). Assume that the movement takes place in a vertical plane.

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Consider the system where dynamic responses for M1 and M2 are to be obtained. Determine the transfer function relating X1(s)and F2(s)?
Do each step and solve it with right answer.
Draw Free body diagram for M1 and M2

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A spring-mass system is shown in the following figure. Use m=3.5 kg and k=100 N/m.
a. Determine the static deflection δst . Insert your answer in meters correct up to at least a third decimal place.
b. Determine the system period τ. Insert your answer in seconds correct up to at least a third decimal place.
c. Determine the maximum velocity vmax which results if the cylinder is displaced 140mm downward from its equilibrium position and released from rest. Insert your answer in m/s correct up to at least a third decimal place.

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Find the reaction forces for the following problems

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Figure 1.29
shows the suspension system of a freight truck with a parallel-spring arrangement. Find the equivalent spring constant of the suspension if each of the three helical springs is made of steel with a shear modulus G = 100 GPaand has 10 effective turns, mean coil diameter D = 50 cm, and wire diameter d = 5 cm

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Determine the equivalent spring constant of the system shown in the figure.

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Under some circumstances, when two parallel springswith constants k1 and k2 support a single mass, theeffective spring constant of the system is given byk 4k1k2/(k1 + k2). A mass weighing 20 pounds stretchesone spring 6 inches and another spring 2 inches. Thesprings are first attached to a common rigid supportand then to a metal plate. As the figure illustrates(see image), the mass is attached to the center of the plate in the distributiondouble spring. Determine the constant of theeffective spring for this system. find the equationof motion if the mass is initially released fromequilibrium position with downward speed of2 ft/sec.

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