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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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)
Determine the equations to find the nodal displacements using the finite element direct method for the
system as shown below. Assume that all free nodes undergo translation in x (1 DOF at each node) and
that external forces Fı and F2 are known. Nodes 3 and 4 are fixed. The spring constants are known to0.
Assume +x is to the right.
Derive all equations and apply boundary conditions-leave your answer in terms of all known variables
Do not rename the nodes or elements!
Node 3
Node 4
k
F1
F2
U2
Node 2
Node 1
Please solve all parts send only handwritten
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
- Write the global stiffness matrix of the spring assemblage shown. Assume that all springs remain horizontal, the vertical bars at nodes 2 and 3 are rigid and allowed to slide horizontally to the left or right. Node 1 K1 = 2000 lb/in K2 = 2000 lb/in Node 2 m K3 = 1500 lb/in K4 = 1500 lb/in Node 3 F = 250 lb ma K5 = 3000 lb/in Node 4arrow_forwardFind the global stiffness matrix, displacement at node 1&2, reaction forces at 1&4, and force in spring for the following figure shown below. N ki=90 mm k2=1800, mm N k3=80, P=600 N and mm U1=U4=0 k, k, P ks 1 2 4arrow_forwardConsider the following spring system. m, C2 C3 with spring constants c = |2 m2 Assume down is the positive direction. Write the stiffness matrix K = %3D 23 • Compute the displacements caused by the external forces f = -21 Displacement =arrow_forward
- 2arrow_forwardSee attached problem.arrow_forwardA spring system is shown here: k₁ 3 Ę k3 2 K₂ www ma 4 Ę₂ Part 1: For this specific system, develop the: a. Global stiffness matrix . b. Boundary condition vector • c. Load vector • d. Reduced system of equations • e. Reaction force equations (i.e., the equations eliminated by the boundary conditions) Part 2: Given: k1 = 70 N/mm, k2 = 110 N/mm, k3 = 165 N/mm, F1 = 150 N, F2 = 100 N, and nodes 1 and 3 are fixed; calculate the: a. Global stiffness matrix b. Displacements of nodes 2 and 4 c. Reaction forces at nodes 1 and 3 d. Spring force in each of the springsarrow_forward
- please solve step by stepsarrow_forward2- Derive the rule-of-mixtures expression for the composite extensional modulus E₁ assuming the existence of an interphase region. The starting point for the derivation would be the model shown below. For simplicity, assume the interphase, like the matrix, is isotropic with modulus E¹. With an interphase region there is a volume fraction associated with the interphase (i.e.,V;). For this situation: vf + vm + vi = 1 H |w²||wm|arrow_forwardFor the simple pendulum shown in the figure, write the governing equation in s-domain. Assume small angles and linearize your model. Initial conditions are zero. Explain each step clearly. - 0(1) L, length m, massarrow_forward
- solve using laplacearrow_forwardQ1: The system shown has two masses. Beam of mass (Jo#m L² kg.m²) rotates about fixed point (O) and its free end is connected to disk rotates about fixed point (O₂). Consider all connecting links are massless and rigid. Find 1- The displacements of points A, B, and C in addition to the rotations of masses, all in terms of 0. 2- Find the equation of motion (EOM) in terms of 0. 3- What is the natural frequency of the system? 0 L/2 8 Energy methods A Jo=m L²2 L/2 Joz-m R² R C B C 128arrow_forwardFind the Global Stiffness Matrix for the following Spring Structure. Use your answer to set up matrix Equation F=KX.arrow_forward
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