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 4E
a.
To determine
The approximate solution of the boundary value problem using one term approximation.
b.
To determine
The approximate solution of the boundary value problem using given approximation term by Galerkin’s method.
c.
To determine
The approximate solution of the boundary value problem using one term approximation for nodal values.
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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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- 2-the pivot value is the point of the intersection of the row of the leaving variable and the column of the solution. * true falsearrow_forwardCompletely solve. Box the final answer. WRITE LEGIBLY OR TYPEWRITE THE SOLUTIONS. Prove that the steady-state solution is yp = 4.8 sin 3t - 7.6 cos 3arrow_forwardSolve for the general solution and type of auxiliary equation of (2D3 – D² + 36D – 18)y= 0 c,ež* + c,cos3v3x+ czsin3v3x; c,ei + €zcos3vZx+ €3$in3v2x; distinct real roots distinct imaginary roots OB. c,e* + c2cos3v4x + C3sin3v4x; repeated imaginary roots c,e* + ¢zcos3v5x+ C3sin3/5x; repeated real roots Oc. OD.arrow_forward
- 2. Solve the system linear of Equation using Gauss- Jordan elimination (row operations), find the value of x1, x2 and x3. 2X1 - 2X2 + X3 = 3 3X1 - X3 + X2 = 7 X1 - 3X2 + 2X3 = 0arrow_forwardQ-Find the solution by using the simplex method? 1- Max Z=3X1+2X2 S. T: X1+X2 ≤ 4 X1-X2 ≤2 X1, X2 ≥0arrow_forwardDetermine if the system is consistent or inconsistent. Justify your answer and find all solutions to the system of linear equations. Justification should be written on your solution paper. Transform the matrix into ROW ECHELON FORM (REF) using row operations. 2x +8y+ 6z = 20 4x+2y-2z =-2 3x-y+z = 11 Enter final answer: (x, y, z) =(arrow_forward
- Solve the system of equation by Gaussian eliminationarrow_forward3. Answer the question completely and write down the given, required and formula that had been used. Provide graph and accurate/comple solution. The value are: V- 1 X- 5 W- 7 Y- 6 Z- 8arrow_forwardSolve the following differential equation: y'"-2y' +y= e*Inx Select one: a. YG.s=C;Xe¯*+Czx²e*+e* Jinx+ xe-* [Inx = C, sinx+ c>cosx+ sinx Inx+cosx /Inx b. YG.S c. None O d. YG.s=C,xe*+czx²e*-e* ] xInx+e* ]x?inx YG.s=Ce*+c2xe* - e* | xlnx+ xe* | Inx е.arrow_forward
- = Find the general solution to the following 2nd Order O.D.E., where y" y" + y + y = 0 (³x) - ₂ - C₂ sin sin (√³7)} ○ y(x) = e. {c₁ cos (³0) - -x)+ + C₂ sin(x)} y(x) = e{c₁ cos y(x) = e{c₁ cos(x) + ₂ sin(x)} ○ y (x) = c₁ · e¯7 · cos (³x) + c₂ · ež · sin (√³x) ○ y(x) = c₁ ·e· cos(x) + c₂ · €¯ · sin (³x) d² y(x) dx²arrow_forward7. Consider an element that conducts heat as shown below with length L, cross sectional area A, and heat conductance k. Nodes 1 and 2 have temperatures of T, and T2. The heat flux q due to conduction is given by: dT ΔΤ q = - k dx Ax This relationship is analogous to Hooke's Law from the prior problem. Heat transfer by conduction Qc is given by: Oc = qA Use equilibrium requirements to solve for the heat transfer by conduction Qci and Qcz at the nodes and use these equations to derive a "conductance matrix" (or the stiffness matrix due to conduction which is the analog of the stiffness matrix) for this heat conducting element. For the sign convention, consider heat flux positive when heat flows into the element and negative when it flows out of the element. Show your full matrix equation and the conductance matrix. Oci T T2 Oc2 2arrow_forwardQ3/ Solve the following system of three linear equations: 2.5a-b+3c+1.5d-2e 3a +4b-2c+2.5d-e -4a+3b+c-6d+2e= -81.2 2a+3b+c-2.5d+ 4e = -22.2 a+2b+5c-3d+4e -12.2 = 57.1 = 27.6arrow_forward
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