1. The equation governing the deflection y of a simply supported beam of length L under uniform loading w is d² y ΕΙ dx2 wLx wx² = 2 2 with boundary conditions y(0) = y(L) = 0. Let E = 150GPa, I=20000cm², = w 20kN/m, and L = 2. (a) Determine the discretized template equation by substituting in a central finite difference approximation. Put all terms involving the dependent variable on the left side, and other terms on the right. Eliminate the denominators if possible (5 pts). (b) Use the template equation, along with the boundary condition equations to write a set of equations in matrix form that could be solved for the nodal values of y. Use 5 nodes, such that Ax 0.5 (5 pts). =
1. The equation governing the deflection y of a simply supported beam of length L under uniform loading w is d² y ΕΙ dx2 wLx wx² = 2 2 with boundary conditions y(0) = y(L) = 0. Let E = 150GPa, I=20000cm², = w 20kN/m, and L = 2. (a) Determine the discretized template equation by substituting in a central finite difference approximation. Put all terms involving the dependent variable on the left side, and other terms on the right. Eliminate the denominators if possible (5 pts). (b) Use the template equation, along with the boundary condition equations to write a set of equations in matrix form that could be solved for the nodal values of y. Use 5 nodes, such that Ax 0.5 (5 pts). =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. The equation governing the deflection y of a simply supported beam of length L under uniform
loading w is
d² y
ΕΙ
dx2
wLx
wx²
=
2
2
with boundary conditions y(0) = y(L) = 0. Let E = 150GPa, I=20000cm²,
=
w 20kN/m, and L = 2.
(a) Determine the discretized template equation by substituting in a central finite difference
approximation. Put all terms involving the dependent variable on the left side, and other terms on
the right. Eliminate the denominators if possible (5 pts).
(b) Use the template equation, along with the boundary condition equations to write a set of
equations in matrix form that could be solved for the nodal values of y. Use 5 nodes, such that
Ax 0.5 (5 pts).
=
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