School

Texas A&M UniversityDepartment

Aerospace EngineeringCourse Code

AERO 306Professor

John WhitcombStudy Guide

FinalThis

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Convergence Behavior for Beam

This section summarizes the results from the following file.

beamConvergence.

mw

V1=10, M1=-400, L= 20, f0=5

This configuration was discussed earlier. This time we will consider the convergence behavior a

bit more seriously. This time we will consider polynomial approximations going up to a 9-term

solution.

Virtual work was used to obtain approximate solutions for the following problem. Three

approximations are used. Here are the interpolation functions.

So that we know the errors, the exact solution was also obtained by solving the fourth order

differential equation. This example demonstrates that a solution that appears to be exact for

displacements can actually have significant errors show up when three derivatives are taken to

calculate shear. It also demonstrates that if you take enough terms, the errors are very small.

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