AERO 306 Study Guide - Final Guide: Virtual Work, Finite Element Method, Piecewise

• School: Texas A&M University
• Department: Aerospace Engineering
• Course: AERO 306
• Professor: John Whitcomb

Document Summary

This section summarizes the results from the following file. beamconvergence. mw. 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. 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. Shear: now there is some significant error showing up for the lowest order approximation. Now we will examine the error in satisfying 4th order differential equation of equilibrium. Only the error for the most accurate approximation is shown.