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Aerospace Structures Extra Credit Project: Beam Bending

The Pennsylvania State University – Dr. Jose Palacios

A comparison of experimental data with different analytical methods of finding deformations of a bent beam

December 2021

This report was written for an extra credit grade in an Aerospace Structures course. I used mathematical concepts and CAD simulations of beam bending to determine their accuracy compared to experimental results. After data was gathered, a formal report was written in LaTeX using the standard AIAA format.

solidwork

Background

This experiment was conducted with the purpose of testing the accuracy of beam-bending principles and simulation methods when compared to experimental data. The Aerospace Structures course several different methods of predicting deformation of a beam that is subjected to an external force. The first method covered was in relation to Euler-Bernoulli beam theory. This theory considers direct stress at a point and models a deflection relationship by considering loading, load placement, and geometry of the beam. Euler-Bernoulli assumes that plane sections perpendicular to the mid-plane remain plane and perpendicular to the beam axis after deformation. It also assumes that the object under analysis is a long, slender beam. The second method covered was Finite Element Analysis (FEA). This method breaks a beam up into an N number of sections for analysis. This theory considers energy methods, both strain energy and external work, to model displacement and angle of a beam’s Nth element. The third method of data collection in this experiment was the SolidWorks computer software. SolidWorks uses FEA methods to simulate the behavior of objects and assemblies, considering loads applied. With three varying methods of collecting deflection data, this experiment was set up to analyze the difference in data collected from the theories compared to experimental data. This will reveal the accuracy of the three beam-bending theories.

Comparing data revealed that the beam under analysis had undergone hysteresis and had a non-loaded deformation of .7 cm. Adjusted data then revealed that Euler-Bernoulli and FEA break down at large deformations. Thus, SolidWorks had the best model of the deformations.