So I just started learning to use the finite element package abaqus for modelling beam tip deflection under different loading conditions. I think I understand the theory behind it but was wondering if some one could answer a few questions about it to further my understanding.(adsbygoogle = window.adsbygoogle || []).push({});

Firstly, how do more elements in a simple beam with linear displacement deformation change the results compared to the classical beam bending theory results?

secondly, what would be the difference if i used a quadratic or cubic displacement function defining the deformation behaviour compared to the bending theory calculations while also increasing the number of elements?

Lastly, what would happen if i used a uniformly distributed load for the above cases?

I believe that more elements leads to closer agreement between theory and computer results as the derivation is a integral. however, I am not sure how the different deformation distributions (cubic and quadratic) affect the agreement from the theoretical results. Or for that matter how uniformly distributed loads are not perfectly represented by the modelling either.

These were just some points in the conceptual part of the book that like always have no direct answer. My beam bending theory has always been a little bit sketch, and I thought this would be a good time to rectify that.

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# How finite element analysis differs from mathematic derivation in beam bending?

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