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http://www.mechanicsandmachines.com/?p=330
The minimum deflection occurs when the deflection at each end is the same as the deflection in the middle of the beam. For a Euler-Bernoulli beam, this minimum deflection occurs with supports placed 0.2232 L from each end.
https://www.engineeringtoolbox.com/beam-stress-deflection-d_1312.html
Beams - Supported at Both Ends - Continuous and Point Loads; Beams - Fixed at One End and Supported at the Other - Continuous and Point Loads; Beams - Fixed at Both Ends - Continuous and Point Loads ; The calculator below can be used to calculate maximum stress and deflection of beams with one single or uniform distributed loads.
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.6.6654&rep=rep1&type=pdf
maximum bending moment of the beam. For a beam with simple supports at the ends, one heuristic places the blocks so that the maximum deflection is no more than 16/9 √ 3 ≈ 1.027 times the theoretical minimum and the maximum bending moment is within 4 times the minimum. Another heuristic allows maximum deflection up to 2.054 times the theoretical
https://www.eng-tips.com/viewthread.cfm?qid=67385
Aug 14, 2003 · For a uniformly distributed load, deflection at centre of beam to equal deflection at ends of beam, place supports at 0.553 x Length of beam. I …
https://www.structural101.com/Design-To-Minimize-Deflection.html
For a simple beam with uniform load (w), deflection varies with the fourth power of span length. However, total load (wL) is increased. If beam length is doubled, deflection increases by factor of 16 (for the same beam). One way to reduce effective span length is to move supports …
https://www.optimalbeam.com/index.php
Get a simplified analysis of your beam model which includes support reactions and interactive charts for shear force, bending moment, deflection and stress in a matter of seconds. Supports & loads Support types that can be applied includes fixed, pinned, and roller supports.
https://www.quora.com/How-would-you-support-the-beam-of-giving-length-to-produce-minimum-bending
Now minimize the sum of the moments produced at supports. You can find the value of 'x' which will give the minimum value of moment. Here, in this case for x=3L/5, moments will be minimum at support. Bottom-line is, you can always find the support condition and position to minimize the moment in a beam but there is no generalized method.
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