Deflection of simply supported plate with multiple points of application

[WK95]

How can I estimate the deflection at the center of a simply support plate (and a sandwich one) with multiple points but same intensity of load application?

The points of application are symmetrical and form the shape of a rectangle and the loading at each point is the same.

An approximation by using quasi-isotropic layups is acceptable.

 

[RPstress]

One method used by the infamous evil genius MW in the 1980s at Boeing was to add up the point loads and divide by the plate area and use that pressure with a simply supported plate under pressure formula from Roark. Roark also has formulas for plates with a rectangular area in the center under pressure. Bear in mind that MW was/is an evil genius...

 

[WK95]

Who is this MW?

I'd like to learn more of his evil genius tricks.

 

[RPstress]

After some thought I'll say that his name is Mike Williams and I wrote up a description of his methods when I was at Boeing in about 1996 (there was a real need to understand his methods) and than again several times, last in about 2010, more for fun... If I can find it I'll post it but subsequent moves make that hard. He would do about three pages of hand calcs which would take about three weeks to interpret but at the time got positive margins quickly. Years later this drove the salvage people nuts (they dreaded finding MW on a damaged part's calcs sheets) (and me when we were designing the next model which was based on the one he worked on) but must have pleased his design-stressing leads immensely at the time. Brilliantly beautiful and what made it beautiful made it dangerous... Like high explosive, use with care and only when its limitations are fully understood. Representing point loads by a pressure has obvious non-conservatism so make sure margins are ample and make sure you do a simple FE ananysis for the final iteration. MW used a pressure but it would have been safer to use a central point load equal to the sum (provided margin was positive). I've no doubt that MW chose the method that gave a good result and was in his opinion safe. No part I'm aware of him working on ever gave trouble, but...

 

[SWComposites]

RP - what Boeing site was he at?

For OP, think Roark has solution for plate loaded with an offset point load. For multiple loads just superimpose solutions.

 

[RPstress]

This was 757 so Renton (I was on the -300).

Superposing multiple cases was the sort of thing that MW avoided. He'd rather do something that seemed initially to make no sense to us but would give him the results he needed much more rapidly. He also took KISS to extremes with no explanations and diagrams of what was analysed that often bore little apparent similarity to what was actually there. His final result was often uncannily similar to a much more complicated (and time consuming) analysis using more conventional methods generating many more pages of calcs. Brilliant and dangerous.

 

[SWComposites]

Well, '80s were before spreadsheets. Now it should be easy to set up superposition of cases.

 

[RPstress]

Unless he retired he must have found even more scope for his (comsiderable) creativity with PCs and spreadsheets. One of his methods was to assess the capacity (in terms of life) of each of parallel loadpaths in fatigue (Boeing had good methodology for this) and then share a static load between them accordingly (all with no explanation - that really tested us trying to see what he'd been up to). The original 757 didn't have that much composite either which would have given him even more freedom.