After a bit more thought, I think that the following would be feasible. An erf/erg dome cut off at some point with radius r, r fairly large, so when you're close to the outer edge of the dome, it looks like a flat wall at a very slight angle towards the dome. We now place a "skirt" around the outside of this dome which "starts" perhaps halfway up (down?) the dome side and gracefully (e.g., exp(-r) or exp(-r^2)) expands out from the dome in all directions. Note that the volume between the ground plane and underneath the skirt outside the dome is _filled in_ with material. The vertical weight of the erf/erg dome is carried by the lip of this dome itself; the only purpose of the skirt & filled in material is to provide the horizontal force towards the origin. If the dome is quite high, the angle of the wall at the lip is very nearly vertical, so the horizontal force required is relatively weak. The purpose of the skirt is to spread the horizontal force over as large a perimeter as possible. One way to analyze the circular "buttress" is to look at a section of it and turn it 90 degrees, so that the infinite lip is pointing down. The almost-horizontal top (after rotation) is now 1/2 of a standard arch bridge, except that in our case, the force coming down from the top is the original horizontal spreading force of the dome, and most importantly, the material of the bridge doesn't have to hold itself up (because gravity is pulling essentially orthogonally to the spreading force of the dome). At 01:08 PM 11/12/2012, Warren Smith wrote:

On 11/12/12, Henry Baker <hbaker1@pipeline.com> wrote:

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You've got a valid point, Warren.

1. I think it might be possible to get a pure compressive dome, but the base might have to be infinite.

--1. The area of dome-cap goes like radius^2 or greater. But its perimeter is 2*pi*radius. Hence the compressive stress would be at least proportional to radius for a uniform-thickness dome. Hence growing the radius to infinity is impossible with uniform thickness.

So, suppose the thickness were q(r), nonuniform. Roughly how would q grow? Integral q(r) * r * dr is proportional to a lower bound on weight for a radius-r cap, and this for uniform compressive stress would be proportional to r*q (perimeter*thickness).

Hence q' * r + q = C * r * q with solution q(r) = K*exp(C*r)/r.

So therefore, an infinite-width dome with uniform compressive stress would perhaps be possible provided its thickness grew as above, i.e. roughly exponentially with r.

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2. I think that there may be a solution that looks something roughly like a Gaussian revolved around the y axis.

Basically, the "skirt" of the Gaussian pushes out on an ever increasing radius.

--2. I don't think so because a nonconvex object like that will get tension at points of negative curvature.