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I want to find the volume of a 3D shape with parallelogram as base and it has like a half ellipsoid on it. The following figure has a tube with bulges on it. I want to find the volume of each bulge given that we know the base dimensions and height of each bulge https://uofi.box.com/s/f39z93o4ldhd6tks216aelff3cuem0e8

Can someone tell me how to calculate the volume for such a shape or even a hint will work, I will try to build on it.

qwerty123
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  • It depends what shape it is (the picture looks close to half of the intersection of two cylinders, but you said parallelogram so we don't know how your shape differs) and what you know (are you comfortable with multivariate calculus already?). – Mark S. Aug 14 '15 at 14:02
  • I am comfortable with multivariate calculus. The shape is just for reference because I couldn't post the figure due to no reputation. The base is a parallelogram and it has like a continuous smooth curved surface with one maximum at the center of the parallelogram. I hope this gives an idea of what I am actually looking for. – qwerty123 Aug 14 '15 at 14:13
  • But there are infinitely many smooth surfaces that fit the description... – user21820 Aug 14 '15 at 15:01
  • updated with a new figure for what exactly I am looking for. – qwerty123 Aug 14 '15 at 15:34
  • How are the bulges defined? They don't look like pieces of a sphere. Do you have a parametric formula for the shape? What error would you allow? Etc. – Mark S. Aug 14 '15 at 15:37
  • Its actually an elastic material and it is constrained by inextensible fibers. On pressure actuation the elastic tube wants to bulge but because of this fibers constrains it will bulge. I need the change in volume to solve this using conservation of strain energy of the elastic material. I could have approximated the base to be an ellipse and solved for it but I prefer exact volume for correction factor in my analysis. If nothing works may be very tiny error can be permitted because they sum up when calculating for a longer tube. – qwerty123 Aug 14 '15 at 15:53
  • You need to describe "accurately enough" the stricture of a bulge. It could be as intersection between the central cylinder and some well defined shape and relative location. The more accurate your definition, more accurate the estimate., – Moti Aug 14 '15 at 17:22
  • It sounds like there are (differential?) equations about elastic materials that could help pin down the shape, but even if you asked on another site where people are more likely to know the relevant equations, you'd still need to give data about the initial conditions (where are the fibers that dont move, what are the constants related to how elastic the material is,etc.). Alternatively, if you have the code that generated that image, perhaps it could be reverse engineered and/or the volume approximated with a Monte Carlo method. – Mark S. Aug 14 '15 at 17:41
  • @Moti the constraints are a helical matrix of two fibers (one helix is right handed and other is left handed). Both have same radius and pitch. This helical matrix is on the circumference of the elastic tube which can expand on actuation. – qwerty123 Aug 14 '15 at 18:46

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