Minimal Surface

Iran University of Science & Technology / Fall 2018

Description.

Finding a minimal surface of a boundary with specified constraints is a problem in the calculus of variations, sometimes known as Plateau’s problem. Minimal surfaces may also be characterized as surfaces with minimal surface area for given boundary conditions.

The only known complete (boundaryless), embedded (no self-intersections) minimal surfaces of finite topology known for 200 years were the catenoid, helicoid, and plane. Hoffman discovered a three-ended genus 1 minimal embedded surface, and demonstrated the existence of an infinite number of such surfaces. A four-ended embedded minimal surface has also been found. L. Bers proved that any finite isolated singularity of a single-valued parameterized minimal surface is removable.

location:

Iran University of Science & Technology

field:

Computational design & Fabrication

Data:

Fall 2018

Brief & Idea.

This project is focused on topics such as form finding of minimal surfaces, processing techniques, and fabrication with hot wire machines. For form finding, a base form batwing with a basic mathematical formula with different parameters from the original surface has been made with the Grasshopper plugin. The chosen form feature is having three alternatives for pavilion as architectural design.

Create Blocks.

The challenge faced by the Project is the limitation of the Hot Wire Machine, which cuts the minimal surfaces and dimensions of the base material to create blocks to fabricate. So, for transforming minimal surface to ruled surface for machine, and making blocks and setting the blocks in sheet of material, load transforming and stability of final form after assembling used grasshopper coding, analysis and optimization. After getting g-code and cutting, the blocks are ready to fabricate.

In the fabrication process, three wings of the final form are assembled separately and then added to the base form. Final coat of the final form is plaster and paint with iron particles that is oxidized in open air.

Minimal Surface

Description.

location:

field:

Data:

Brief & Idea.

Create Blocks.

Analysis.

Curvature

01.

02.

Karamba

03.

Slope