Seawall Geometry

Minimal Surface Geometry

Goal: The purpose of the seawall geometry project is to understand the mathematical foundation and expressions of Minimal Surface (MS), use 3D graphing & modeling tool to create 3D-printable models of MS, TPMS (Triply Periodic Minimal Surface) and their transformations/variations, and apply them to design and build shoreline protection structures (breakwaters and seawalls). The digital models will be used for simulations and the 3D-printed physical models will be used for wave tank experiments.

Minimal Surface (MS) & Tools: In nature, minimal surface (MS) can be formed effortlessly through the surface tension. For example, a soap film at equilibrium will have a constant thickness, and minimal surface area. MS can be modeled by math expressions. There are many types of minimal surfaces and some of them can form 3D periodic structures. These 3D MS structures are called TPMS (Triply Periodic Minimal Surface). We will study the properties of TPMS and how to transform them and how to create variations. Grapher in Mac is a convenient tool for visualizing the MS. MathMod (running on all platforms) can be used to create the MS and TPMS, manipulate their math equations, and export them as 3D surface files. Blender (running on all platforms) can import the 3D surface files and "thicken" them into 3D models. Blender can further modify the 3D models, render them, and create 3D-printable files.

We are looking forward to further investigate the ways to transform the TPMS and create variations using advanced software tools such as MSLattice and nTopology.

Triply Periodic Minimal Surface (TPMS)

A minimal surface is the surface of minimal area between any given boundaries. Soap films are minimal surfaces. Minimal surfaces have a constant mean curvature of zero, i.e. the sum of the principal curvatures at each point is zero. Particularly fascinating are minimal surfaces that have a crystalline structure, in the sense of repeating themselves in three dimensions, i.e, Triply Periodic Minimal Surface (TPMS).

TPMS have porous structures that have many merits:

The whole TPMS structure can be precisely expressed by mathematical functions.
Basic performances, such as porosity or volume specific surface areas can be directly controlled by adjusting the function parameters.
The surfaces of TPMS are very smooth, without sharp edges or junctions as the lattice structures.
The TPMS porous structures are highly interconnected with non-tortuous pores, which are important advantages for applications.

In light of these merits, TPMS have high potential to be applied to the coastal protection structure - seawalls and breakwaters. The following are some latest resources about TPMS: