Overview

In this manual, all paths are provided relative to the root directory MembraneAleFem.jl/. The source code is provided in src/, which contains the following files and folders:

$ tree src/
src/
├── analysis
│   ├── FiniteElement.jl
│   ├── GeoDynStress.jl
│   └── PullForce.jl
├── Analysis.jl
├── input
│   ├── Bc.jl
│   ├── Dof.jl
│   ├── Enums.jl
│   ├── GaussPoint.jl
│   ├── GpBasisFn.jl
│   ├── Mesh.jl
│   ├── Params.jl
│   └── Spline.jl
├── Input.jl
├── MembraneAleFem.jl
└── Output.jl

The function solve in the main program file src/MembraneAleFem.jl carries out all calculations, which are divided into three parts:

Input (pre-processing)
Analysis (solution)
Output (post-processing)

We briefly overview the three modules before presenting further details below.

src/Input.jl and corresponding files in src/input/ deal with the problem set-up, mesh generation, and degree-of-freedom initialization. Since the parametrization $\zeta^\alpha$ of the parametric domain $\Omega \subset \mathbb{R}^2$ does not change, all basis functions are determined once $\Omega$ is initially discretized. We employ B-spline basis functions, as they are well-characterized and satisfy $C^1$-continuity across finite elements. The local-to-global mapping between elements and degrees of freedom is also determined here.

All finite element analysis is carried out in src/Analysis.jl and the files in the src/analysis/ folder. In particular, src/analysis/GeoDynStress.jl takes as arguments the elemental degrees of freedom, and calculates all relevant geometric and dynamic quantities—including the stresses and couple-stresses of the membrane and mesh. The file src/analysis/FiniteElement.jl carries out all finite element analysis, including the calculation of the residual vector and tangent diffusion matrix. src/analysis/PullForce.jl calculates the pull force on a tether, and is thus specific to one of the available scenarios.

Currently, src/Output.jl includes a minimal set of functions that process the results of our simulations.

MembraneAleFem.jl

The main file src/MembraneAleFem.jl contains a single function, solve(), which then calls relevant functions in the aforementioned files.

MembraneAleFem.solve — Function

solve(p::Params; args...)

Main function, which solves any Scenario for the given Parameters.

The Mesh struct (mesh), initial positions (xms), and initial control points (cps) are first generated by calling prepare_input. With these initial data, run_analysis! is called to solve for the membrane unknowns and positions at a series of discrete times—for which xms and cps are repeatedly updated. Appropriate data is written to output at each time step, and the final mesh, xms and cps are returned.

source