Finite Cell (FC)

Table of Contents

• Overview
• General settings
• Boundary condition settings

In the following the Finite Cell (FC) solver is briefly discussed. That is, a short overview about how to start the solver, the general settings, and an overview about boundary condition settings is given. Further information about the mathematical modelling, i.e., the principle of virtual work (PVW) and the numerical method of the FC is presented here (PVW and FC).

Overview

The finite cell (FC) solver can be used to simulate structural mechanic problems. The solver works in 2D and 3D. However, the 2D applications have not yet been tested. To start the solver, the following properties have to be specified in the property file:

gridGenerator = false
 
flowSolver = true
 
solvertype.* = "MAIA_FINITE_CELL"

Note

So far, only linear-elastic materials can be simulated. Furthermore, the simulation is static, i.e., no dynamic forces can be applied.

General settings

At first, simulation specific properties are set. These are, the dimension of the application, the p-refinement, i.e., the number of nodes per cell, and the depth of the subcell integration per boundary.

dim = 3
 
polyDeg = 1
 
subCellLayerDepth = [0, 0, 0, 0, 2]

These setting result in a 3D simulation using a p-refinement with \( (p+2)(p+2)(p+2) = 27 \) nodes per cell, a subcell integration depth of \(0\) at boundaries \(0 - 3\), and a subcell integration depth of \(2\) at boundary \(4\). Next, the material properties, i.e., the Young's modulus and the Poisson's ratio, are set. For example use:

EModule = 100000.0
 
PoissonRatio = 0.3

The method to solve the linear system of equations is the BiCGStab method. The number of maximum iterations and the precision of the solution is set by:

epsBiCG = 1e-12
 
noIterations = 10000

To get extra debug output use:

testRun = true

To calculate the resulting stresses from the strains use

saveStress = true

Boundary condition settings

In the FC solver, two different types of boundaries, i.e., natural and essential boundaries, exist. At essential boundaries the displacement is set. At natural boundaries the traction is set. The ids of the boundaries, to be specified in the geometry file of the simulation, are given in BC. Additionally, further properties are required in the properties file of the simulation. These are the number of essential and natural boundaries, the direction of the displacement and the load, and the load vector:

noFixedSeg = 2
 
noForceSeg = 2
 
segFixationDirs_0 = [1.0, 0.0, 0.0]
 
segFixationDirs_4 = [1.0, 1.0, 1.0]
 
segLoadDirs_1 = [1.0, 0.0, 0.0]
 
segLoadDirs_2 = [0.0, 1.0, 0.0]
 
segLoadValue_1 = [10.0, 0.0, 0.0]
 
segLoadValue_2 = [0.0, 10.0, 0.0]

In this setup, two essential and two natural boundaries exist. The displacement of the essential boundaries is \( 0 \) in x-direction (boundary \( 0 \)) and \( 0 \) in x-, y-, and z-direction (boundary \( 4 \)). At the natural boundaries, a traction of \( 10 \) is set in x-direction (boundary \( 1 \)) and y-direction (boundary \( 2 \)).