Computational Design
Elements were created from line segments along the interface. Each element was allowed to move at its nodal points. Starting with the weak statement, vn and δrn were calculated for each element, generating the following for each element;
Where [Hij] is a 4 × 4 symmetric matrix, also known as the viscosity matrix, is calculated from
Where N is a shape function
The forces on each node were calculated from free energy variation, giving
The force and and viscosity matrix are then assembled into a global matrix representing the contributing from all elements, yield the general expression;
Then, the velocities are then solved for using Gaussian elimination, and positions are updated using a modified euler method using matlab. (see code)
For a detailed description of the technique used in the finite element method, refer to (1).