MATLAB: How are the DOF arranged in the state vector of an ode system obtained by the function assembleFEMatrices

Question

Hello,

I want to extract a stiffness and mass matrix of a 3D-object. For this purpose I use the pde toolbox, import the .stl file, specifiy the pde coefficients, create the mesh and compute the matrices M and K via "assembleFEMatrices", see code below. Now, I have the system M*u_dd + K*u=0.

How do I now find out how the DOFs are arrangend in u? I haven't found any hint in the documentation of function assembleFEMatrices.

model = createpde(3);
% geometry
gm = multicuboid(1,1,1); % simple example
model.Geometry=gm;
% mesh
generateMesh(model,'Hmin',0.5);
pdeplot3D(model,'NodeLabels','on');
% pde coefficients
m = 8000; % Material density in kg/m^3
E = 200e9; % Modulus of elasticity in Pascals
nu = .3; % Poisson's ratio
c = elasticityC3D(E,nu);
a = 0;
f=[0; 0;0];
specifyCoefficients(model,'m',m,'d',0,'c',c,'a',a,'f',f);
% matrices
FEM = assembleFEMatrices(model);
M=FEM.M;
K=FEM.K;

Thank you

Martin

Answer 1

The answer I found out myself:

u*_n displacment of node n in x direction

v*_n displacment of node n in y direction

w*_n displacment of node n in z direction

u=[u*_1, u*_2, ... u*_n, v*_1, v*_2, ... v*_n, w*_1, w*_2, ... w*_n]'