Mesh crack tip

Download Im2mesh package https://www.mathworks.com/matlabcentral/fileexchange/71772

Im2mesh package require Matlab Mapping toolbox

Before we start, please set folder "Im2mesh_Matlab" as your current folder of MATLAB.

clearvars

Function bounds2mesh use a mesh generator called MESH2D (developed by Darren Engwirda). We can use the following command to add the folder 'mesh2d-master' to the path of MATLAB.

addpath(genpath('mesh2d-master'))

Create polyshape

x = [0 150 150 75 150 150 0];
y = [0 0 72.5 75 77.5 150 150];
ps = polyshape(x,y);

plot(ps);
axis equal

Convert to a nested cell array of polygon

psCell = {ps};
bounds = polyshape2bound(psCell);

% plot boundaries and show all vertices
plotBounds(bounds,false,'ko-')

Generate mesh

hmax = 20;
grad_limit = 0.25;
opt = [];
opt.disp = inf;     % silence verbosity

[vert,tria,tnum,vert2,tria2] = bounds2mesh( bounds, hmax, grad_limit, opt );
plotMeshes(vert,tria,tnum);

refine mesh locally

hmax = 20;
grad_limit = 0.25;
opt = [];
opt.disp = inf;     % silence verbosity

pnt = [75, 75];     % 1 point
hsize = 1;          % mesh size at point
opt.pnt_size = [ pnt, hsize ];  % p-by-3 array

[ vert,tria,tnum,vert2,tria2 ] = bounds2mesh( bounds, hmax, grad_limit, opt );
plotMeshes(vert,tria,tnum);

Please refer to the following link for how to refine mesh locally https://mjx888.github.io/im2mesh_demo_html/demo17.html

Create matlab pde model object

% linear model
model_linear = createpde();
geometryFromMesh( model_linear, vert', tria', tnum' );

% qudratic model
model_quad = createpde();
geometryFromMesh( model_quad, vert2', tria2', tnum' );

show geometry

pdegplot(model_quad, 'EdgeLabels','on','VertexLabels','on', 'FaceLabels','on' )

Show mesh

pdemesh( model_quad )

end

Published with MATLAB® R2021b