Z-Corner Rounding¶

Learning targets

Use scripting to describe a complicated dependency in $z-direction$

This example describes a unit cell of a hexagonal lattice (equilateral triangular lattice) of cones with capping layer and corner rounding. The computational domain is specified as extruded polygon, the cone is specified as extruded circle where radius and material change with the z-coordinate. The x- and y-positions of the polygon points as well as the height-dependence of the cone parameters are computed in few lines of Matlab code in a template file which is run from a script (please see also the documentation for the JCMsuite Matlab® Interface).

The following figure shows an image of parts of the geometry and mesh:

Input Files

layout.jcm [ASCII]

Layout3D {
  Name = "TutorialExample3D"
  UnitOfLength = 1e-09
  MeshOptions {
    MaximumSideLength = 100
    MinimumMeshAngle = 20
  }
  Extrusion {
    Objects {
      Polygon {
        Name = "ComputationalDomain/Air"
        DomainId = 101
        Priority = -1
        Points = [125.000 216.506 -125.000 216.506 -250.000 0.000 -125.000 -216.506 125.000 -216.506 250.000 -0.000]
        Boundary {
          Number = [1 2 3 4 5 6]
          Class = Periodic
        }
      }      
      Circle {
        DomainId = 102
        Radius = 123.601319405876
      }
    }
    MultiLayer {
      LayerInterface {
        GeometryValues = [Circle{1}/Radius:156.139]
        BoundaryClass = Transparent
      }
      Layer {
        Thickness = 50
        DomainIdMapping = [101 1, 102 1]
      }
      LayerInterface {
        GeometryValues = [Circle{1}/Radius:150.000]
      }
      Layer {
        Thickness = 350
        DomainIdMapping = [101 4, 102 2]
      }
      LayerInterface {
        GeometryValues = [Circle{1}/Radius:107.025]
      }
      Layer {
        Thickness = 50
        DomainIdMapping = [101 4, 102 3]
      }
      LayerInterface {
        GeometryValues = [Circle{1}/Radius:100.886]
      }
      Layer {
        Thickness = 15
        DomainIdMapping = [101 4, 102 3]
      }
      LayerInterface {
        GeometryValues = [Circle{1}/Radius:95.025]
      }
      Layer {
        Thickness = 10.9807621135332
        DomainIdMapping = [101 4, 102 3]
      }
      LayerInterface {
        GeometryValues = [Circle{1}/Radius:82.696]
      }
      Layer {
        Thickness = 4.01923788646684
        DomainIdMapping = [101 4, 102 3]
      }
      LayerInterface {
        GeometryValues = [Circle{1}/Radius:67.203]
      }
      Layer {
        Thickness = 50
        DomainIdMapping = [101 4, 102 4]
      }
      
      LayerInterface {
        GeometryValues = [Circle{1}/Radius:91.063]
        BoundaryClass = Transparent
      }
    }
  }
}

Matlab script run_geometry.m [ASCII]

% Interface for 3D unit cell of a hexagonal lattice 
% 2D-periodic hexagonal array of 3D cones 
% with capping layer and with corner rounding

keys.uol = 1e-9;
keys.p = 500.0; % periodicity length
keys.h1 = 350.0; % height of lower material
keys.h2 = 80.0; % height of top material (capping layer)
keys.radius_bottom = 150; % cone radius bottom
keys.cone_swa = 83.0; % cone sidewall angle
keys.corner_rounding_r = 30.0; % top corner rounding radius
keys.corner_rounding_n = 2; % corner rounding number of segments

keys.slc1 = 100; % maximum triangle sidelength

jcmwave_geo('.', keys, 'jcmt_pattern', 'matlab', 'show', inf);

Layout template file layout.matlab.jcmt [ASCII]

<?
% Matlab definition of a hexagon
angles = [1:6]*2*pi/6; points = keys.p/2*exp(1i*angles);
keys.points_cd(1:2:12) = real(points(:));
keys.points_cd(2:2:12) = imag(points(:));

% build the cone from layers of different heights
offset = 50; % computational domain offset in +/-z-direction
heights = [-offset, 0, keys.h1, keys.h1 + keys.h2, keys.h1 + keys.h2 + offset];
% additional corner rounding at the top
angles = linspace(0, 90, keys.corner_rounding_n + 2);
r = keys.corner_rounding_r;
heights = unique([heights keys.h1 + keys.h2 - r + r*sind(angles)]);
% thicknesses of the different layers
thicknesses = heights(2:end) - heights(1:end-1);
% radii of the cone at different heights
radii = keys.radius_bottom - tand(90-keys.cone_swa)*heights;
keys.radius_mean = radii(1)/2+radii(end)/2;
indices_rounded_corner = find(heights >= keys.h1 + keys.h2 - r ...
                            & heights <= keys.h1 + keys.h2);
radii(indices_rounded_corner) = radii(indices_rounded_corner) - r*(1 - cosd(angles));
?>
Layout3D {
  Name = "TutorialExample3D"
  UnitOfLength = %(uol)e  
  MeshOptions {
    MaximumSideLength = %(slc1)e
    MinimumMeshAngle = 20
  }
  Extrusion{    
    Objects {
      Polygon {
        Name = "ComputationalDomain/Air"
        DomainId = 101
        Priority = -1
        Points = %(points_cd)3f
        <?
          for counter = 1:length(keys.points_cd)/2
              keys.number_ = counter;
?>      Boundary {
          Number = %(number_)d
          Class = Periodic
        }
       <?
         end
?>     }
      
       Circle {
         DomainId = 102
         Radius = %(radius_mean)e
       }
     }
     MultiLayer {    
      <?
for counter = 1:length(thicknesses)
  keys.thickness_ = thicknesses(counter);
  keys.radius_ = radii(counter);
  if heights(counter) < 0
    keys.material_1 = 1;
    keys.material_2 = 1;
  elseif heights(counter) < keys.h1;
    keys.material_1 = 4;
    keys.material_2 = 2;
  elseif heights(counter) < keys.h1+keys.h2;
    keys.material_1 = 4;
    keys.material_2 = 3;
  else
    keys.material_1 = 4;
    keys.material_2 = 4;
  end
?>    LayerInterface {
      GeometryValues = [Circle{1}/Radius:%(radius_)3f]
      <? 
    if counter==1
?>      BoundaryClass = Transparent
      <? 
    end
?>    }
      Layer {
        Thickness = %(thickness_)e
        DomainIdMapping = [101 %(material_1)d, 102 %(material_2)d]
      }
      <?
end
keys.radius_ = radii(counter+1);
?>
      LayerInterface {
        GeometryValues = [Circle{1}/Radius:%(radius_)3f]
        BoundaryClass = Transparent
      }
    }  
  }
}
  