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In trying to create a graded mesh can I connect a corner point of one surface to the middle of another side?

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In trying to create a graded mesh can I connect a corner point of one surface to the middle of another side?

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The figure on the left shows a construction which is not permitted. Corner point of one surface connected to the middle of a side of another surface. The figure in the right shows the correct way of connecting the points and the surfaces. Use the wireframe analogy in building up the mesh. Adjacent surfaces should share the side wholly not partly. Otherwise this will lead to mismatching nodes along these sides when the mesh is generated. If the idea is to create a graded mesh and confine the density of elements to a local region then can use the following scheme to prevent propagation of geometry changes throughout the structure. The above construction confines the density of the elements to the neighbourhood of surface 1.

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