Mesh density and resulting stress quality
The finite element method breaks down a component into many small segments (elements) that are subject to a deformation and stress approach. Each element consists of 9 nodes with their assigned degrees of freedom w, u, v, φ, θ and can only simulate a quadratic deformation. The sum of all degrees of freedom from a lot of such elements forms a large system of equations after summing up their stiffness components, which now allows a mapping of the deformation behaviour of a complex system. This system of equations must then be solved. The larger the system of equations (the more elements there are), the longer it takes to solve the deformations to be determined.
Care must be taken to ensure that the finite element mesh is sufficiently finely structured in areas where high stress gradients occur (local load introductions, stress peaks at recesses and fillet radii, local support points, etc.) in order to be able to map the expected deformations and stress information well. In other areas where no major changes in bending are expected, the mesh can be made coarser.
The old version SJ Mepla 5.0 could only offer an automatically refined mesh for point fixings in order to achieve good accuracy here. At bearing, line- and point loads, only a globally uniform mesh over the entire surface of the glass panel was possible. As a result, a large number of elements are required to map fine details, which increases the computational effort enormously.
The new version MEPLA Pro 2025 now allows the local refinement of the mesh only at the areas where a fine mesh is required. The remaining areas are automatically made coarser. This increases the quality of the local results even though fewer elements in sum are used.
Example - Lineload
A simple 1500x3000mm pane is subjected to a line load. In order to achieve a good convergent stress result (10.24 - 10.27 N/mm²) in SJ Mepla 5.0, an element size of 45 mm must be selected so that a sufficiently fine mesh is created in the area of the line load.
The same stress result can be achieved in the new MEPLA Pro version with a global mesh size of 120 mm, as the mesh is only reduced to 45 mm locally.
While the SJ Mepla 5.0 mesh requires 2187 elements to create a fine mesh even in the line load area, the new MEPLA Pro only requires 507 elements.
Therefore, the calculation time is now only 0.6 sec instead of 2.3 sec. This is an increase in calculation speed by a factor of 3.8, while the quality of the calculation remains the same! In both cases, an equally good result of approx. 10.27 N/mm² has been generated.
With an element size of 180 mm, the system is even calculated in 0.3 seconds and is therefore 7.6 times faster than without automatic mesh refinement. At 10.25 N/mm², the results are still as accurate.
If such a coarse global mesh of only 180 mm had been used in SJ Mepla 5.0, the calculation time would be 0.8 sec (i.e. still almost 3 times as long) - but the stress result would also be unsatisfactorily inaccurate at 9.85 N/mm² (error > 5%), as the bending behaviour in the area of the line load can no longer be mapped here. This can also be seen from the colour jumps in the graph.
Example - Recesses with fillet radii
The difference is also very clear for panes with corner recesses and fillet radii.
The old version could only form elements of a constant size. The smallest corner length therefore specified the required element size. In this case, there was only a single element, which is too small for mapping the stress concentration at the corner. An even smaller element size therefore had to be selected here, which would further increased the computational effort.
Even now, 2566 elements had to be generated for this mesh, which takes 3.3 seconds to calculate. The quality of the stresses in the corner area is nevertheless very inaccurate at 24.77 N/mm² (only 1 element in the rounding).
The new MEPLA PRO version, on the other hand, only refines the mesh in the corner rounding area. This results in just 341 elements. The calculation of the stress concentration is also much more accurate at 27.74 N/mm², as almost 10 elements are now arranged in the fillet area.
The calculation is 6.6 times faster at 0.5 sec!
Example - cantilever plate with point load
If a cantilever plate with intermediate support is considered, on which a point load and surface load act, the element density was not adjusted in the old version, neither for the point load nor for the intermediate support. In order to achieve good results, a correspondingly fine element size had to be selected. If only the standard size of 80 mm was used for the calculation, the stresses in the area of the point load as well as at the intermediate support are still inaccurate.
The new MEPLA PRO version automatically refines the mesh both in the point load area and at the intermediate support. This means that the mesh can be made coarser again in the remaining area (120 mm in this case), although the quality of the stress results still increases considerably.
The graphical representation as well as the maximum values in the old 5.0 calculation shows stress peaks of 33.50 N/mm² and an unsteady color behavior (indicator for too large elements).
The new version achieves a very accurate result of 36.6 N/mm² due to the local mesh density, although the other mesh was set even coarser at 120 mm.
Even compared to the still inadequate 80 mm mesh size with 0.9 sec, the new mesh with 317 elements can be calculated in 0.4 sec. If you use a mesh size of 30 mm to calculate the local peaks just as well, version 5.0 needs a whole 2.4 seconds for the 2178 elements - which is 6 times slower in comparison!