Effect of Mesh Density and Element Types on FEA Results

Problem Description

We have chosen a simple cantilever beam clamped at one end and loaded at the tip of the other end. Displacements and peak stresses are then compared for a variety of element types and mesh densities.

The beams dimensions are 100 mm long, 10 mm tall and 1 mm thick. Loading is 1000 N, distribute by applying 500 N to each edge node of the beam tip. You can plug in these numbers to our online Beam Bending Stress Calculator to determine the theoretical stress at the clamped end which should be 6000 MPa.

In all cases 3D elements are used. Material is linear elastic steel. However since we are just doing a comparative analysis it is not relevant to show the scale with the result plots.

The beam's left most edge is clamped, with all 3 degrees of freedom of each node fixed to ground.

The solver used was Calculix using the SPOOLES solver.

The reference case to which all results are compared to is the finely meshed model with 20-noded quadratic brick element, C3D20.

In all models the Von Mises stress is compared at a node that is 5 mm from the clamped end of the beam in the top fiber. The displacement that is compared is the maximum in the model, which occurs at the loading point. Nodal stresses are extrapolated from integration points .

The relative errors reported are percent difference from the reference case model, i.e the finely meshed 20-node brick model. All percentages are rounded to the nearest 5 or 10, i.e 16 becomes 15 and 72 is rounded to 70. FEA results can have an inherent error of 1-2% so reporting accuracy to the nearest whole number is typically not realistic.

The purpose of doing this is so the new analyst should not think a design with 92 MPa stress is better than a design with 94 MPa stress. For all practical purposes the numbers are the same in FEA world. The analyst should treat both results as the same and NOT make a design decision solely on a relative difference of 2%.

<-- Return to article