Visual Instruction of Stress Smoothing

Visual Instruction of Stress Smoothing

Solving the finite element equations gives the values of the primary variables such as displacements in structural analysis or temperatures in heat conduction analysis. Stresses, strains, or heat fluxes are the secondary variables computed from the primary variables. For example, strains are functions of the displacement derivatives. In finite element analysis, they are computed from the nodal displacements based on the strain versus nodal displacement relationship, which is expressed by the equation,

e = BD^e

where e, B and D^e represent respectively the strain vector, the straindisplacement matrix, and the nodal displacement vector. Then, stresses are computed from the strains using the constitutive relationship. In actual finite element computation, the secondary variables are obtained first at integration points and then evaluated at nodal points. This process is called “Stress recovery and smoothing.” VisualFEA has an educational function to simulate and visualize graphically the stress recovery and smoothing procedure. The computational aspects and characteristics of the procedure can be studied and understood easily using this educational function. The results can be visualized for an individual element or for any selected part of the model. Different methods of recovery and smoothing can be compared with each other. Strains instead of stresses, in spite of the function title, are used for visualization of the stress recovery and smoothing process, because the stresses can be obtained directly from the strains.

< Displaying the strain recovery >