On the determination of boundary stresses in finite elements

A new method for determining the stresses in a finite element analysis on the surface of a body is proposed. The body is meshed using standard quadratic isoparametric elements and the nodal displacements determined in the normal way. The stresses are then determined within any surface element by letting the quadratic become a cubic element, applying the corner nodal displacements and known boundary stresses as penalty functions, and then performing a finite element analysis on the single element. The solution then yields a further set of displacements from which the stresses can be determined. The method is applied to various two-dimensional bodies and the improvements in the predicted boundary stresses shown.