Some remarks on the optimal choice of finite element grids

The results of Prager's Note [1]of similar title are discussed and expanded. By minimizing the potential energy associated with an assumed approximate deformation field, general criteria are developed for the optimal grid spacing of bars under varying axial forces and of beams under lateral loads, both with arbitrary variation of the cross section. It is shown that Prager's tentative energy criterion is indeed confined to the special case treated in his Note, as originally conjectured by himself.For constant cross section all optimality conditions assume a simple and easily realizable form. It is shown that in this case the computed nodal displacements are exact, irrespective of the grid spacing or of the value of the potential energy. Nevertheless, optimal spacing is still useful in reducing the average error in the computed stress values.