Bounding Plane Stress Solutions by Finite Elements

The stiffness properties of a finite sized model element of a plate under plane stress are presented. The mathematical model is a piece of the material itself and not a configuration of bars that replace the material. It is shown that an additional deformation condition should be specified instead of an arbitrary arrangement of bars. An example shows that this extra condition considerably increases the accuracy of the model and so reduces the number of degrees of freedom required to approximate the continuous system. A system of bounding the deflection under a single load is shown by assigning values to a free parameter. Thus, the maximum error is known and can be reduced without going to a fine grid.