Use of graded finite elements to model the behavior of nonhomogeneous materials

A finite element with a spatially varying material property field is formulated and compared to a conventional, homogeneous element Sor solving boundary value problems involving continuously nonhomogeneous materials. The particular element studied is a two-dimensional plane stress element with linear interpolation and an exponential material property gradient. However the main results are applicable to other types of elements and property gradients. Exact solutions for a finite rectangular plate subjected to either uniform displacement or traction either perpendicular or parallel to the property gradient are used as the basis for comparison. The results show that for identical meshes with equal number of degrees-of-freedom, the graded elements give more accurate local stress values than conventional elements in some boundary value problems, while in other problems the reverse is true.