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

A finite element with a spatially varying material property field is formul ated and compared to a conventional, homogeneous element Sor solving bounda ry value problems involving continuously nonhomogeneous materials. The part icular element studied is a two-dimensional plane stress element with linea r interpolation and an exponential material property gradient. However the main results are applicable to other types of elements and property gradien ts. Exact solutions for a finite rectangular plate subjected to either unif orm displacement or traction either perpendicular or parallel to the proper ty gradient are used as the basis for comparison. The results show that for identical meshes with equal number of degrees-of-freedom, the graded eleme nts give more accurate local stress values than conventional elements in so me boundary value problems, while in other problems the reverse is true.