Ritz finite elements for curvilinear particles

摘要

A general finite element is presented for the representation of fields in curvilinear particles in two and three dimensions. The formulation of this element shares many similarities with usual finite element approximations, but differs in that nodal points are defined in part by contact points with other particles. Power series in the geometric coordinates are used as the starting basis functions, but are recast in terms of the field variables within the particle interior and the points of contact with other elements. There is no discretization error and the elements of the finite element matrices can all be evaluated in closed form. This approach is applicable to shapes in two and three dimensions, including discs, ellipses, spheres, spheroids, and potatoes. Examples are included for two-dimensional applications of steady-state heat transfer and elastostatics.