New Polyhedral Elements Based on Virtual Node Method for Solid Mechanics and Heat Transfer Applications

Finite element method (FEM) is a well-established method and commonly utilized to solve complex engineering problems which cannot be solved analytically. Various element types have been formulated over the years to facilitate engineering analyses using FEM. In this paper, new polyhedral elements are developed by utilizing virtual node method. This paper covers the formulation of shape functions and integration schemes for the new polyhedral elements. These new polyhedral elements have advantages due to the nature of their shape functions which consist of monomials uavbwc. Integration of functions within the element can be accomplished by utilizing an exact integration technique. These polyhedral elements can be utilized to solve real 3 dimensional problems which arise in solid mechanics and heat transfer phenomena.