ABSTRACT
This chapter discusses current and possible future applications of polyhedral finite elements in solid mechanics. These applications include rapid engineering analysis through novel meshing and discretization techniques, and fracture and fragmentation modeling. Several finite element formulations of general polyhedra have been developed. The chapter utilizes a polyhedral formulation based on the use of harmonic shape functions. The analysis of stress and strain in a mechanical part or structure is critically important to the overall engineering design and development process. The chapter reviews governing equations of solid mechanics. It provides an overview of a finite element formulation based on harmonic shape functions. The chapter discusses several approaches of rapid meshing/analysis. It also discusses the use of polyhedral elements in modeling fracture and fragmentation. The chapter generalizes that barycentric coordinates are used to form the finite element shape functions directly in the initial configuration of the domain.
