Direct stiffness method

Abstract

At the core of the finite element modelling process are a diverse possible range of solution approaches for any particular problem. Each of these approaches are adapted for the type of problem that one is interested in, for example structural, fluid, thermal or acoustic problems. The commonest type of problems that FEM addresses are the structural and solid mechanics problems and the direct stiffness method is the heart of the solution strategy. This chapter describes the principles of the direct stiffness method. Simple truss elements are introduced as the crudest finite elements for demonstrating the direct stiffness method, although other more advanced discretization finite elements can also be used. The mechanics of the direct stiffness method will be explained. In particular, the discussion highlights the use of nodal properties for the truss elements to determine displacements, velocities, internal and external forces, etc. for a given truss system. The chapter concludes with practical example problems.