Finite Element Method for Solids and Structures A Concise Approach

In this chapter we introduce the concept of an arbitrary virtual displacement which may also be considered as an arbitrary weight function. This will be used to express the equilibrium equation for 3D solids and structures in a scalar integral form. Subsequently, the divergence theorem is applied to transform the scalar integral into another form to which the force boundary condition can be introduced. This results in the statement for the principle of virtual work involving internal virtual work and external virtual work. Internal virtual work and external virtual work will then be expressed in matrix form so that they can be used for the finite element formulation in later chapters. We then consider plane stress and plane strain problems in which the principle of virtual work can be expressed in 2D domains in accordance with simplifying conditions. In the last section, the Lagrange equation is derived within the context of deformable solid bodies, starting from the principle of virtual work.