Energy principles in structural mechanics express the relationships between
stresses,
strains or
deformations,
displacements, material properties, and
external effects in the form of energy or work done by internal and external forces. Since energy is a scalar quantity, these relationships provide convenient and alternative means for formulating the governing equations of deformable bodies in
solid mechanics. They can also be used for obtaining approximate solutions of fairly complex systems, bypassing the difficult task of solving the set of governing
partial differential equations.