Linear elasticity solutions

The linear equations of elasticity form a set of coupled partial differential equations that are elegantly simple but like most partial differential equations, are often quite difficult to solve for realistic problems. Considerable simplification can be achieved when the general, three-dimensional formulation is reduced to a two-dimensional formulation by assuming the problem to be either plane stress or plane strain, as discussed in sections 1.3 or 1.6, respectively. Further simplification can be achieved for problems presenting specific symmetries. For example, the governing equations for two-dimensional problems featuring cylindrical symmetry reduce to ordinary differential equations. It is often necessary, however, to reformulate the elasticity equations in cylindrical or spherical coordinates to take advantage of specific symmetries or easily impose boundary conditions.