in | (7) |

where

(8) |

In the above equations, is the domain of the body, is the Cauchy stress tensor, is the small strain tensor, is the body force per unit volume, is the material moduli tensor, is the displacement, is the gradient operator, and is the symmetric gradient operator.

The essential and natural boundary conditions are

on on | (9) |

where is the boundary of , and and are prescribed displacements and tractions, respectively.

The weak form (principle of virtual work) is

On substituting the trial and test functions in the above equation and using the arbitrariness of nodal variations, the following discrete system of equations is obtained:

where

In the above equation, is the shape function vector and is the matrix of shape function derivatives.