Formulation of the element matrices and vectors for elasticity problem > Incorporation of boundary conditions > Imposing prescribed displacements (Penalty method)

This method uses the fact that computer computations have limited precision. The BC's conditions are handled by adding a "large" number, to the leading diagonal of the stiffness matrix in the row in which the prescribed value (i.e. a zero values means full fixity of degree of freedom) is required. The term in the same row of the right hand side vector is then set to the prescribed value multiplied by the augmented stiffness coefficient. Any structural degree of freedom can be prescribed in this way. Each prescription adds a large diagonal stiffness value to the stiffness matrix and also a large value to the load vector if the prescribed degree of freedom is nonzero. This procedure is successful if "small" terms are small relative to "large" terms (i.e. the stiffness matrix coefficients are indeed more small than the "large" value assumed).