The penalization technique used is the “power law representation of elasticity properties,” which can be expressed for any solid 3D or 2D element as follows:
K(r) = K*ρ^p
where K and K represent the penalized and the real stiffness matrix of an element, respectively, ρ is the density and p the penalization factor which is always greater than 1.
In OptiStruct, the DISCRETE parameter corresponds to (p - 1). DISCRETE can be defined on the DOPTPRM bulk data entry. P usually takes a value between 2.0 and 4.0. For example, compared to the non-penalized formulation (which is equivalent to p=1) at ρ=0.3, p=2 reduces the stiffness of the element from 0.3 to 0.09 times the stiffness of the fully dense element. The default DISCRETE is 1.0 for shell dominant structures, and 2.0 for solids dominant structures (the dominance is defined by the proportion of number of elements)