# Design Elements

## Solid Elements

Where,
$\tilde{K}$
is the penalized stiffness matrix of an element,
$K$
is the real stiffness matrix of an element, ^{
$\rho $
} is
the density, and
$p$
is the penalization factor (always greater than 1).

## Shell Elements

Where,
$\tilde{K}$
is the penalized stiffness matrix of an element,
$K$
is the real stiffness matrix of an element, ^{
$\rho $
} is
the density, and
$p$
is the penalization factor (always greater than 1).

For isotropic material a non-zero base plate thickness can be defined. For a composite plate or a plate with anisotropic material, the base plate thickness must be zero (the limitation of the current development).

Topology optimization of composites has certain unique characteristics and is discussed in Composite Topology and Free-size Optimization.

## 1D Elements

^{ $\rho $ }of this element that varies between 0 (numerically a small value is used) and 1.0. In essence, 0 represents nonexistence and 1.0 represents full existence of the corresponding element. The following power law representation of elastic properties is used to penalize intermediate density:

Where,
$\tilde{K}$
and
$K$
represent the penalized and the real stiffness matrix of an
element, respectively,
$p$
is the penalization factor which is always greater than 1. The
penalty is controlled by the `DISCRETE` or `DISCRT1D`
parameters, the value of these parameters correspond to (
$p$
- 1).