ABSTRACT
E(xi) = E0x pi (2) where E0 denotes the Young’s modulus for solid material, p is the penalty exponent. The gradient of the objective function with respect to individual element density can be easily derived by the adjoint method as
∂C
∂xi = −px
2 uTi K
where K0i are the elemental stiffness matrix for solid elements. By specifying a value of p higher than one (normally p ≥ 3), the SIMP method leads to nearly solid-void optimal designs.
