  Topology optimization (TO) has experienced a dramatic development over the
last decades aided by the arising of metamaterials and additive manufacturing
(AM) techniques, and it is intended to achieve the current and future
challenges. In this paper we propose an extension for linear orthotropic
materials of a three-dimensional TO algorithm which directly operates on the
six elastic properties -- three longitudinal and shear moduli, having fixed
three Poisson ratios -- of the finite element (FE) discretization of certain
analysis domain. By performing a gradient-descent-alike optimization on these
properties, the standard deviation of a strain-energy measurement is minimized,
thus coming up with optimized, strain-homogenized structures with variable
longitudinal and shear stiffness in their different material directions. To
this end, an orthotropic formulation with two approaches -- direct or
strain-based and complementary or stress-based -- has been developed for this
optimization problem, being the stress-based more efficient as previous works
on this topic have shown.
  The key advantages that we propose are: (1) the use of orthotropic ahead of
isotropic materials, which enables a more versatile optimization process since
the design space is increased by six times, and (2) no constraint needs to be
imposed (such as maximum volume) in contrast to other methods widely used in
this field such as Solid Isotropic Material with Penalization (SIMP), all of
this by setting one unique hyper-parameter. Results of four designed load cases
show that this orthotropic-TO algorithm outperforms the isotropic case, both
for the similar algorithm from which this is an extension and for a SIMP run in
a FE commercial software, presenting a comparable computational cost. We remark
that it works particularly effectively on pure shear or shear-governed problems
such as torsion loading.
