  This paper firstly presents an implementation of multi-material topology
optimization (MTO) for in-plane bi-directional functionally graded (IBFG)
non-uniform thickness Reissner-Mindlin plates. The mathematical formulation of
the MTO is associated with a first shear deformation theory (FSDT) to solve the
minimization of compliance as the objective function. From a multi-phase TO
problem with multi-volume fraction constraints, the problem is transferred into
many binary phases TO sub-problems with only one volume fraction constraint
using an alternating active-phase algorithm in conjunction with the block
Gauss-Seidel method. In the study's scope, IBFG materials following effective
local bulk and shear modulus are considered to show a more accurate interaction
of materials. Besides, the numerical technique of the well-established mixed
interpolation of tensorial components 4-node elements (MITC4) is utilized to
overcome the shear locking problem occurring to thin plate models. The study
formulates in great detailed mathematical expressions for IBFG plates MTO.
Several numerical examples of IBFG plates are presented to verify the
efficiency and reliability of the current methodology.
