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.

翻译：本文首次实现了面内双向功能梯度（IBFG）非均匀厚度Reissner-Mindlin板的多材料拓扑优化（MTO）。该MTO的数学表述基于一阶剪切变形理论（FSDT），以最小化柔度为目标函数。通过将具有多体积分数约束的多相拓扑优化问题，采用交替主动相算法结合块状Gauss-Seidel方法，转化为仅含单一体积分数约束的多个二值相拓扑优化子问题。在研究范围内，考虑基于等效局部体积模量和剪切模量的IBFG材料，以更精确地反映材料间的相互作用。此外，利用成熟的张量分量混合插值四节点单元（MITC4）数值技术，克服了薄板模型中存在的剪切闭锁问题。本研究详细推导了IBFG板MTO的数学表达式，并通过多个IBFG板数值算例验证了所提方法的有效性与可靠性。