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：本文首先介绍了对机内双向功能分级(IBFG)非单向厚厚Reissner-Mindlin板块实施多物质地形优化(MTO)的情况。MTO的数学配方与第一个剪切变形理论(FSDT)相关联,以解决尽量减少作为客观功能的合规性。从一个多阶段到多量分数制约问题,问题被转移到多个二进制阶段,仅涉及一个体积分数限制的子问题。在研究范围内,IBFG材料根据有效的当地大宗和剪模版材料,被视为更准确的材料相互作用。此外,已经利用成熟的抗声元件4节点元素混合猜测的数值技术(MITC4)克服了在薄质板模型中出现的尖性锁定问题。研究用极详细的数学表达方式表述了IBFG板MTO。一些IBFG牌块当前可靠性方法的数字例子,以核实其效率。