Abstarct: Abstract This research aims to analyze and design the optimal topology of the size-dependent plate under the consistent couple stress theory. First, the governing equations for bending, free vibration, and buckling of the plate are determined. Regarding the requirement of considering geometrical nonlinear behavior in the frxamework of structural buckling analysis, the curvature tensor and the mean curvature vector are determined baxsed on the Van Karman strain components. To determine the properties of functionally graded nanocomposite materials, a unified model baxsed on the Halpin-Tsai method is used to homogenize the parameters of the matrix phase and the reinforcement phase, each exhibiting separate functionally graded behavior. Subsequently, weak-form equations for the nanocomposite plate are developed baxsed on the unified model. To satisfy the first-order continuity C1 requirement under the consistent couple stress theory, a 4-node consistent rectangular element with 20 degrees of freedom at each node is established using the Hermitian approach. This approach reduces the number of degrees of freedom in the out-of-plane and in-plane motion to 12 and 8, respectively. Next, the general equilibrium equations of the plate are established baxsed on generalized degrees of freedom. By solving these equations, the displacements, eigenfrequencies, and corresponding mode shapes, along with the critical buckling load, are determined in relation to various parameters, including characteristic length, functionally graded pattern, dispersion pattern, and aspect ratio of the reinforcement phase, with benchmark examples provided. Subsequently, the optimal values baxsed on of structural buckling analysis, the curvature tensor and the mean curvature vector are determined baxsed on the Van Karman strain components. To determine the properties of functionally graded nanocomposite materials, a unified model baxsed on the Halpin-Tsai method is used to homogenize the parameters of the matrix phase and the reinforcement phase, each exhibiting separate functionally graded behavior. Subsequently, weak-form equations for the nanocomposite plate are developed baxsed on the unified model. To satisfy the first-order continuity C1 requirement under the consistent couple stress theory, a 4-node consistent rectangular element with 20 degrees of freedom at each node is established using the Hermitian approach. This approach reduces the number of degrees of freedom in the out-of-plane and in-plane motion to 12 and 8, respectively. Next, the general equilibrium equations of the plate are established baxsed on generalized degrees of freedom. By solving these equations, the displacements, eigenfrequencies, and corresponding mode shapes, along with the critical buckling load, are determined in relation to various parameters, including characteristic length, functionally graded pattern, dispersion pattern, and aspect ratio of the reinforcement phase, with benchmark examples provided. Subsequently, the optimal values baxsed on the size of these parameters are presented to minimize the plate's mass while adhering to frequency constraints. Next, the size-dependent optimal design of the plate's topology is performed. First, the topology optimization problem is explored to minimize plate compliance under volume constraints. The material properties interpolation scheme is established using the SIMP. The updating scheme is derived using the generalized optimality criteria method. The density filter method addresses numerical instabilities. In the following, the topology optimization problem is carried out to maximize the natural frequency of the plate while adhering to the volume constraint. To avoid the occurrence of repeated frequencies and mode switching, a modified bounded approach defines the optimization problem. In addition, the sensitivity filter method and modified interpolation relations for stiffness and mass are applied to handle numerical instabilities and local mode phenomena. During topology optimization to minimize compliance, the eigenfrequencies of the plate can change and fall into undesirable ranges, leading to phenomena such as resonance. Hence, in the following, the optimal topology design problem for minimizing compliance is defined with volume and frequency band constraints. Frequency band constraints baxsed on the modified Heaviside function are used to provide continuity and differentiability. Also, to reduce the number of constraints, a maximum value baxsed on the p-norm method is used to define the frequency band constraint. Similarly, maximizing the natural frequency of the plate can also lead to changing the eigenfrequencies and bringing them into undesirable ranges. Therefore, the problem of optimal design of the plate topology for maximizing the natural frequency with volume and frequency band constraints is investigated. In the following, two problems are considered, including the size-dependent optimal topology design of the nanocomposite plate to minimize compliance and maximize the natural frequency, considering the volume and frequency band constraints. For this purpose, a three-step design process is defined. In the first step, the optimal topology of the matrix phase is determined using the artificial density design variable and the SIMP. The second and third steps involve determining the optimal distribution of the reinforcement phase and eliminating undesirable frequency bands. In these steps, the volume fraction of the reinforcement phase is defined as a design variable, and the unified homogenization form is used to interpolate the material properties. The design variable obtained from the first step design is used as a fixed coefficient without penalty power in the interpolation relations of the second and third steps. The study of the optimal topologies obtained in the generalized model for in-plane, out-of-plane motions, and in-plane and out-of-plane coupling shows that the load transfer paths and connection of its topology components, different from the classical model and the truss form have an arc-like form and shear and bending performance. Also, the proposed reinforced model with an optimal distribution of nano-sized reinforcement at a volume fraction of only 1% on the surface of the matrix material and, by eliminating undesirable frequency bands, significantly increases the stiffness and natural frequency of the nanocomposite plate.