Buckling and Vibration Characteristics of Functionally Graded Sandwich Structures with Conventional and Auxetic Core: Analytical and Finite Element Study

Abstract

Functionally graded sandwich plates (FGSPs) have emerged as an importance class of structural components in modern engineering fields such as in aerospace, mechanical, and marine structures due to their superior stiffness-to-weight ratio, improved thermal resistance, and enhanced structural stability. The present thesis presents a comprehensive analytical and numerical investigation of the buckling and vibration behaviour of FGSPs based on the Inverse Trigonometric Shear Deformation Theory (ITSDT). The governing equations are formulated using the principle of virtual work in combination with linear structural kinematics and generalized Hooke’s law. An analytical employing ITSDT is developed to obtain-closed form solutions for plates with simply supported boundary conditions (SSSS). In addition, a finite element (FE) formulation is established to analyze the structural response of plates subjected to more complex boundary conditions such as clamped-clamped-clamped-clamped (CCCC) and clamped simply supported-clamped-simply supported (CSCS). In order to evaluate the influence of different material arrangements within the sandwich structure, three configurations of FGSPs - Type-A, Type-B, and Type-C, are considered. In the Type-A configuration, the core layer is made of ceramic material while the face sheets consist of functionally graded materials whose properties vary according to a power-law distribution. For Type-B plates, the core is composed of functionally graded, whereas the top and bottom face sheets are made of ceramic and metallic materials, respectively. In the Type-C configuration, the core is modeled as an auxetic honeycomb structure characterized by a negative Poisson’s ratio, while the face sheets are composed of functionally graded materials. The equivalent elastic properties of the auxetic honeycomb core are evaluated using analytical expressions based on the geometric parameters of the honeycomb unit cell. A detailed parametric study is carried out to investigate the influence of several important parameters on the structural behaviour of FGSPs. These parameters include the span-to-thickness ratio (a/h), aspect ratio (a/b), power-law index (p), auxetic cell angle (θ), core thickness configurations of the sandwich layers, and different boundary conditions. The structural performance is evaluated in terms of the dimensionless fundamental natural frequency and the dimensionless critical buckling load. For the buckling analysis, both uniaxial and biaxial in-plane compressive loading conditions are considered in order to study their influence on the stability characteristics of the plates. The results obtained from the analytical solutions and finite element simulations show excellent agreement with previously reported results in the literature, confirming the accuracy and reliability of the proposed ITSDT-based formulation and the developed numerical model. The parametric investigation indicates that the power-law index significantly affects the structural response of FGSPs. The dimensionless fundamental frequency and the critical buckling load decrease with an increase in the power-law index. The span-to-thickness ratio also has a strong influence on the vibrational behaviour of the plates. It is observed that the dimensionless fundamental frequency increases as the span-to-thickness ratio increases, primarily due to the reduction in transverse shear deformation effects and the predominance of bending behaviour in relatively thinner plates. Similarly, the aspect ratio influences the stability characteristics of the plates, with the dimensionless critical buckling load decreasing as the aspect ratio increases. Furthermore, the nature of the applied in-plane compressive loading plays an important role in the buckling response, as the critical buckling load under uniaxial compression is found to be considerably higher than that under biaxial compression for plates with simply supported boundary conditions. The study further demonstrates that the thickness of the core layer has a significant influence on the vibrational response of FG sandwich plates. An increase in the core thickness enhances the bending rigidity of the sandwich structure, which results in higher natural frequencies. Moreover, boundary conditions considerably affect both the vibration and buckling responses of the plates. Structures with clamped boundary conditions exhibit higher natural frequencies and greater buckling resistance compared with plates having simply supported boundary edges. The thickness distribution scheme of the sandwich layer also plays a crucial role in determining the structural performance, where configurations with thicker core regions generally lead to improved stiffness and higher natural frequencies. For Type-C plates, the inclusion of an auxetic honeycomb core introduces distinctive mechanical characteristics due to its negative Poisson’s ratio behaviour. The results indicate that the auxetic core enhances the stiffness and stability of the sandwich plates while also providing additional flexibility in structural design through the variations in geometric parameters such as the cell angle. Overall, this work establishes a robust analytical and numerical framework for the investigation of vibration and buckling behaviour of functionally graded sandwich plates. The outcomes of this study provide valuable insights into the influence of material gradation, geometric configuration, boundary conditions, and auxetic core characteristics on the structural performance of sandwich plates, thereby contributing to the optimal design and development of advanced lightweight structural systems for modern engineering applications.