The present study focuses on the thermo-mechanical bending investigation of functionally graded material (FGM) sandwich plates with temperature-dependent material properties. For engineering applications, FGMs are typically made of metal and ceramic, where metal provides high rigidity and ceramic delivers high thermal resistivity. Material properties of FGM sandwich plate are considered temperature dependent and assumed to be continuously graded in thickness direction. Sigmoid and power law distributions are adopted to obtain the smooth and continuous variation of mechanical and thermal properties of FGM plate. To carry out thermo-mechanical bending, one dimensional heat conduction equation is utilized to obtain temperature variation in thickness direction. Sinusoidal shear deformation theory (SSDT) is a type of non-polynomial shear deformation theory which accounts for sinusoidal distribution of transverse shear stress and satisfies the traction free boundary condition. The governing equations for thermo-mechanical bending analysis for FGM sandwich plates are derived using Hamilton’s variational principle following SSDT and Navier’s solution. Closed form solutions are obtained to predict centre deflection, and normal and shear stresses of simply supported FGM sandwich plates. The effect of temperature-dependent material properties, power and sigmoid law, gradation index, temperature difference, side to thickness ratio, and aspect ratio over central deflection, normal stress, and shear stress are carried out and analysed. It may be concluded from the analysis that temperature-dependent material properties and gradation index for power and sigmoid law considerably influence the central deflection, normal stress, and shear stress. A good agreement amongst the obtained and available results of existing shear deformation theory is found to validate the accuracy of the SSDT.

Purpose – The purpose of this study is to examine the impact of material gradation and porosity distributions on the buckling response of metal (Al) ceramic (Al2O3) unidirectional functionally graded material (UDFGM) Sandwich plate considering sinusoidal shear deformation theory (SSDT). To carry out the buckling analysis of UDFGM Sandwich plate, both uniaxial and biaxial compressive loads are considered. Design/methodology/approach – In the case of UDFGM plate, material properties are considered to be continuously graded in only one direction, i.e. thickness direction. To consider the porosity effect, four different types of distribution models, even, uneven, linear uneven and sinusoidal uneven, are considered. It is assumed that the FGM faces of the Sandwich plate are porous while the ceramic core is nonporous. Functionally graded material (FGM) plates have been studied against conventional single-material plates because these ceramics provide good thermal resistance properties (e.g. alumina), which are very hard and brittle, along with excellent toughness and ductility from metals (e.g. aluminium). These Sandwich plates are made of two constituent phases with volume fractions changing continuously and gradually. To model the variation in material properties, four classical models, namely Power Law, Trigonometric, Exponential and Sigmoid are employed to describe the phase distribution. The governing equations have been obtained by using the Hamilton's Principal and the Navier's solution technique for buckling response of UDFGM using SSDT. Findings – The effect of unidirectional material gradation, gradation law index, geometrical parameter, even and uneven porosity distribution patterns and porosity coefficient over buckling behaviour of UDFGM Sandwich plate has been discussed and analysed. Results are presented through comprehensive plots and tables, comparing the buckling behaviour under different porosity distributions and material gradation models. It is noticed that gradation models, i.e. power, trigonometric, exponential and sigmoid and porosity distributions, i.e. even, uneven, linear uneven and sinusoidal uneven have a significant impact over critical buckling load for UDFGM under uniaxial and biaxial compressive load considering SSDT. Originality/value – For the first time, the impact of various material gradation models and porosity distribution patterns over critical buckling load of UDFGM plate has been investigated, considering non-polynomial shear deformation theory, namely SSDT. The analysis reveals that porosity distribution significantly influences the buckling response. Results indicate that buckling resistance is highest in sinusoidal porosity coupled with Sigmoid gradation, whereas the weakest resistance comes from trigonometric gradation with uneven porosity. These results may provide a benchmark toward the optimization of UDFGM Sandwich plates for structural applications of higher order.

Additive manufacturing (AM) has emerged as a transformative technology, enabling the fabrication of complex geometries through a layer-by-layer approach. This advancement aligns with the goals of Industry 4.0, offering substantial benefits for large-scale sectors such as aerospace and automotive. Notably, AM not only facilitates the production of intricate parts but also enables efficient and cost-effective repair solutions. This review examines the novel application of laser powder-directed energy deposition (LP-DED) in fabricating functionally graded materials (FGMs). These are engineered to exhibit a gradual change in composition and properties across their volume. The study highlights how LP-DED offers precise control over processing parameters, such as laser power, scan speed, and powder feed rate, to tailor material characteristics such as hardness, thermal resistance, and corrosion behavior. A key novelty of this work lies in its focus on dynamically altering powder composition during deposition to achieve customized gradients in material performance. Furthermore, the paper synthesizes findings from the recent literature, analyzing the microstructural evolution, defect formation, and mechanical behavior of LP-DED-processed FGMs. By addressing both the opportunities and challenges of this advanced method. The review provides actionable insights for selecting optimal materials and process settings, emphasizing the growing role of LP-DED in next-generation manufacturing strategies.

The objective of this study is to investigate the buckling response of imperfect uni-directional functionally graded material (UDFGM) sandwich plates. To conduct the buckling analysis of UDFGM sandwich plate, bi-axial compressive load is considered. In the case of the UDFGM plate, the material properties are continuously graded in only one direction, specifically the thickness direction. Typically, UDFGM plates are composed of metal and ceramic materials that exhibit different thermal and mechanical properties. In this study, we consider both even and uneven porosity distribution patterns to examine their effects on the critical buckling loads of UDFGM sandwich plates under uni-axial and bi-axial compressive loads. The effective material properties of the UDFGM plate are determined using Voigt’s micro-mechanical model with power law distributions. The sandwich plate consists of two UDFGM faces with a ceramic core. Hamilton’s Principle is employed to derive the governing equations for the buckling response of the UDFGM, using the sinusoidal shear deformation theory (SSDT). The study analyzes how uni-directional gradation, the power law index, geometric parameters, and both even and uneven porosity distribution patterns, along with the porosity coefficient, influence the buckling behaviour of UDFGM sandwich plates.

Functionally graded material is a novel composite in which the properties vary with the dimension. Numerous industrial sectors and applications, including aerospace, automotive, biomedical implants, optoelectronic devices, energy-absorbing structures, geological models, and heat exchangers, are highly interested in FGMs. The present study analyzes the natural frequencies of a functionally graded metal-ceramic (FGMC) sandwich plate that has been accomplished considering refined shear deformation theory. Since the parabolic variance in shear strain through the thickness is such that shear stresses vanish on the plate surfaces, the shear correction factor is not required. Hamilton’s principle has been utilized to derive the equation of motion to perform the free vibration analysis. Additionally, the eigen value equation for the FGMC sandwich plate is obtained via Navier's solution. For the analysis, the three variations of sandwich plate are selected. Three various types of FGMC sandwich plate types viz. 1-1-1, 1-2-1, and 2-2-1 have been taken into consideration for conducting the free vibration study to analyze natural frequency. The material properties of each layer of the sandwich plate and the volume gradation index are obtained considering power law. Lastly, the influence of parameters such as volume fraction, length-towidth ratio, and aspect ratio on frequency parameter is investigated. It is observed that geometrical parameters volume fraction index, and thickness ratio of FGMC sandwich plate has a considerable impact on frequency parameter.

The current study presents a free vibration analysis of a porous functionally graded material (FGM) sandwich plate via refined shear deformation theory. The FGM sandwich plate employed in this investigation has a homogeneous ceramic core and FGM faces. To incorporate the porosity, three varied kinds of porosity distribution models, namely even, uneven, and linear uneven are chosen. The boundary conditions for the FGM sandwich plate are considered to be simply supported. Further, the eigenvalue equation for the sandwich plate is obtained using Hamilton’s principle following Navier's solution. The free vibration analysis is carried out for three variants of the porous FGM sandwich plate model, namely 1-1-1, 1-2-1, and 2-1-2. The gradation of material properties of the distinct layers of the FGM sandwich plate is defined using the power law distribution (P-FGM). Finally, the impact of parameters such as porosity distribution models, porosity coefficient, volume fraction, and aspect ratio over frequency parameters is investigated. It is observed that geometrical parameters and porosity coefficient, thickness ratio, and volume fraction of FGM sandwich plate have a significant impact on frequency parameter.

This study shows the free vibration response of functionally graded metal-ceramic sandwich plates for the validation of the frequency parameter according to classical plate theory (CPT) using ANSYS software by considering the finite element solution approach. The faces of the functionally graded sandwich plate have layers, which are considered to be isotropic. Volume fraction, modulus of elasticity, density, and Poisson’s ratio of the different faces of the functionally graded material (FGM) plate are presumed to differ with power law distribution. For this study, the Functionally graded plate is symmetric from the middle plane. The core layer or the middle layer is ceramic and has an isotropic and homogenous nature. The model chosen for the analysis is 1:1:1 having same thickness ratio for top, core, and bottom, and frequency variation with different volume index is obtained for the clamped boundary condition considering classical plate theory. Impacts of change in aspect ratio, volume fraction index over frequency have been studied. Variation of frequency for different mode shapes is studied. Also, the impact of nodes and elements on frequency is investigated.

Purpose: The purpose of this study is to investigate the bending analysis of metal (Ti-6Al-4V)-ceramic (ZrO2) functionally graded material (FGM) sandwich plate with material property gradation along length and thickness direction under thermo-mechanical loading using inverse trigonometric shear deformation theory (ITSDT). FGM sandwich plate with a ceramic core and continuous variation of material properties has been modelled using Voigt’s micro-mechanical model following the power law distribution method. The impact of bi-directional gradation of material properties over the bending response of FGM plate under thermo-mechanical loading has been investigated in this work. Design/methodology/approach: In this study, gradation of material properties for FGM plates is considered along length and thickness directions using Voigt’s micromechanical model following the power law distribution method. This type of FGM is called bi-directional FGMs (BDFGM). Mechanical and thermal properties of BDFGM sandwich plates are considered temperature-dependent in the present study. ITSDT is a non-polynomial shear deformation theory which requires a smaller number of field variables for modelling of displacement function in comparison to poly-nominal shear deformation theories which lead to a reduction in the complexity of the problem. In the present study, ITSDT has been utilized to obtain the governing equations for thermo-mechanical bending of simply supported uni-directional FGM (UDFGM) and BDFGM sandwich plates. Analytical solution for bending analysis of rectangular UDFGM and BDFGM sandwich plates has been carried out using Hamilton’s principle. Findings: The bending response of the BDFGM sandwich plate under thermo-mechanical loading has been analysed and discussed. The present study shows that centre deflection, normal stress and shear stress are significantly influenced by temperature-dependent material properties, bi-directional gradation exponents along length and thickness directions, geometrical parameters, sandwich plate layer thickness, etc. The present investigation also reveals that bi-directional FGM sandwich plates can be designed to obtain thermo-mechanical bending response with an appropriate selection of gradation exponents along length and thickness direction. Non-dimensional centre deflection of BDFGM sandwich plates decreases with increasing gradation exponents in length and thickness directions. However, the non-dimensional centre deflection of BDFGM sandwich plates increases with increasing temperature differences. Originality/value: For the first time, the FGM sandwich plate with the bi-directional gradation of material properties has been considered to investigate the bending response under thermo-mechanical loading. In the literature, various polynomial shear deformation theories like first-order shear deformation theory (FSDT), third-order shear deformation theory (TSDT) and higher-order shear deformation theory (HSDT) have been utilized to obtain the governing equation for bending response under thermo-mechanical loading; however, non-polynomial shear deformation theory like ITSDT has been used for the first time to obtain the governing equation to investigate the bending response of BDFGM. The impact of bi-directional gradation and temperature-dependent material properties over centre deflection, normal stress and shear stress has been analysed and discussed.

Purpose: The purpose of this article is to carry out the thermal buckling analysis of power and sigmoid functionally graded material Sandwich plate (P-FGM and S-FGM) under uniform, linear, nonlinear and sinusoidal temperature rise. Design/methodology/approach: Thermal buckling of FGM Sandwich plates namely, FGM face with ceramic core (Type-A) and homogeneous face layers with FGM core (Type-B), incorporated with nonpolynomial shear deformation theories are considered for an analytical solution in this investigation. Effective material properties and thermal expansion coefficients of FGM Sandwich plates are evaluated based on Voigt's micromechanical model considering power and sigmoid law. The governing equilibrium and stability equations for the thermal buckling analysis are derived based on sinusoidal shear deformation theory (SSDT) and inverse trigonometric shear deformation theory (ITSDT) along with Von Karman nonlinearity. Analytical solutions for thermal buckling are carried out using the principle of minimum potential energy and Navier's solution technique. Findings: Critical buckling temperature of P-FGM and S-FGM Sandwich plates Type-A and B under uniform, linear, non-linear, and sinusoidal temperature rise are obtained and analyzed based on SSDT and ITSDT. Influence of power law, sigmoid law, span to thickness ratio, aspect ratio, volume fraction index, different types of thermal loadings and Sandwich plate types over critical buckling temperature are investigated. An analytical method of solution for thermal buckling of power and sigmoid FGM Sandwich plates with efficient shear deformation theories has been successfully analyzed and validated. Originality/value: The temperature distribution across FGM plate under a high thermal environment may be uniform, linear, nonlinear, etc. In practice, temperature variation is an unpredictable phenomenon; therefore, it is essential to have a temperature distribution model which can address a sinusoidal temperature variation too. In the present work, a new sinusoidal temperature rise is proposed to describe the effect of sinusoidal temperature variation over critical buckling temperature for P-FGM and S-FGM Sandwich plates. For the first time, the FGM Sandwich plate is modeled using the sigmoid function to investigate the thermal buckling behavior under the uniform, linear, nonlinear and sinusoidal temperature rise. Nonpolynomial shear deformation theories are utilized to obtain the equilibrium and stability equations for thermal buckling analysis of P-FGM and S-FGM Sandwich plates.

This work examines the effect of porosity distributions on thermal buckling analysis of functionally graded material (FGM) sandwich plates. To consider the porosity effect, five different types of distribution models, even, uneven, logarithmic uneven, linear uneven, and sinusoidal uneven are considered. It is assumed that the FGM faces of the sandwich plate are porous while the ceramic core is nonporous. To investigate the thermal buckling behavior of porous FGM sandwich plates, four different types of thermal loads, such as uniform, linear, nonlinear, and sinusoidal temperature rise along the thickness direction are considered. Effective material properties and thermal expansion coefficients of FGM sandwich plates are evaluated based on Voigt's micromechanical model considering power law FGM (P-FGM) and sigmoid function FGM (S-FGM). The analytical solution is carried out using Hamilton's variational principle considering the von Karman nonlinearity. The equilibrium and stability equations are derived based on sinusoidal shear deformation theory (SSDT). Numerical results are obtained to observe the influence of different porosity distributions, porosity coefficients, thermal loadings, and geometrical parameters over critical thermal buckling temperature.

In this article, the free vibration and buckling of multi-directional porous FGM sandwich plates are investigated. The material properties of FGM sandwich plates are assumed to be varying continuously in the longitudinal and transverse direction. The material properties are evaluated based on Voigt's micro-mechanical model considering power law distribution method with arbitrary power index. Equilibrium equations for the vibration and buckling analysis of porous multi-directional FGM sandwich plate are obtained based on sinusoidal shear deformation theory. Analytical solution for simply supported multi-directional porous FGM sandwich plate is carried out using Navier's solution technique. The FGM sandwich plate considered in this work has a homogeneous ceramic core and two functionally graded face sheets. To incorporate porosity in the FGM face sheet, even, uneven, logarithmic uneven, linear uneven, and sinusoidal uneven porosity distribution models are considered and analyzed. Influence of volume fraction index in the longitudinal and transverse direction, layer thickness, porosity models, porosity coefficient, and geometrical parameter over natural frequency and critical buckling load of multi-directional FGM sandwich plate is investigated.

Purpose: The purpose of this paper is to carry out free vibration and buckling analysis of functionally graded material (FGM) plate. Design/methodology/approach: Equilibrium and stability equations of FGM rectangular plate under different boundary conditions are derived using finite element method-based inverse trigonometric shear deformation theory (ITSDT). Eight-noded rectangular plate element with seven degrees of freedom at each node is used for the present analysis. The power-law distribution method has been considered for the continuously graded variation in composition of the ceramic and metal phases across the thickness of a functionally graded plate. Findings: The finite element formulation incorporated with ITSDT and provisions of the constitutive model of FGM plate has been implemented in a numerical code to obtain the natural frequency and critical buckling load under uniaxial and biaxial compressive load. The influence of material gradation, volume fraction index, span to thickness ratio and boundary constraints over free vibration and buckling response has been studied. Originality/value: Development and validation of finite element methodology using ITSDT to predict the structural response of the FGM plates under different loading, geometric and boundary conditions.