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The purpose of this paper is to investigate the linear and non-linear free vibration of a functionally graded material (FGM) rotating cantilever plate in the thermal environment. The study employs the development of a non-linear mathematical model using the higher order shear deformation theory in which the traction free condition is applied to derive the simplified displacement model with seven field variables instead of nine.

A mathematical model is developed based on the higher order shear deformation theory using von-Karman type non-linearity. The rotating plate domain has been discretized into C0 eight-noded quadratic serendipity elements with node wise 7 degrees of freedom. The material properties are considered temperature dependent and graded along the thickness direction obeying a simple power law distribution in terms of the volume fraction of constituents, based on Voigt’s micromechanical method. The governing equations are derived using Hamilton’s principle and are solved using the direct iterative method.

The importance of the present mathematical model developed for numerical analysis has been stated through the comparison studies. The results provide an insight into the vibration response of FGM rotating plate under thermal environment. The influence of various parameters like setting angle, volume fraction index, hub radius, rotation speed parameter, aspect ratio, side-thickness ratio and temperature gradient on linear and non-linear frequency parameters is discussed in detail.

A non-linear mathematical model is newly developed based on C0 continuity for the functionally graded rotating plate considering the 1D Fourier equation of heat conduction. The present findings can be utilized for the design of rotating plates made up of a FGM in the thermal environment under real-life situations.

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.

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.

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.

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.

The purpose of this paper is to study the effect of the addition of silicon carbide (SiC) microparticles and their contributions regarding the tensile and shear properties of the T800 fiber reinforced polymer composite at various fiber volume fractions. The tensile and shear properties of the hybrid composites where continuous T800 fibers are used as reinforcements in an epoxy matrix embedded with SiC microparticles have been studied.

The results were obtained by implementing a micromechanics approach assuming a uniform distribution of reinforcements and considering one unit cell from the whole array. Using the two-step homogenization process, the properties of the materials were determined by using the finite element analysis (FEA). The predicted elastic properties from FEA were compared with the analytical results. The analytical models were implemented in the MATLAB Software. The FEA was performed in ANSYS APDL.

The mechanical properties of the hybrid composite had increased when compared with the properties of the conventional FRP. The results suggest that SiC particles are a good reinforcement for enhancing the transverse and shear properties of the considered fiber reinforced epoxy composite. The microparticle embedment has significant effect on the transverse tensile properties as well as in-plane and out-of-plane shear properties.

This is significant because improving the properties of the composite materials using different methods is of high interest in the materials community. Using this study people can work on the process of including different type of microparticles in to their composite designs and improve their performance characteristics. The major influence of the particles can be seen only at lower volume fractions of the fiber in the composite. Only FEA and analytical methods were used for the study.

Material property improvements lead to more advanced designs for aerospace and defense structures, which allow for high performance under unpredictable conditions.

This type of study proves that the embedment of different microparticles is a method that can be used for improving the properties of the composite materials. The improvement of the transverse and shear properties will be useful especially in the design of shell structures in the different engineering applications.

Functionally graded materials are a special class of composites in which material are graded either continuously or layered wise depending upon its applications. With such variations of materials, the properties of structure vary either lengthwise or thickness wise. This paper aims to investigate models for effective estimation of material properties, as it is necessary for industries to identify the properties of composites or functionally graded materials (FGM’s) before manufacturing and also to develop novel material combinations.

Available models were compared for different material combinations and tested with experimental data for properties such as Young’s modulus, density, coefficient of thermal expansion (CTE) and thermal conductivity. Combinations of metal–ceramic and metal–metal were selected such that their ratios cover a wide range of materials.

This study reveals different models will be required depending on the material used and properties to be identified.

The results of the present work will help researchers in the effective modeling of composites or FGM’s for any analysis.

This paper presents a comparison and review of various analytical methods with experimental data graphically to find out the best suitable method. For the first time, the Halpin-Tsai model was extended in the analysis of the CTE which shows good approximations.

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.

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.

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.

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.

The purpose of this paper is to evaluate the efficiency of the fast multipole boundary element method (FMBEM) in the analysis of stress and effective properties of 3D linear elastic structures with cavities. In particular, a comparison between the FMBEM and the finite element method (FEM) is performed in terms of accuracy, model size and computation time.

The developed FMBEM uses eight-node Serendipity boundary elements with numerical integration based on the adaptive subdivision of elements. Multipole and local expansions and translations involve solid harmonics. The proposed model is used to analyse a solid body with two interacting spherical cavities, and to predict the homogenized response of a porous material under linear displacement boundary condition. The FEM results are generated in commercial codes Ansys and MSC Patran/Nastran, and the results are compared in terms of accuracy, model size and execution time. Analytical solutions available in the literature are also considered.

FMBEM and FEM approximate the geometry with similar accuracy and provide similar results. However, FMBEM requires a model size that is smaller by an order of magnitude in terms of the number of degrees of freedom. The problems under consideration can be solved by using FMBEM within the time comparable to the FEM with an iterative solver.

The present results are limited to linear elasticity.

This work is a step towards a comprehensive efficiency evaluation of the FMBEM applied to selected problems of micromechanics, by comparison with the commercial FEM codes.

The purpose is to analyze the mechanical behavior of the arterial wall in the degraded region of the arterial wall and to determine the stress distribution, as an important factor for predicting the potential failure mechanisms in the wall. In fact, while the collagen fiber degradation process itself is not modeled, zones with reduced collagen fiber content (corresponding to the degradation process) are assumed. To do so, a local weakness in the media layer is considered by defining representative volume elements (RVEs) with different fiber collagen contents in the degraded area to investigate the mechanical response of the arterial wall.

A three-dimensional (3D) large strain hierarchical multiscale technique, based on the homogenization and genetic algorithm (GA), is utilized to numerically model collagen fiber degradation in a typical artery. Determination of material constants for the ground matrix and collagen fibers in the microscale level is performed by the GA. In order to investigate the mechanical degradation, two types of RVEs with different collagen contents in fibers are considered. Each RVE is divided into two parts of noncollagenous matrix and collagen fiber, and the part of collagen fiber is further divided into matrix and collagen fibrils.

The von Mises stress distributions on the inner and outer surfaces of the artery and the influence of collagen fiber degradation on thinning of the arterial wall in the degraded area are thoroughly studied. Comparing the maximum stress values on outer and inner surfaces in the degraded region shows that the inner surface is under higher stress states, which makes it more prone to failure. Furthermore, due to the weakness of the artery in the degraded area, it is concluded that the collagen fiber degradation considerably reduces the wall thickness in the degraded area, leading to an observable local inflation across the degraded artery.

Considering that little attention has been paid to multiscale numerical modeling of collagen fiber degradation, in this paper a 3D large strain hierarchical multiscale technique based on homogenization and GA methods is presented. Therefore, while the collagen fiber degradation process itself is not modeled in this study, zones with reduced collagen fiber content (corresponding to the degradation process) are assumed.

The purpose of this study is the comprehensive numerical assessment of multidirectional (1D/2D/3D) functionally graded composite panel structures with different material gradation patterns and degrees of material heterogeneity. Here, deformation characteristics are obtained under different loading and support conditions.

The finite element solutions of multidirectional functionally graded composite panels subjected to uniform and sinusoidal transverse loads are presented under different support conditions. Here, different functionally graded composites, such as unidirectional (1D) and multidirectional (2D/3D), are considered by distributing constituent materials in one, two and three directions, respectively, using single and multivariable power-law functions. A constitutive model with fully spatial-dependent elastic stiffness is developed, whereas the kinematics of the present structure is defined using equivalent single-layer higher-order theory. The weak form, based on the principle of virtual work, is established and solved consequently using isoparametric finite element approximations via quadrilateral Lagrangian elements.

The appropriate mesh-refinement process is carried out to achieve the mesh convergence; whereas, the correctness of proposed heterogeneous model is confirmed through a verification test. The comprehensive numerical assessment of multidirectional functionally graded panels under various loading and support conditions depicts the importance of degree of material heterogeneity with different gradation patterns and volume-fraction exponents.

A comprehensive analysis on the deformation behaviour of 1D-functionally graded materials (FGMs) (X-FGM, Y-FGM and Z-FGM), 2D-FGMs (XY-FGM, YZ-FGM and XZ-FGM) and 3D-FGM composite panels FGM structures is presented. Multifaceted heterogeneous FGMs are modelled by varying constituent materials in one, two and three directions, using power-law functions. The constitutive model of multi-directional FGM is developed using fully spatial-dependent elastic matrix and higher-order kinematics. Isoparametric 2D finite element formulation is adopted using quadrilateral Lagrangian elements to model 1D/2D/3D-FGM structures and to obtain their deflection responses under different loading and support conditions.

The purpose of the paper is to propose a homogenization-based topology optimization method to optimize the design of variable-density cellular structure, in order to achieve lightweight design and overcome some of the manufacturability issues in additive manufacturing.

First, homogenization is performed to capture the effective mechanical properties of cellular structures through the scaling law as a function their relative density. Second, the scaling law is used directly in the topology optimization algorithm to compute the optimal density distribution for the part being optimized. Third, a new technique is presented to reconstruct the computer-aided design (CAD) model of the optimal variable-density cellular structure. The proposed method is validated by comparing the results obtained through homogenized model, full-scale simulation and experimentally testing the optimized parts after being additive manufactured.

The test examples demonstrate that the homogenization-based method is efficient, accurate and is able to produce manufacturable designs.

The optimized designs in our examples also show significant increase in stiffness and strength when compared to the original designs with identical overall weight.