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Present study is concerned with three dimensional natural frequency analysis of functionally graded sandwich rectangular plates using Meshless Focal Petrov-Galerkin (MLPG) method and Artificial Neural Networks (ANNs). The plate consists of two homogeneous face sheets and a power-law FGM core. Natural frequencies of the plate are obtained by 3D MLPG method and are verified with available references. Convergence study of the first four natural frequencies for different node numbers is the next step. Also, effects of two parameters of \"FG core to plate thickness ratio\" and \"volume fraction index\" on natural frequencies of plate are investigated. Then, four distinct ANNs are used to predict the first four natural frequencies of the plate. Back-Error Propagation (BEP) method is used to train the ANNs. The predicted data shows a good agreement with respect to the actual data. Finally, the trained ANNs are used for prediction of natural frequencies of some conditions where MLPG data are not available.

Topology optimization is a mathematical method used to determine the optimal design of a structure to achieve desirable functional performance. Traditional single-material topology optimization can be extended to include multiple materials, offering greater design freedom, and the potential for superior layouts. Additive manufacturing technologies have become powerful tools to build up such multi-material solutions. However, inherent limitations in these processes must be considered in the optimal design. One significant challenge in additive manufacturing is the trapping of either unmelted or non-solidified powder, or in some cases, support structures in enclosed voids. This study investigates a gradient-based 3D bi-material topology optimization method that considers not only the volume fraction of each material and total mass constraints but also an additional virtual temperature constraint to avoid enclosed voids. To this end, the virtual temperature method is extended to identify and mitigate enclosed voids in bi-material structures. An efficient and straightforward technique is proposed for interpolating the elemental virtual heat conduction matrix and the elemental thermal load. Additionally, a discrete material optimization approach is employed to interpolate the elemental stiffness matrix. The problem formulation and sensitivities are thoroughly discussed. The method of moving asymptotes is used to update the design variables, which are the element densities of each material. 3D numerical results are presented to demonstrate the capability and feasibility of the proposed implementation, thereby providing superior performing designs with minimal impact on the structural performance.

An analytical method is proposed for the dynamic response analysis of functionally graded thick hollow cylinders under impact loading. The wave motion equation is solved using an analytical method that is based on the composition of Bessel functions. The mechanical properties are considered as power functions of the radius across the thickness of FG cylinder. The FG cylinder is excited by an impact loading at the inner surface of the cylinder, and the plane strain and axisymmetry conditions are assumed for the problem. The time histories of radial displacement and radial and hoop stresses are presented. Also the dynamic response of the FG cylinder is obtained and discussed for various kinds of power function exponents.

This paper investigates the bandgap properties of a piezoelectric periodic nano-beam considering size and surface effects using a modified couple stress theory. The nano-beam is made of some finite periodic arrays of piezoelectric (PZT-5H) and epoxy segments. The Bloch theorem for periodic materials together with the transfer matrix method are employed for analyzing the problem. The band structure analyzed by the current model incorporates both the material length scale parameter and surface effects in the bulk and surface layer of the beam, respectively. The main objective of this study is to investigate the effects of different parameters such as external electrical loading, length scale parameter, surface effects and geometrical properties of the nano-beam on the width of bandgaps and the starting frequencies. It is found that when the external electrical field is increased, the surface effects on the bandgaps are increased. Also, for high values of length to height ratio, ignoring the surface effects reduces the number of bandgaps. The results of the current study may be helpful in designing piezoelectric periodic nano-sensing devices.

In this article, an analytical method for dynamic and transient analysis of coupled non-Fick diffusion–elasticity is presented. The governing equations of the problem are transferred to the frequency domain using Laplace transform technique. The unknown parameters are then obtained in the series form using the presented analytical method. By employing the fast Laplace inverse technique, the unknown parameters are determined in time domain. It is concluded that the presented analytical method has a high capability for wave propagation analysis in mass transfer and elastic wave propagation problems. The propagation of wave fronts for displacements and molar concentration are studied in detail. It is shown that both molar concentration and elastic wave are propagated in the domain with finite speeds in the non-Fick theory of diffusion.

The time history analysis and propagation of molar concentration, temperature, and displacement waves are studied in details using an analytical method. The method is applied to coupled non-Fickian diffusion-thermoelasticity analysis of a strip. The governing equations are derived using non-Fickian theory of diffusion and classic theories for coupled thermoelasticity. Molar concentration and thermoelastic wave propagations are considered to be of finite speed. The governing equations are first transferred to the frequency domain using Laplace transform technique. The unknown parameters are then obtained in analytical forms proposed by the presented method. By employing the Talbot technique, the unknown parameters are eventually determined in time domain. It can be concluded that the presented analytical method has a high capability for dynamic and transient analysis of coupled diffusion-thermoelasticity problems. The wave fronts in displacement, temperature, and molar concentration fields can be tracked at various time instants employing the presented analytical method.