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AbstractFunctionally graded triply periodic minimal surface (FG-TPMS) structures are known as bio-inspired structures. They possess some remarkable advantages such as porous structures with high inter-connectivity, mathematically controllable geometry features and smooth surfaces. As another advantage, FG-TPMS structures can be fast and numerously manufactured by 3D printing technology. Nevertheless, modeling these structures is a challenging task. This paper investigates static bending and free vibration behaviors of FG-TPMS shells. The proposed formulation is established upon isogeometric analysis (IGA) and first-order shear deformation shell theory (FSDT). The governing equations are discretized by a Galerkin weak form and numerically solved by using non-uniform rational B-Spline (NURBS) basis functions. Exact geometries of structures are described via NURBS basis functions. A fitting technique is used to compute the mechanical characteristics of FG-TPMS materials. We investigate behaviors of FG-TPMS shells considering three types of cell geometries which are primitive (P), gyroid (G), I-graph and wrapped package-graph (IWP), and six porosity distribution patterns. The present solutions are verified with the reference ones in the literature. Effects of boundary, type of cell geometry, porosity distribution pattern, length-to-radius and thickness ratios on behaviors of FG-TPMS shells are rigorously studied. Especially, many numerical results of FG-TPMS shells are first proposed in this paper. [ABSTRACT FROM AUTHOR]

The current study examined the linear and nonlinear bending results of functionally graded graphene nanoplatelet reinforced composite beams. The equation system was constructed using Reddy's third order shear deformation theory and a von Kármán type nonlinear strain-displacement relationship. The nonlinear bending results of this system were solved using the Gram-Schmidt-Ritz method in conjunction with the direct iteration technique. By employing the Gram-Schmidt orthogonalization procedure for generating shape functions in the method, numerically stable functions for nonlinear bending analysis of beams were obtained. Our solutions were validated for accuracy by comparing them to some published results. The numerical results indicate that the geometrical nonlinearity of beams subjected to uniform distributed load is greater than that of beams subjected to sinusoidal, linear, or parabolic distributed loads. New results on several significant effects of reinforcement patterns, graphene nanoplatelet weight fraction, and different types of distributed loads are presented and discussed in this study, in which the findings can serve as a benchmark for future research. [ABSTRACT FROM AUTHOR]

Globally, there is an increasing need for ceramic materials that have a variety of applications in the environment, for precision tools, and for the biomedical, electronics, and environmental industries. However, in order to obtain remarkable mechanical qualities, ceramics have to be manufactured at a high temperature of up to 1600 °C over a long heating period. Furthermore, the conventional approach presents issues with agglomeration, irregular grain growth, and furnace pollution. Many researchers have developed an interest in using geopolymer to produce ceramic materials, focusing on improving the performances of geopolymer ceramics. In addition to helping to lower the sintering temperature, it also improves the strength and other properties of the ceramics. Geopolymer is a product of polymerization involving aluminosilicate sources such as fly ash, metakaolin, kaolin, and slag through activation using an alkaline solution. The sources of the raw materials, the ratio of the alkaline solution, the sintering time, the calcining temperature, the mixing time, and the curing time may have significant impacts on the qualities. Therefore, this review aims to study the effects of sintering mechanisms on the crystallization of geopolymer ceramics, concerning the strength achieved. A future research opportunity is also presented in this review. [ABSTRACT FROM AUTHOR]

In this research, free and forced vibration of functionally graded sandwich beams is considered using Timoshenko beam theory which takes into account the significant effects of transverse shear deformation and rotary inertia. The governing equations of motion are formulated from Lagrange's equations and they are solved by using The Ritz and Newmark methods. The results are presented in both tabular and graphical forms to show the effects of layer thickness ratios, boundary conditions, length to height ratios, etc. on natural frequencies and dynamic deflections of the beams. According to the numerical results, all parametric studies considered in this research have significant impact on free and forced behaviour of the beams; for example, the frequency is low and the dynamic deflection is large for the beams which are hinged at both ends.

This study explored the disparities in bending, buckling, and vibration results of ideal and non-ideal functionally graded graphene nanoplatelet reinforced composite (FG-GPLRC) beams. The smooth and continuous profiles of material distributions of ideal FG-GPLRC beams were modified for making the controlling tracks to produce two different forms of non-ideal FG-GPLRC beams which had in-and out-stepwise distributions of material constituents across the beam's thickness. The Halpin–Tsai model and the rule of mixture were used to predict the effective material properties of the nanocomposite beams. The closed-form solution possessing less time of computation was provided for predicting the mechanical behavior of the beams, and it was validated for accuracy by comparing with the results of the Ritz method. The study's results suggest that non-ideal beams with an out-stepwise distribution of material constituents have a better dispersion of reinforcing nanomaterials than in-stepwise distribution. Therefore, the results of the beams with an out-stepwise distribution are closer to those of ideal beams than with in-stepwise distribution. [ABSTRACT FROM AUTHOR]

This study examined the transient or dynamic response of sandwich plates with a functionally graded porous core under the action of time-dependent loads. The plates had two isotropic faces at the top and bottom layers, and the middle layer was made of an open-cell material with functionally graded internal pores. By using the first-order shear deformation theory, the equations of motion used to describe the dynamic behavior of the plates were applied to generate accurate results with less computational effort. To solve the equations of motion, the Ritz method based on the Jacobi polynomials for the admissible displacements, cooperating with the time integration of Newmark, was used to find out the dynamic response of the plates. The results of the numerical experiments revealed that the plates carrying a larger number of internal pores at the middle zone of the core had a great improvement in flexural stiffness, providing less deflection under dynamic loads. The observed results of the plates' dynamic behavior related to the effects of the porosity coefficient, plate's geometrical ratio, dynamic loading types, porous distributions of the core, etc. are shown in the form of graphs and tables, which can be used as a benchmark for future research. [ABSTRACT FROM AUTHOR]

The objective of this study is to apply Gram-Schmidt orthogonalization procedure for generating displacement functions. This procedure allows us to obtain numerically stable functions to be used in vibration analysis of novel composite beams via the Ritz method. Within this study, the theoretical modeling based on third-order shear deformation beam theory is derived to deal with free and forced vibration of functionally graded graphene nanoplatelet-reinforced composite beams subjected to multiple moving loads. To solve the problems of the beams with various end supports, the Ritz method-based Gram-Schmidt polynomial series is adopted to obtain the accurate results. In forced vibration due to the applied multiple moving loads, the time integration technique of Newmark is also employed to find out time history of dynamic deflection of such beams associated with several parametric studies such as patterns of reinforcement, weight fraction of graphene nanoplatelets, and the number of moving loads. According to the numerical results, it is found that the composite beams with low content of graphene nanoplatelets can result in enhancing performance of dynamic bending resistance. Increasing number of moving loads on the beams yields the increases of dynamic deflection and critical velocity. [ABSTRACT FROM AUTHOR]

This paper aims to present accurate solutions for flexural vibration of functionally graded sandwich plates resting on two-parameter elastic foundation with any combined boundary conditions. The governing equations of free vibration problem are derived from the first-order shear deformation theory that covers the important effects of shear deformation and rotary inertia. To solve the coupled differential equations governing vibration behavior of the plates with various boundary conditions, an effective tool, namely Chebyshev collocation method, is implemented to obtain the accurate solutions with several parametric studies. The influences of material volume fraction index, layer thickness ratio, side-to-height ratio, boundary conditions, etc., on natural frequencies of the plates are taken into investigation and discussed in details. Our numerical experiments reveal that the proposed method can offer the accurate frequency results of the plates as compared to those available in the literature. Additionally, the spring constants of elastic foundation have a significant impact on frequency changes of the plates. Increasing the values of spring constants leads to considerable increases of the frequencies. [ABSTRACT FROM AUTHOR]

This paper investigates flexural vibration of functionally graded sandwich microbeams supported by different axially immovable boundary conditions. The governing equations of free vibration problem are based on Timoshenko beam theory and the modified couple stress theory which are taking into account the important effects of shear deformation, rotary inertia and material length scale parameter. To solve the governing equations presented in the forms of coupled differential equations for vibration analysis of the beams with various boundary conditions, an effective tool, namely Chebyshev collocation method, is employed to find out accurate solutions with many important parametric studies. The effects of material volume fraction index, layer thickness ratio, slenderness ratio, boundary condition, temperature rise, etc. on natural frequencies of the beams are taken into account and discussed in details. The numerical results of the beams in ambient temperature and high thermal environment are presented in several tables and figures that can serve as benchmarks for further investigations in the field of FG sandwich microbeam analysis. [ABSTRACT FROM AUTHOR]