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The purpose of this paper is concerned with the study of nonlinear ultrasonic waves in a magneto-flexo-thermo (MFT) elastic armchair single-walled carbon nanotube (ASWCNT) resting on polymer matrix.

A mathematical model is developed for the analytical study of nonlinear ultrasonic waves in a MFT elastic armchair single walled carbon nanotube rested on polymer matrix using Euler beam theory. The analytical formulation is developed based on Eringen’s nonlocal elasticity theory to account small scale effect. After developing the formal solution of the mathematical model consisting of partial differential equations, the frequency equations have been analysed numerically by using the nonlinear foundations supported by Winkler-Pasternak model. The solution is obtained by ultrasonic wave dispersion relations.

From the literature survey, it is evident that the analytical formulation of nonlinear ultrasonic waves in an MFT elastic ASWCNT embedded on polymer matrix is not discussed by any researchers. So, in this paper the analytical solutions of nonlinear ultrasonic waves in an MFT elastic ASWCNT embedded on polymer matrix are studied. Parametric studies is carried out to scrutinize the influence of the nonlocal scaling, magneto-electro-mechanical loadings, foundation parameters, various boundary condition and length on the dimensionless frequency of nanotube. It is noticed that the boundary conditions, nonlocal parameter and tube geometrical parameters have significant effects on dimensionless frequency of nanotubes.

This paper contributes the analytical model to find the solution of nonlinear ultrasonic waves in an MFT elastic ASWCNT embedded on polymer matrix. It is observed that the increase in the foundation constants raises the stiffness of the medium and the structure is able to attain higher frequency once the edge condition is C-C followed by S-S. Further, it is noticed that the natural frequency is arrived below 1% in both local and nonlocal boundary conditions in the presence of temperature coefficients. Also, it is found that the density and Poisson ratio variation affects the natural frequency with below 2%. The results presented in this study can provide mechanism for the study and design of the nano devices such as component of nano oscillators, micro wave absorbing, nano-electron technology and nano-electro--magneto-mechanical systems that make use of the wave propagation properties of ASWCNTs embedded on polymer matrix.

The purpose of this study is to investigate the post-buckling analysis of functionally graded columns by using three analytical, approximate and numerical methods. A pre-defined function as an initial assumption for the post-buckling path is introduced to solve the differential equation. The finite difference method is used to approximate the lateral deflection of the column based on the differential equation. Moreover, the finite element method is used to derive the tangent stiffness matrix of the column.

The non-linear buckling analysis of functionally graded materials is carried out by using three analytical, finite difference and finite element methods. The elastic deformation and Euler-Bernoulli beam theory are considered to establish the constitutive and kinematics relations, respectively. The governing differential equation of the post-buckling problem is derived through the energy method and the calculus variation.

An incremental iterative solution and the perturbation of the displacement vector at the critical buckling point are performed to determine the post-buckling path. The convergence of the finite element results and the effects of geometric and material characteristics on the post-buckling path are investigated.

The key point of the research is to compare three methods and to detect error sources by considering the derivation process of relations. This comparison shows that a non-incremental solution in the analytical and finite difference methods and an initial assumption in the analytical method lead to an error in results. However, the post-buckling path in the finite element method is traced by the updated tangent stiffness matrix in each load step without any initial limitation.

The properties of materials under impact load are introduced in terms of metal, nonmetallic materials and composite materials. And the application of impact load research in biological fields is also mentioned. The current hot research topics and achievements in this field are summarized. In addition, some problems in theoretical modeling and testing of the mechanical properties of materials are discussed.

The situation of materials under impact load is of great significance to show the mechanical performance. The performance of various materials under impact load is different, and there are many research methods. It is affected by some kinds of factors, such as the temperature, the gap and the speed of load.

The research on mechanical properties of materials under impact load has the characteristics as fellow. It is difficult to build the theoretical model, verify by experiment and analyze the data accumulation.

This review provides a reference for further study of material properties.

The purpose of this article is to analyze the optimization process in depth, elaborating on the components of the entire process and the techniques used. Researchers have been drawn to the expanding trend of optimization since the turn of the century. The rate of research can be used to measure the progress and increase of this optimization procedure. This study is phenomenal to understand the optimization process and different algorithms in addition to their application by keeping in mind the current computational power that has increased the implementation for several engineering applications.

Two-dimensional analysis has been carried out for the optimization process and its approaches to addressing optimization problems, i.e. computational power has increased the implementation. The first section focuses on a thorough examination of the optimization process, its objectives and the development of processes. Second, techniques of the optimization process have been evaluated, as well as some new ones that have emerged to overcome the above-mentioned problems.

This paper provided detailed knowledge of optimization, several approaches and their applications in civil engineering, i.e. structural, geotechnical, hydraulic, transportation and many more. This research provided tremendous emerging techniques, where the lack of exploratory studies is to be approached soon.

Optimization processes have been studied for a very long time, in engineering, but the current computational power has increased the implementation for several engineering applications. Besides that, different techniques and their prediction modes often require high computational strength, such parameters can be mitigated with the use of different techniques to reduce computational cost and increase accuracy.

This article aims to study the tensile properties of a functionally graded composite structure with Al–18wt%Si alloy as the matrix material and silicon carbide (SiC) particles as the reinforcing element. More specifically, the study's primary objective is to optimize the composition of the material elements using a robust statistical approach.

In this research, the composite material is fabricated using a combination of stir casting and the centrifugal casting technique. Moreover, the test specimen required to study the tensile strength are prepared according to the ASTM (American Society for Testing and Materials) standards. Eventually, optimal composition to maximize the tensile property of the material is determined using the mixture design approach.

The investigation results imply that the addition of the SiC plays a crucial role in increasing the tensile strength of the composite. The optical microstructural images of the composite show the adequate distribution of the reinforcing particles with the matrix. The proposed regression model shows better predictability of tensile strength. In addition, the methodology aids in optimizing the mixture component values to maximize the tensile strength of the produced functionally graded composite structure.

Little work has been reported so far where a hypereutectic Al–Si alloy is considered the matrix material to produce the composite structure. The article attempts to make a composite structure by using a combination of stir casting and centrifugal casting. Furthermore, it employs the mixture design to optimize the composition and predict the model of the study, which is one of a kind in the field of material science.