Journal of Computational Applied Mechanics
Volume:55 Issue: 3, Jun 2024

The spacecraft and space shuttles demand novel engineering materials to meet the required properties. This can be accomplished by altering the material properties in more than one direction. The introduction of inplane bidirectional functionally graded materials with porosity are expected to exhibit these properties. This paper presents the buckling analses of inplane bidirectional (2-D) functionally graded porous plates (IBFGPPs) considering uniform porosity distribution in uni-axial and bi-axial compression. The effective modulus of elasticity of the material is varied in in x-and y-axes by employing the rule of mixtures. The higherorder theory used for the study of buckling response meets the nullity requirements at plate’s upper and lower surface and derived the equations of motion thru Lagrange equations. The displacement functions are formulated in simple algebraic polynomials, incorporating admissible functions to satisfy the simply supported conditions in both axial and transverse directions. The components of admissible functions are derived by Pascal’s triangle. Accurateness of this theory is judged by comparing it to existing numerical data in the literature. The effect of thickness ratio’s (a/h), aspect ratio’s (b/a), exponents (ζ_1and ζ_2) in η_1 and η_2-direction, and the porosity on the buckling response of IBFGPPs are examined comprehensively. The numerical findings provided here serve as reference solutions for evaluating diverse plate theories and for comparing them against results obtained through alternative analytical and finite element techniques. From the obtained results, it can be inferred that the proposed theory facilitates the assessing of buckling tendencies of in-plane bi-directional porous FG plates produced through sintering process and could be deemed as a pivotal in the process of optimizing the design of the IBFGPPs.

In this inspection, the control of the magnetic power on the onset of Casson fluid convection formed by purely inner warming in a porous medium layer is examined. The modified Darcy model is employed to designate the rheological arrival of Casson liquid flow in a porous matrix. Two types of thermal boundaries are exploited, namely, type (I) both isothermal and type (II) lower insulated and top isothermal boundaries. Using the linear stability inspection and Galerkin technique, the approximate analytical solution and numerical solution correct to one decimal place are offered. It is detected that for type (I) boundary conditions, the convective wave concentrates in the upper layer if it occurs, whereas for type (II) boundary conditions, it emphases in the whole layer. The magnetic Chandrasekhar number postpones the convection movement while the Casson constraint accelerates it. The facet of the convective cells drops with enhancing the magnetic strength and the Casson constraint. In the absenteeism of magnetic field, the Casson constraint has no regulation on the dimension of convective cells. It is also found that the presented analytical result with two term Galerkin process has overall 5% error, while with one term Galerkin process the error was overall 19%.

Investigating the stability of cylindrical shells made of composite materials is a valuable subject in mechanical engineering due to their plethora of usages across various industries. In the present investigation, the stability behavior of graphene platelets (GPLs) enhanced nanocomposite shells is methodically examined. The calculation of the composite material's properties is conducted by utilizing the modified rule of mixtures approach. Additionally, a first-order shear deformation theory is employed in conjunction with the principle of virtual work to establish the essential differential equations for the analysis. The solution to these equations is achieved by applying Galarkin’s method, which is renowned for its accuracy and efficiency in resolving both static and dynamic problems. Verification of the formulated model is done by comparing the results with existing literature. Novel findings are presented showing the variation in buckling behavior of GPL-reinforced nanocomposite shells for assorted circumferential wave numbers. Moreover, the study delves into the impact of variations in GPLs' weight fraction, length and radius to thickness ratios, and the presence of an elastic medium on the critical buckling loads of these advanced composite shell structures.

This comprehensive study investigates the behavior of functionally graded (FG) nanoplates, providing insights into their characteristics and important design considerations. By examining factors such as homogenization models (Voigt Reuss, LRVE, and Tamura), volume fraction laws (power-law model, Viola-Tornabene four-parameter model, trigonometric model), eigenmode, aspect ratios, index material, and small-scale length parameters, the study evaluates their influence on the natural frequency response of simply supported nanoplates. A novel twisting function is introduced and its accuracy in predicting natural frequencies in FG square nanoplates is rigorously validated through numerical comparisons with existing literature. The findings obtained from this research offer valuable guidance for optimizing the design of FG nanoplates and significantly contribute to advancing our understanding of their dynamics and practical applications.

In this paper, an analytical solution for exploring the buckling characteristics of functionally graded (FG) plate is presented based on a quasi-3D shear deformation theory. It is considered that the plate is subjected to different types of in-plane compressive load. The FG plate is placed on three-parameter foundation Winkler-Pasternak-Kerr. The overall material properties of FG plate are assumed to be varied across the thickness and are estimated through the Voigt micromechanical model. The governing equations are obtained on the base of the quasi-3D deformation theory that contain undetermined integral forms and involves only four unknowns to derive. Equations of motion are derived from the principal of virtual work and the analytical solution is used to determine the critical buckling loads. By the discussion of numerical examples and the comparison with those of the reports in the literature, the convergence and the reliability of the present approach are validated. Finally, the parametric investigations of the in-plane buckling are carried out, including the influence of boundary conditions, elastic foundation, plate geometric parameters and power law index. The results reveal that the critical buckling loads are strongly influenced by several parameters such as boundary conditions, elastic foundation parameters and geometric shape of the plate.

Glycogen Synthase Kinase 3β (GSK3β) is a multifunctional serine/threonine-protein kinase that serves as a pivotal regulator of various human pluripotent stem cell (hPSCs) functions, including self-renewal, adhesion, survival, and differentiation in addition to have an effect on motility of sperm. Despite advancement in understanding the critical roles of GSK3β inhibition in various stem cell functions, the exact molecular basis of its inactivation using various small-molecule inhibitors remains poorly understood. Investigating the mechanistic details of the actions of inhibitors targeting GSK3 proteins, such as CHIR99021, Azakenpaullone, and Tricantin, could be extremely beneficial for improving novel defined stem cell culture systems and cancer research. The present study aimed to predict the binding mode of the aforementioned ligands with GSK3β, by molecular docking and metadynamic simulation, and compare the three-dimensional structure of the inactive conformation of GSK3β in the presence of three inhibitors. Also, the pharmacokinetic or ADMET properties of ligands, such as Lipinski's rule of five violations for drug-likeness, QPlog S, QPlog K, and bioactivity scoring, were predicted. The analysis of protein stability revealed that in the absence of inhibitors, the GSK3β has higher flexibility, while in the presence of CHIR and AZA, the rate of flexibility of most protein regions, especially the envelope area, decreased. It was found that though all small molecules are capable of facilitating the inhibition of GSK3β protein, but the flexibility of protein is a bit higher for CHIR than those for other two ligands.

The study of compressible flow plays a fundamental role in the design of heat exchangers at high temperature and pressure. Compressible flow is used to design the aerodynamic structure, engines, and high-speed vehicles. In view of these utilities, this paper is deliberated to acquire the analysis of the unsteady compressible flow of a viscous fluid through an inclined asymmetric channel with thermal effects. Special attention is paid to convective heat transfer with impact of viscous dissipation, source/sink, and joule heating effects. In addition, thermal flow is analyzed through slip boundary conditions. The current problem is modeled through the laws of energy, momentum, and mass with the help of a fluid’s response towards compression. As a result, the coupled nonlinear partial differential equations are obtained, which are investigated through a well-known numerical approach, the explicit finite difference method. The study examines impact of several parameters on the flow rate, velocity, and temperature with the help of graphical representations. The behavior of flow rate is intended to change with time.

Physical systems frequently exhibit nonlinear behavior that remains unresolved in the majority of cases. In this study, we employ the Aboodh transform-based variational iteration method (ATVIM) to resolve the nonlinear model of a tapered beam. In order to solve the governing equation, the periodic motion is sought, and the explicit relationship between frequency and amplitude is revealed. The outcomes of the ATVIM approach are compared with those of other prevalent techniques, and a satisfactory concordance is observed between them. This study also provides an analytical approximation of the tapered beam for a detailed understanding of the effects of factors on the nonlinear frequency, which can be beneficial to researchers and engineers working on the analysis and design of structural projects.

A novel data-driven control methodology is introduced in this paper, specifically designed for unknown linear time-invariant systems. Schur stability is established through the application of Linear Matrix Inequality (LMI) conditions, and system performance is improved by leveraging the concept of D-stability. Stability and performance are ensured by incorporating LMI features, with reliance solely on a finite set of collected data, eliminating the necessity for system model identification. Hence, the original performance mapping problem undergoes a transformation into a stability issue, incorporating modified system matrices. Then, the stability condition is formulated within the framework of LMI. The effectiveness of our approach is exemplified through two specific examples, highlighting the significant and impactful results obtained. These examples serve to showcase the practical application and outcomes of our methodology within the defined scope, providing a clear demonstration of its performance and efficacy in addressing relevant scenarios.

Multiscale modeling (MM) has broadened its scope to encompass the calculation of mechanical properties, with a particular focus on investigating how the dimensions of single-walled carbon nanotubes (SWCNTs), specifically their diameters, affect the mechanical properties (Longitudinal and Transverse Young’s modulus) of simulated nanocomposites through Molecular Dynamics (MD) simulations. The MD method was employed to construct nanocomposite models comprising five different SWCNTs chiralities: (5, 0), (10, 0), (15, 0), (20, 0), and (25, 0), serving as reinforcements within a common Polymethyl methacrylate (PMMA) matrix. The findings indicate a correlation between the SWCNT diameter increase and enhancements in mechanical and physical properties. Notably, as the diameter of SWCNTs increases, the density, Longitudinal Young’s modulus, Transvers Young’s Shear modulus, Poisson’s ratio, and Bulk modulus of the simulated nanocomposite transition from (5, 0) to (25, 0) by approximately 1.54, 3, 2, 1.43, 1.11, and 1.75 times, respectively. To corroborate these results, stiffness matrices were derived using Materials Studio soft ware.

The aim of the present work is to use the spectral method to plot the dispersion curves of ultrasonic guided waves in anisotropic pipelines. We begin by describing the mathematical formulation of the problem, followed by the application of the spectral method algorithm to plot these curves, covering different levels of anisotropy to test the robustness of the method to various mechanical behaviors. Particular attention is paid to complex modes, poorly studied in the pipeline literature. Results are compared with analytical solutions, and computation time and coding effort are also compared with those of previous analytical methods. These studies demonstrate the significant advantage of the spectral method in terms of accuracy efficiency and computational time savings for plotting the dispersion curves of complex modes in anisotropic pipelines.

Sandwich structures are composites comprising a core layer sandwiched between two face layers; each layer has a distinctive characteristic, and the structure can also include composite layers. This study presents an investigation of the free vibration behavior of a cored hybrid sandwich plate. The research demonstrates an analytical and numerical analysis. Sandwich plate models made of aluminum face sheets with reinforced cores are used in this study. The analytical analysis used in this study of a three-layer sandwich plate is based on Kirchhoff's theorem. An additional mathematical model is constructed by dividing the core layer into two parts to form four layers with a hybrid structure. The governing equations to obtain the mechanical properties and natural frequency of the foam composite, as well as open structural and hybrid cores, were used in this study. The numerical analysis of the various composite structures using the modal analysis was performed through ANSYS version 2021-R1. Analytical outcomes reveal that replacing the foam core with an open-cell structure reduces the natural frequency by 25%. However, the hybrid core structure reduces the natural frequency by 27.6%. Also, the ultimate flexural load in the hybrid structure is increased by 127.7% compared to the open-cell structure core. Finally, numerical results are highly consistent with those obtained analytically.

In a delayed master-slave teleoperation system, if the slave robot interacts with a delicate and sensitive environment, it is essential to control the slave-environment interactions. Variable impedance control has been proposed as a useful method for this aim in the literature. However, changing the impedance parameters based on the system requirements imposes a complex process in the controller design. To address this issue, we propose a variable impedance control strategy for the slave side, where the impedance variables are changed using fuzzy logic. This is carried out based on the environment destruction threshold—defined based on the contact force and the velocity of the slave robot—and system stability range. The proposed method is simulated in MATLAB’s Simulink considering telesurgery conditions and soft tissue environment under an unknown and varying time delay. Simulation results show that the proposed method maintains the velocity of the slave robot and the environment force in the desired interval and performs better in keeping the environment safe compared to the constant-coefficient impedance control.

In this paper a quasi-three-dimensional (3D) refined using a novel higher-order shear deformation theory is developed to examine the static bending with two different type porosity distribution of porous for advanced composite plates such as functionally graded plates. In this present theory, the number of unknowns and governing equations is reduced, takes into account the thickness stretching effect into transverse displacement, bending and shear, using a new shape function. The used plate theory approach satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor and the transverse shear strain and shear stress have a parabolic distribution across the thickness of the plates. The virtual work principle is used to obtain the equilibrium equations. An analytical approach based on the Navier solution is employed to obtain the solution for static bending of simply supported FGM plates. The proposed theory shows a good agreement for static bending of FGM plates with other literature results has been instituted of advanced composite plates. Numerical results are presented to show the effect of the material distribution, the power-law FG plates, the geometrical parameters and the porosity on the deflections and stresses of FG plates.

Determining the elastic constants for composites with fibers is a continuous concern of researchers, being studied and analyzed different types of materials, with different topologies and geometries. In the work, these constants are determined for a composite reinforced with cylindrical fibers with a rectangular packing. The obtained results are applied for the calculation of these constants for a composite used in engineering applications.