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The global methods of generalized differential quadrature (GDQ) and generalized integral quadrature (GIQ) are applied to solve three‐dimensional, incompressible, laminar boundary layer equations. The streamwise and crosswise velocity components are taken as the dependent variables. The normal velocity is obtained by integrating the continuity equation along the normal direction where the integral is approximated by GIQ approach with high order of accuracy. All the spatial derivatives are discretized by a GDQ scheme. After spatial discretization, the resultant ordinary differential equations are solved by the 4‐stage Runge—Katta scheme. Application of GDQ—GIQ approach to a test problem demonstrated that accurate numerical results can be obtained using just a few grid points.

The multi‐domain generalized differential quadrature method is applied in this paper to simulate the flows in Czochralski crystal growth. The effect of interface treatment on the numerical solution is studied through four types of interface approximations. The performance of those four interface approximations is validated by a benchmark problem suggested by Wheeler. It is demonstrated in this study that the multi‐domain GDQ approach is an efficient method which can obtain accurate numerical solutions by using very few grid points, and the overlapped interface approximation provides the most accurate numerical results.

This study aims to demonstrate the numerical application of differential quadrature (DQ) methods and show the experimental application of free vibration analysis of fiber-metal laminated composite (FML) plates with various boundary conditions.

The FMLs are hybrid structures consisting of fiber-reinforced polymer matrix composites such as carbon, glass, aramid and different metal sheets, and are currently widely used in the automobile, aircraft and aerospace industries. Thus, free vibration analysis of these hybrid materials is necessary for the design process. The governing equations of motion are derived based on the classical plate theory. The DQ, generalized DQ (GDQ) and harmonic DQ (HDQ) differential quadrature methods have been used to solve the governing equations of an FML composite plate numerically. The accuracy and convergence of the numerical model have been verified by comparing the results available in the published literature with the results obtained from these methods. Moreover, an experimental procedure has been performed in order to compare the results against those of the numerical methods.

It is noteworthy that a high degree of similarity and accuracy was observed between the numerical results obtained by the DQ methods and the experimental results. Thus, the present study validates the applicability of the DQ methods for designing the FML composite plates.

In this study, the advantages of the DQ methods have been demonstrated differently from previous studies on the vibration analysis of the FML plates.

The purpose of this work is to apply the Fourier–Ritz method to study the vibration behavior of the moderately thick functionally graded (FG) parabolic and circular panels and shells of revolution with general boundary conditions.

The modified Fourier series is chosen as the basis function of the admissible functions of the structure to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges, and the vibration behavior is solved by means of the Ritz method. The complete shells of revolution can be achieved by using the coupling spring technique to imitate the kinematic compatibility and physical compatibility conditions of FG parabolic and circular panels at the common meridian of θ = 0 and 2π. The convergence and accuracy of the present method are verified by other contributors.

Some new results of FG panels and shells with elastic restraints, as well as different geometric and material parameters, are presented and the effects of the elastic restraint parameters, power-law exponent, circumference angle and power-law distributions on the free vibration characteristic of the panels are also presented, which can be served as benchmark data for the designers and engineers to avoid the unpleasant, inefficient and structurally damaging resonant.

The paper could provide the reference for the research about the moderately thick FG parabolic and circular panels and shells of revolution with general boundary conditions. In addition, the change of the boundary conditions can be easily achieved by just varying the stiffness of the boundary restraining springs along all the edges of panels without making any changes in the solution procedure.

This paper aims to numerically investigate the two-dimensional unsteady laminar magnetohydrodynamic bioconvection flow and heat transfer of an electrically conducting non-Newtonian Casson thin film with uniform thickness over a horizontal elastic sheet emerging from a slit in the presence of viscous dissipation. The composite effects of variable heat, mass, nanoparticle volume fraction and gyrotactic micro-organism flux are considered as is hydrodynamic (wall) slip. The Buongiorno nanoscale model is deployed which features Brownian motion and thermophoresis effects. The model studies the manufacturing fluid dynamics of smart magnetic bio-nano-polymer coatings.

The coupled non-linear partial differential boundary-layer equations governing the flow, heat and nano-particle and micro-organism mass transfer are reduced to a set of coupled non-dimensional equations using the appropriate transformations and then solved as an nonlinear boundary value problem with the semi-numerical Liao homotopy analysis method (HAM).Validation with a generalized differential quadrature (GDQ) numerical technique is included.

An increase in velocity slip results in a significant decrement in skin friction coefficient and Sherwood number, whereas it generates a substantial enhancement in Nusselt number and motile micro-organism number density. The computations reveal that the bioconvection Schmidt number decreases the micro-organism concentration and boundary-layer thickness which is attributable to a rise in viscous diffusion rate. Increasing bioconvection Péclet number substantially elevates the temperatures in the regime, thermal boundary layer thickness, nanoparticle concentration values and nano-particle species boundary layer thickness. The computations demonstrate the excellent versatility of HAM and GDQ in solving nonlinear multi-physical nano-bioconvection flows in thermal sciences and furthermore are relevant to application in the synthesis of smart biopolymers, microbial fuel cell coatings, etc.

The numerical study is valid for two-dimensional, unsteady, laminar Casson film flow with nanoparticles over an elastic sheet in presence of variable heat, mass and nanoparticle volume fraction flux. The film has uniform thickness and flow is transpiring from slit which is fixed at origin.

The study has significant applications in the manufacturing dynamics of nano-bio-polymers and the magnetic field control of materials processing systems. Furthermore, it is relevant to application in the synthesis of smart biopolymers, microbial fuel cell coatings, etc.

The originality of the study is to address the simultaneous effects of unsteady and variable surface fluxes on Casson nanofluid transport of gyrotactic bio-convection thin film over a stretching sheet in the presence of a transverse magnetic field. Validation of HAM with a GDQ numerical technique is included. The present numerical approaches (HAM and GDQ) offer excellent promise in simulating such multi-physical problems of interest in thermal thin film rheological fluid dynamics.

The purpose of this paper is to extend the social loafing literature by investigating the role of group development process on perceptions of social loafing within groups. Building on extant literature, it is contended that group members’ association with the group development stages can help in predicting their perceptions of social loafing.

Using a cross-sectional survey data were collected from 164 individuals nested in 39 groups. Mixed-effect modeling in R was unitized to test the proposed hypotheses.

Results of mixed-effect modeling in R show that group development stage of inclusion and dependency (stage 1) has no significant effect on perceptions of social loafing. Whereas, group development stage of counterdependency and fight (stage 2) has positive, and trust and structure (stage 3) and work (stage 4) has negative effect on perception of social loafing by group members.

This study investigates unique relationships between group members’ association with different stages of group development and their perceptions of social loafing. Additionally, a newer, shorter and cost-effective scale to measure four stages of group development is developed.

The purpose of this paper is to study tilt angle effects as design parameters of noncircular bearings, on the linear dynamic analyses of micropolar lubricated circular, two, three and four lobe journal bearings.

Reynolds equation in dynamic state is modified considering the micropolarity characteristics of lubricant, and it is solved using generalized differential quadrature method. The perturbed components of the dynamic pressure are extracted based on the linear dynamic model. To explain the transient state of the governing equation, through the linear dynamic approach, the whirling motion of rotor around the steady state position is assumed to be harmonic.

It is observed from the results that tilt angle has significant effects on the steady state and stability performance of lobed journal bearings. It may be selected suitably to improve the performance of rotor-bearing system, while all other lubricant properties and noncircular bearing design parameters are kept fixed. Results show that among the three types of bearings considered, the dynamic performance of two lobe bearings are more affected by the variation of tilt angle.

The present study is mainly concerned with the effects of tilt angle as a design parameter on the stability performance of a hydrodynamic noncircular journal bearing lubricated with micropolar fluid.

The purpose of this study is to examine the thermo-hydrodynamic performance of tilted non-circular journal bearings lubricated with a micropolar fluid. The investigated bearing types are two- and three-lobe journal bearings with finite length.

For this purpose, modified Reynolds, energy and three-dimensional Laplace equations are solved numerically by using generalized differential quadrature method. The effects of micropolarity characteristics of lubricants, such as characteristic length and coupling number, as well as tilt angle as a design parameter, on the performance of non-circular two- and three-lobe journal bearings are studied.

The results show that the tilt angle can affect the temperature and pressure profiles causing variation in the performance of non-circular bearings. Increasing coupling number and decreasing characteristic length cause the load-carrying capacity to decrease because of the increase in maximum oil temperature of the fluid film of lubricant and decrease in the minimum oil base viscosity. So, it is possible to select suitable values of tilt angle for achieving optimum performance of these bearings.

The non-circular bearings suggest several design parameters such as tilt angle for designers. By considering thermal effects for micropolar lubricant, the requirements of a specific application can be fulfilled.

The purpose of this paper is to parametrically investigate the vibration and damping characteristics of a functionally graded (FG) inhomogeneous and porous curved sandwich beam with a frequency-dependent viscoelastic core.

The FG material properties in this study are assumed to vary through the beam thickness by power law distribution. Additionally, FG layers have porosities, which are analyzed individually in terms of even and uneven distributions. First, the equations of motion for the free vibration of the FG curved sandwich beam were derived by Hamilton's principle. Then, the generalized differential quadrature method (GDQM) was used to solve the resulting equations in the frequency domain. Validation of the proposed FG curved beam model and the reliability of the GDQ solution was provided via comparison with the results that already exist in the literature.

A series of studies are carried out to understand the effects on the natural frequencies and modal loss factors of system parameters, i.e. beam thickness, porosity distribution, power law exponent and curvature on the vibration characteristics of an FG curved sandwich beam with a ten-parameter fractional derivative viscoelastic core material model.

This paper focuses on the vibration and damping characteristics of FG inhomogeneous and porous curved sandwich beam with frequency dependent viscoelastic core by GDQM – for the first time, to the best of the authors' knowledge. Moreover, it serves as a reference for future studies, especially as it shows that the effect of porosity distribution on the modal loss factor needs further investigation. GDQM can be useful in dynamic analysis of sandwich structures used in aerospace, automobile, marine and civil engineering applications.

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.