Journal of Computational Applied Mechanics
Volume:54 Issue: 2, Jun 2023

The bending attributes of a uniformly-loaded thick plate was modelled with three-dimensional (3-D) elasticity plate theory using exact polynomial displacement function. Plates with free support at its third edge and simply supported at other edges (SSFS), were covered in this study. The effect of shear deformation along with the transverse normal strain stress was considered in this model obviating the coefficients of shear correction. The total potential energy expression was formulated from 3-D kinematic and constitutive relations. The slope and deflection relationship was obtained from the equilibrium equation developed from the energy functional transformation. The solution of the equilibrium equation produced an exact polynomial deflection function while the coefficient of deflection of the plate was formed from the governing equation employing a direct variation approach. The formular for computing the displacement-stress components of the plate was established from these solutions in order to evaluate the bending properties of the plate. The solutions realized herein certifies that the 3D model is exact and consistent compared to refined plate theories applied by previous authors in the available literature. The total average percentage variation of the center deflection values obtained by Onyeka and Okeke, (2020) and Gwarah (2019), is 3.28%. This showed that at 97% confidence level, 3D model is most suitable and safe for analyzing the bending characteristics of thick plates unlike the 2-D RPTs.

This article applies the variational Kantorovich-Vlasov method to obtain exact mathematical solutions to the bending problem of thin plate with two opposite simply supported edges and two free edges. Vlasov method was adopted simultaneously in the variational Kantorovich method, and the deflection function w(x, y) is expressed in variable-separable form as single infinite series in terms of the unknown function g(y) and known sinusoidal functions of x coordinate variable f(x) where f(x) satisfies Dirichlet boundary conditions at the simple supports. The total potential energy functional , expressed in terms of g(y) and the derivatives g(y), g(y) is then minimized with respect to g(y) using the Euler-Lagrange differential equations. The resulting equation of equilibrium is a fourth order inhomogeneous ordinary differential equation (ODE) in g(y). The general solution is found and boundary conditions are enforced to find the integration constants. The expression found for w(x, y) satisfies the governing equations on the domain and the boundaries and is thus exact within the scope of thin plate theory adopted to idealize the plate. Moment-deflection equations are used to obtain exact analytical expressions for the bending moments Mxx, Myy. Deflection and bending moments are computed at the plate center; as well as at the middle of the free edges. Comparison of the plate center deflections and bending moments for various aspect ratios illustrate that the exact solutions by the present work are in the agreement with Levy solutions presented by Timoshenko and Woinnowsky-Krieger and symplectic elasticity solutions presented by Cui Shuang. The present results for bending moments at the free edges for various aspect ratios agree with the Levy results presented by Timoshenko and Woinowsky-Krieger and symplectic elasticity results presented by Cui Shuang.

In this paper, we propose a new technique for solving the magnetic hydrodynamic boundary layer equations after converting them to a nonlinear ordinary differential equation using the appropriate similarity transformation. This technique is based on a combination of the q-homotopy analysis method, the Laplace transform, and the Pade´ approximation, named (q-HALPM). To ensure the method's efficiency, we compared the results of q-HALPM with the ones obtained by methods (DTM-Pade´) and M-HPM . Additionally, the effect of the magnetic parameter on the velocity and heat transfer was studied. The results confirm that the new method has high accuracy and efficiency in finding the approximate analytical solution for the current problem. Moreover, the graphs of the new solutions show the validity and usefulness of the proposed method.

In this article, an analytical technique has been proposed for solving the model of heat and mass transfer in the unsteady squeezing flow between parallel plates. The procedure of combining the Fourier transform and the homotopy perturbation method to yield a new technique was successful. The similarity transformation idea has been used to transform the system of governing partial differential equations into the system of ordinary differential equations. The influence of the physical parameters on the velocity, temperature and concentration with different values are discussed. The numerical results of Nusselt and Sherwood numbers, coefficient of skin friction, were compared with previous published works. The convergence of the new method was also discussed theoretically and experimentally. Furthermore, tables and graphs of the new analytical solutions demonstrate possibility, usefulness to use the new algorithm to deal with many nonlinear problems, especially heat transfer problems.

This paper presents a comprehensive investigation of the optimization process of a ‎‎compliant nano-‎‎positioning mechanism based on a high-accuracy metamodel. Within ‎this ‎study, analytical approach, ‎finite ‎element analysis (FEA), and deep neural network ‎‎(DNN) ‎are integrated in order to achieve the ‎optimum ‎design of a parallel 2-degree-of-‎freedom‎ ‎compliant positioner while taking a broad range of ‎factors into ‎account. First, a ‎linear ‎regression analysis is performed on the primary finite element model ‎as a sensitivity ‎‎analysis. ‎Then an analytical model is established to express one of the objective ‎‎functions of ‎design, ‎namely the mechanism working range, as a function of ‎characteristic features: the ‎‎mechanism stiffness ‎and displacement amplification ratio (λ). ‎In the optimization ‎procedure, a single ‎objective constrained ‎particle swarm optimization ‎‎(SOCPSO) algorithm ‎acts on the metamodel to ‎maximize the resonant ‎frequency and ‎provide the minimum ‎acceptable working range. The proposed ‎optimization guideline is ‎‎established for seven ‎different desired working ranges and succeeded in ‎predicting the ‎objective function ‎with ‎an error of less than 3%. The findings provide insights into the ‎‎design and geometric ‎optimization of the ‎mechanical structures. Furthermore, it will be ‎employed as a ‎guideline ‎for implementing DNN for ‎metamodeling in other engineering ‎problems.‎

In this research, using Harris Hawks optimization method, the gasket- plate heat exchangers is studied with an exergy- economic approach. Six parameters of hot fluid inlet temperature, cold fluid inlet temperature, hot fluid mass flow rate, cold fluid mass flow rate, port diameter and the number of plates were selected as design variables. The ratio of hot fluid mass flow rate to cold fluid mass flow rate, λ, is introduced to the analysis of exergy loss. The results showed that using Harris Hawks optimization method, exergy loss and total cost can be reduced by 70% and 81%, respectively. The optimization results showed that minimizing the exergy loss, the efficiency of the gasket- plate heat exchanger increases by 30%. It is also found that for λ>1, with the increase of cold fluid mass flow rate, the exergy loss number decreases and for λ<1, with the increase of cold fluid mass flow rate, the exergy loss number increases.

Aircraft wing design using Multidisciplinary Design Optimization (MDO) techniques is a complex task that involves different disciplines, mainly aerodynamic and structure. This study develops and explores a coupled aero-structural multidisciplinary model that optimizes the performance of CRJ-700 aircraft, taking into account its path-dependent behavior. Two approaches, namely distributed and monolithic architectures, are available to achieve this aim. The decomposition strategies employed in these architectures differ and can significantly impact the design process. Therefore, comparing these methods can assist designers in understanding the design cost and accuracy of the results obtained. Eventually, optimizing the aircraft problem involved leveraging two methods Multidisciplinary feasible (MDF) and Collaborative optimization (CO). Finally, the results obtained by two approaches; CO gives a high range value; MDF will be converged after 6013 times of the call function; but the number of call functions in the system-level of CO is around 4000 and the average of it for aerodynamic and structure optimizers are around 500 and 20, respectively. The range of the optimum wing of MDF approach raise about 41% and for CO approach raise about 66% compared to the baseline wing ranges.

In this article, free and forced vibration analyses of 3D printed FG sandwich beam based on higher order beam theory is investigated. The core and face sheets of sandwich beam are integrally fabricated by 3D printer. Therefore, ignoring the delamination between face sheets and core is a correct assumption. Three different cells are considered for the core including Re- entrant auxetic cell, anti-tetrachiral auxetic cell and conventional honeycomb cell. These cells are arranged along the thickness of structure based on cell thickness in four various patterns. The effective mechanical properties of cells are estimated by analytical relations. Finite element methods and Lagrange equations are employed for obtaining the effective stiffness and mass matrices of the sandwich beam. Finally, the influences of various parameters including various types of cells, various patterns of cell along the thickness of structure, thickness coefficient, the geometry of cells such as the interior angle and dimensions of cells on natural frequencies and transient deflection of structure have been studied. The results denote that the arrangement of cells along the thickness plays an important role on the vibration response of structure. On the other hand, for uniform thickness distribution of cells, Re –entrant auxetic cell has higher natural frequencies than other cells while in FG arrangements of cells, anti-tetrachiral cell with pattern A has higher natural frequencies than Re-entrant auxetic cell.

The dynamics behavior and stability of axially functionally graded fluid-conveying nanotube is investigated, in this paper. The simultaneous influence of both fluid flow and variation of modulus of elasticity on the behavior of simply–simply supported (S-S) and clamp-clamp (C-C) boundary conditions conveying fluid were studied. Small-scale effects are considered using nonlocal couple stress theory in the solid part and in the fluid part. Based on the nonlocal couple stress theory, Bernoulli-Euler beam theory, and Hamilton’s principle, the governing equation of motion, and associated boundary conditions were derived to explain fluid-structure interaction (FSI). These equations were solved using Galerkin numerical method and temporal differential equation analysis method. The effects of some parameters such as Knudsen number, density, size parameter, and … were investigated. According to the results, it can be seen that the present method has created an equilibrium for the effect of the size parameters (μ, l) on the critical velocity. The higher value of the Knudsen number caused sooner divergence and flutter instabilities to happen. The results show that if the parameters of the size effect are not considered, it causes errors in the calculations. The obtained results confirm the crucial effects of size.

Dental implants are one of the restoration methods used to revitalize the function of a lost tooth. The natural tooth has a unique structure and composition that enable it to withstand mastication loads at different rates and angles of applying load in the wet and warm environment of the mouth. To simulate such behavior, the structure, material, and parameters of the design (implant diameter and length, abutment connection, etc.) in the dental implants are under unremitting study. A favorable dental implant should have sufficient strength and ultimate fatigue life on behalf of minimum displacement. It should be wear-resistant to keep the crown profile on the occlusal surface and remain in touch with other teeth. In the review, the effect of the usage of additive manufacturing on the quality of the 3D printed dental implant parts and important guidelines of design, have been studied and analyzed. Collected results are, based on finite element studies and experimental, empirical, and statistical investigations.