Journal of Computational Applied Mechanics
Volume:54 Issue: 1, Mar 2023

A polynomial displacement function was applied with three-dimensional (3-D) elasticity theory to solve the bending problem of isotropic rectangular thick plate that is simply-supported at the first and fourth edges, clamped and free on the second-third edges (SCFS). In the analysis, the model addressed the effect of shear deformation as well as the transverse normal strain-stress, obviating the coefficients of shear correction. The 3-D kinematic and constitutive relations were used to formulate the total potential energy expression, thereafter, the equilibrium equation developed from the energy functional transformation was used to get the relationship for slope and deflection. The solution of the equilibrium equation birthed the exact polynomial deflection function while the coefficient of deflection of the plate was produced from the governing equation using direct variation approach. These solutions were employed to analyze the bending characteristics of the SCFS rectangular plate by establishing the expression for calculating the displacement and stresses of the plate. The outcome of this study certifies that solutions from 3D model is exact and safe compared to refined plate theories applied by previous authors. Compared with the 3-D plate analysis, the percentage differences presented are as close as 2.9% and 3.7% for all span-to-thickness ratios. The comprehensive average percentage variation of the center deflection values obtained by Onyeka et al., (2020) and Gwarah (2019), is 0.39%. This revealed that at the 99.7 % confidence level, the 3-D plate theory is most suitable and reliable for studying the bending characteristics of thick plates.

In this paper, a new approach is proposed for the couple stress analysis of micro-beams. As the main assumption, power series expansions are assumed for the axial displacement. The lateral and transverse displacements are adopted according to the classical beam theories. It is demonstrated that this consideration imposes a decisive constraint of skew-symmetry on the couple-stress tensor. So, in the case of micro-beams, there is no need for referring to the main arguments in modified couple stress theory (M-CST). This approach also allows for revising the conventional boundary conditions in couple stress analysis of micro-beams. For the special case of Timoshenko micro-beams, the axial displacement is approximated by a first-order polynomial and a new set of boundary conditions similar to the classical model is developed. Benchmark problems are then considered for demonstrating the advantages of the proposed model.

An analysis is carried out on the natural or free convective magnetohydrodynamic flow of a non-Newtonian Jeffrey fluid with a Hall current, heat source, and variable suction near vertical plate.Using a flexible, widely validated variable finite element method, the governing nonlinear partial differential equations be transformed into linear partial differential equations using similarity variables, and this equations along with the associated boundary conditions be then solved numerically.The fluctuation of important parameters in the thermal and hydrodynamic boundary layers be thoroughly examined, and the findings are displayed visually. Additionally, a comparison study is offered to reduce verification and arrive at a excellent consensus. This model is beneficial for geothermal reservoirs, subterranean power transmission, MHD pumps, accelerators, and flow metres, as well as industrial heat management, geological flows within mud cover, etc.

Pores have a significant impact on the properties of functionally graded materials. Many other features can be added if the distribution of pores are allowed to progressively increase from the surface into the inside. The bending response on a Functionally graded porous beam (FGPB) is analysed by adopting a unique shear shape function and taking into consideration even and uneven porosity distributions. Material properties of FGPBs with even and uneven porosity distributions along the length and thickness directions are changed using power law. When formulating equilibrium equations for FGPB, principle of virtual displacements is put to use. The method developed by Navier is applied in order to provide solutions to porous FGPB for simply supported boundary conditions and applied to clamped-clamped and clamped-free boundary conditions. Proposed methodology is justified with numerical findings of non-porous and porous FGPBs that are from earlier research. Exponents, porosity, volume fraction, thickness ratios, and aspect ratios are factors that have an influence on the dimensionless deflections and stresses that are being researched.

In this article, shear buckling analysis of functionally graded porous annular sector plate reinforced with graphene nanoplatelets (GPLs) are investigated for the first time. The plate is consisting of a layered model with uniform or non-uniform dispersion of graphene platelets in a metallic matrix including open-cell interior pores. The extended rule of mixture and the modified Halpin-Tsai models and are employed to obtain the effective mechanical properties of the porous nanocomposite plate. Three different porosity distributions in conjunction with five patterns for dispersion of GPL nanofiller are considered through the thickness of plate. Governing equations derived according to the principle of minimum total potential energy based on 3D elasticity theory and generalized geometric stiffness concept. Finally, finite element method is applied for solving the governing equations of structure. The influence of different parameters including various porosity distribution, porosity coefficient, patterns of GPL dispersion, weight fraction of GPL nanofiller, boundary conditions and sector angles on shear buckling loads of the annular sector plate has been surveyed.

This paper presents a novel and low-cost formula based on the first-order shear deformation theory and Eringen’s nonlocal elasticity theory for the stability analysis of tapered Timoshenko nanobeams with axially varying materials. The coupled governing differential equations of the problem, involving both the transverse displacements and rotations, stem from the energy method. Based on a mathematical manipulation, the system of equilibrium equations is converted to a novel single fifth-order differential equation with variable coefficients in terms of the vertical deflection, which is solved numerically to obtain the axial buckling load. The accuracy of the proposed formulation is first verified against the available literature, with the additional advantage related to its reduced computational effort, compared to other formulations. A systematic investigation is, thus, performed to check for the influence of the non-local parameter, power-law index, tapering ratio and length-to-thickness aspect ratio on the linear buckling strength of simply supported functionally graded nano-tapered Timoshenko beams. Due to the generality of the derived formula, it can be adjusted for the optimal design of Timoshenko nanobeams with favorable axial changes in material properties as well as the geometrical features.

The purpose of the present study is to observe when suction/injection is present, effects of thermophoresis and Brownian motion, emphasises the combined influence of convective heat radiation and the magnetic field nanofluid flow in the direction of a permeable stretched sheet. The Rosseland approximation is used to explain the radiative heat flux in the heat convective analysis. Hypersonic flight, power plants and vehicles, gas turbines and reactors of nuclear power, and the modelling of relevant equipment, among other applications, applicable from radiative heat transfer. The boundary wall is designed into account for stretching and suction/injection circumstances. In order to simplify the dimensionless version of fundamental governing equations, the governing nonlinear partial differential equations (PDEs) are changed to ordinary differential equations (ODEs) by using transformations of similarity.In the final numerical result version of fundamental equations is simplified through the use of the numerical approach of the shooting technique by the Runge-Kutta method and a shooting scheme. Graphical data demonstrations are in order to study the effect on dissimilar physical constraints, such as velocity, temperature, and concentration of surrounding environment the numerical data is also used to look into changing trends in rates of coefficient of skin friction, mass and heat transfer. Additionally in which proposed model is validated is by making comparisons to an isolated instance of a previously researched issue.

Landslides are a common geological hazard that can cause harm to human lives and property. Effective measures are necessary to prevent landslides and reduce their impact. This study investigates the effectiveness of micropiles in stabilizing a soil slope against landslides. The researchers used a computer simulation based on an example from the Plaxis software manual to model the soil slope. The simulation results showed that the safety factor, a measure of the stability of the slope, was 9% higher in the 3D model than in the 2D model when all three rows of nails were applied. In the 3D model of the soil slope, the researchers suggested using a pattern of steel pipes as micropiles to increase the safety factor of the slope and prevent landslides. It was found that a simple arrangement of steel pipes in the middle of the slope was able to stabilize the slope and result in the same level of stability as all three rows of nails. The results showed that this micropile system could be used as a low-cost and easily implementable alternative method for stabilizing soil slopes. The system is a fast and efficient way to prevent landslides, making it a potentially valuable option for those seeking to reduce the risk of landslides.

Biomechanical simulation and analysis of human organs are of paramount importance for improving the treatment and prevention of a variety of disorders and injuries. One of the organs that is very prone to injuries, especially among athletes and active individuals, is the foot. However, these injuries can be well-prevented by numerical modeling and analysis of the foot in different conditions. In the current study, after constructing a detailed parametric finite element (FE) model of the foot and ankle complex, a surrogate-based sensitivity analysis is performed to evaluate how the material and geometric properties of the bones, the ligaments, the soft tissue, and the skin affect the natural frequencies of the FE model. Based on the obtained results, Young’s modulus and the density of the cortical bone, the trabecular bone and the soft tissue have considerable effects on the natural frequencies. Also, Poisson’s ratio of the soft tissue and the thickness of the skin have significantly larger sensitivity indices compared to those of other similar parameters. The cross-sectional area of the fascia plantar also plays a more important role in the natural frequencies compared to those of other ligaments. These results are preliminary good indicators to rank the material and geometrical parameters based on their effects on the natural frequencies of the FE model.

In this paper, the effect of impactor shape and type of porcelain layer on the surface of composite sandwich panels under the impact of drop weight has been investigated. The core of the sandwich plate is A356 aluminum foam reinforced with SiC particles produced by fusion method using CaCO3 foaming agent. The surface of the plates is made of epoxy glass with a quasi-isotropic, orthogonal porcelain layer and also a pure aluminum layer is used. For the impact test, the drop weight impact device was used and to investigate the effect of the impactor shape spherical, parabolic and cone impactor manufactured. Some of the effective parameters in evaluating the behavior of materials at impact load including maximum impact force, maximum displacement and the amount of specific energy absorbed by the plate for different situations are compared with each other. The results indicate that the greater the radius of curvature of the impactor, the greater the maximum impact force. Also, plates with quasi-isotropic composite surface have the highest adsorbed energy and plate with aluminum surface has the lowest amount of adsorbed energy. The orthogonal surface performs better in terms of maximum impact force and maximum center displacement. Therefore, depending on the use of sandwich panels, the use of composite surfaces (quasi-isotropic or orthogonal) instead of aluminum in the design of energy-absorbing structures was recommended.