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The purpose of this paper is to present an efficient return mapping algorithm for elastoplastic constitutive problems of ductile metals with an exact closed form solution of the local constitutive problem in the small strain regime. A Newton Raphson iterative method is adopted for the solution of the boundary value problem.

An efficient return mapping algorithm is illustrated which is based on an elastic predictor and a plastic corrector scheme resulting in an implicit and accurate numerical integration method. Nonlinear kinematic hardening rules and linear isotropic hardening rules are used to describe the components of the hardening variables. In the adopted algorithmic approach the solution of the local constitutive equations reduces to only one straightforward nonlinear scalar equation.

The presented algorithmic scheme naturally leads to a particularly simple form of the nonlinear scalar equation which ultimately scales down to an algebraic (polynomial) equation with a single variable. The straightforwardness of the present approach allows to find the analytical solution of the algebraic equation in a closed form. Further, the consistent tangent operator is derived as associated with the proposed algorithmic scheme and it is shown that the proposed computational procedure ensures a quadratic rate of asymptotic convergence when used with a Newton Raphson iterative method for the global solution procedure.

In the present approach the solution of the algebraic nonlinear equation is found in a closed form and accordingly no iterative method is required to solve the problem of the local constitutive equations. The computational procedure ensures a quadratic rate of asymptotic convergence for the global solution procedure typical of computationally efficient solution schemes. In the paper it is shown that the proposed algorithmic scheme provides an efficient and robust computational solution procedure for elastoplasticity boundary value problems. Numerical examples and computational results are reported which illustrate the effectiveness and robustness of the adopted integration algorithm for the finite element analysis of elastoplastic structures also under elaborate loading conditions.

There exists a clear paucity of models for curved bi-directional functionally graded (BDFG) beams wherein the material properties vary along the axis and thickness of the beam simultaneously; such structures may help fulfil practical design requirements of the future and improve structural efficiency. In this context, the purpose of this paper is to extend the analytical model developed earlier to thick BDFG circular beams by using first-order shear deformation theory which allows for a non-zero shear strain distribution through the thickness of the beam.

Smooth functional variations of the material properties have been assumed along the axis and thickness of the beam simultaneously. The governing equations developed have been solved analytically for some representative determinate circular beams. In order to ascertain the effects of shear deformation in these structures, the total strain energy has been decomposed into its bending and shear components and the effects of the beam thickness and the arch angle on the shear energy component have been studied.

Closed-form exact solutions involving through-the-thickness integrals carried out numerically are presented for the bending of circular beams under the action of a variety of concentrated/distributed loads.

The results clearly indicate the importance of capturing shear deformation in thick BDFG beams and demonstrate the capability of tuning the response of these beams to fit a wide variety of structural requirements.

In Simo and Taylor, the classical radial return algorithm of Wilkins and Krieg and Key for plane strain and three‐dimensional J2‐flow theory, is extended to the case of plane stress. In three dimensions (or plane strain), enforcement of the discrete consistency condition reduces to a simple radial scaling of the trial stress onto the yield surface; i.e., the return map is radial. In plane stress, on the other hand, the return map, that restores the trial stress back to the yield surface, is constrained to remain in the plane stress subspace, and thus no longer reduces to a simple radial scaling. The determination of the final stress point from the trial stress now involves the solution by Newton's method of a non‐linear scalar equation, referred to as the discrete consistency equation in what follows, that yields the discrete consistency parameter λn+>0. The requirement that λn+>1 be positive is a direct consequence of the discrete Kuhn‐Tucker optimality conditions.

This work aims to investigates exact solutions of the classical Glauert’s laminar wall jet mass and heat transfer under wall suction, wall contraction or dilation, and two thermal transport boundary conditions; prescribed constant surface temperature and prescribed constant surface flux in nanofluidic environment.

The flow system arranged in terms of partial dif- ferential equations is non-dimensionalized with suitable dimensionless transformation variables, and this new set of equations is reduced into ordinary differential equations via a set of similarity transformations, where they are treated analytically for closed form solutions.

Exact solutions of nanofluid flow for velocity distributions, momentum flux, wall shear stress and heat transfer boundary layers for commonly studied nanoparticles; namely copper, alumina, silver, and titanium oxide are presented. The flow behavior of alumina and titanium oxide is identical, and a similar behavior is seen for copper and silver, making two pairs of identical traits. The mathematical expressions as well as visual analysis of wall shear drag and temperature gradient which are of practical interest are analyzed. It is shown that wall stretching or shrinking, wall transpiration and velocity slip together influences the jet flow mechanism and extends the original Glauert’s jet solutions. The exact solutions for the two temperature boundary layer conditions and temperature gradients are analyzed analytically. It is found that the effect of nanopar- ticles concentration on thermal boundary layer is intense, causing temperature uplift, whereas the wall transpiration causes a decrease in thermal layers.

The analysis carried out in nanofluid environment is genuinely new and unique, as our work generalizes the Glauert’s classical regular wall jet fluid problem.

The purpose of this paper is to investigate the buckling strength of simply supported plates with mechanical extension-twisting coupling. Bounds of the compression buckling strength are presented for a special sub-class of extension-twisting coupled laminate that is free from the thermal distortions that generally arise in this class of coupled laminate as a result of the high temperature curing process. These special laminates are generally referred to as hygro-thermally curvature-stable (HTCS).

This paper gives an overview of the methodology for developing laminates with extension-twisting coupling properties, which are derived from a parent laminate with HTCS properties. A closed form buckling solution is applicable for this special class of coupled laminate, which facilitates an assessment of compression buckling strength performance for the entire laminate design space.

Extension-twisting coupled laminates have potential applications in the design of aero-elastic compliant rotor blades, where the speed of the rotating blade, and the resulting centrifugal force, can be used to control blade twist. Extension-twisting coupling reduces the compression buckling performance of the blade, which represents an important static design constraint. However, the performance has been shown to be higher than competing designs with extension-shearing coupling in many cases.

Bounds of the buckling curves have been presented for the entire HTCS laminate design space, possessing extension-twisting and shearing-bending coupling, in which the laminates contain standard ply angle orientations and up to 21 plies. These laminates can be manufactured without the undesirable thermal warping distortions that generally affect this class of coupled laminate, and in particular, those containing angle plies only; previously thought to be the only form of laminate design from which this particular type of mechanical coupling can be derived.

The purpose of this paper is to focus on convective heat and mass transfer characteristics of Cu-water nanofluid inside a porous microchannel in the presence of a uniform magnetic field. The walls of the microchannel are subjected to constant asymmetric heat fluxes and also the first order catalytic reaction. To represent the non-equilibrium region near the surfaces, the Navier’s slip condition is considered at the surfaces because of the non-adherence of the fluid-solid interface and the microscopic roughness in microchannels.

Employing the Brinkman model for the flow in the porous medium and the “clear fluid compatible” model as a viscous dissipation model, the conservative partial differential equations have been transformed into a system of ordinary ones via the similarity variables. Closed form exact solutions are obtained analytically based on dimensionless parameters of velocity, temperature and species concentration.

Results show that the addition of Cu-nanoparticles to the fluid has a significant influence on decreasing concentration, temperature distribution at the both walls and velocity profile along the microchannel. In addition, total heat transfer in microchannel increases as nanoparticles add to the fluid. Slip parameter and Hartmann number have the decreasing effects on concentration and temperature distributions. Slip parameter leads to increase velocity profiles, while Hartmann number has an opposite trend in velocity profiles. These two parameters increase the total heat transfer rate significantly.

In the present study, a comprehensive analytical solution has been obtained for convective heat and mass transfer characteristics of Cu-water nanofluid inside a porous microchannel in the presence of a uniform magnetic field. Finally, the effects of several parameters such as Darcy number, nanoparticle volume fraction, slip parameter, Hartmann number, Brinkman number, asymmetric heat flux parameter, Soret and Damkohler numbers on total heat transfer rate and fluid flow profiles are studied in more detail. To the best of author’s knowledge, no study has been conducted to this subject and the results are original.

Recent progress in element technology in large scale explicit finite element codes has opened the way for the solution of elastoplastic shell problems of unprecedented complexity. This new capability has focused attention on the numerical issues involved in the implementation of elastoplastic material models for shells, particularly when vectorizable algorithms are required for supercomputer applications. This paper reviews four algorithms currently in the literature for plane stress and shell plasticity. First, each of the four methods is described in detail. Next, an accuracy analysis is presented for each algorithm for perfectly plastic, linear kinematic hardening, and linear isotropic hardening cases. Finally, a comparison is made of the relative computational efficiency of the four algorithms, and the importance of vectorization is illustrated.

In this paper, an analysis is performed to find the solution of a nonlinear ordinary differential equation that appears in a model for MHD viscous flow caused by a shrinking sheet.

The cases of two dimensional and axisymmetric shrinking have been discussed. When the sheet is shrinking in the x‐direction, the analytical solutions are obtained by the Hankel‐Padé method. Comparison to exact solutions reveals reliability and high accuracy of the procedure, even in the case of multiple solutions. The case of sheet shrinking in the y‐direction is also considered, with success.

When the sheet shrinks in the x‐direction, the analytical solutions are obtained by Hankel‐Padé method. Also, when the sheet shrinks in the y‐direction, the obtained results with Hankel‐Padé method are presented.

Comparison to exact solutions reveals reliability and high accuracy of the procedure and convincingly could be used to obtain multiple solutions for certain parameter domains of this case of the governing nonlinear problem.

The numerical solutions are given for both two‐dimensional and axisymmetric shrinking sheets by using Hankel‐Padé method. It is clear that the Hankel‐Padé method is, by far, more simple, straightforward and gives reasonable results for large Hartman numbers and suction parameters.

The purpose of this paper is to investigate the wave propagation of wave in an infinite poroelastic cylindrical bone. The dynamic behavior of a wet long bone that has been modeled as a piezoelectric hollow cylinder of crystal class 6 is investigated.

An exact closed form solution is presented by employing an analytical procedure. The frequency equation for poroelastic bone is obtained when the boundaries are stress free and is examined numerically.

The study of wave propagation over a continuous medium is of practical importance in the field of engineering, medicine and bio-engineering. Application of the poroelastic materials in medicinal fields such as orthopedics, dental and cardiovascular is well known. In orthopedics, wave propagation over bone is used in monitoring the rate of fracture healing. There are two types of osseous tissue, such as cancellous or trabecular and compact or cortical bone, which are of different materials, with respect to their mechanical behavior.

The frequencies are calculated for poroelastic bone for various values for different values of rotation, angular velocity and density. In wet bone little velocity dispersion was observed, in contrast to the results of earlier studies on wet bone. Large values of attenuation were observed. Such a model would in particular be useful in large-scale parametric studies of bone mechanical response.

The purpose of this paper is to present both an analytical and a numerical analysis of the unsteady magnetohydrodynamic (MHD) rear stagnation-point flow over off-centred deformable surfaces.

The numerical MATLAB solver bvp4c suitable for routine boundary value problem is used for the set of ordinary differential equations reduced from the governing partial differential equations.

Multiple solutions are found for particular eigenvalues. The physical solution is computed by the help of a linear stability analysis. The authors have succeeded in discovering the second solutions, and it is suggested that these solutions are unstable and not physically realisable in practice. The current findings add to a growing body of literature on MHD stagnation-point flow problems. It is also found that the governing parameters have different effects on the flow characteristics.

Even though problems of steady MHD flows have been extensively studied for stagnation-point flows, limited findings can be found on the unsteady MHD rear stagnation-point flow over off-centred deformable surfaces.

The originality of this work is the application of a magnetic field on a time-dependent MHD rear stagnation-point flow over off-centred deformable surfaces.