Thermal Analysis of Non-linear Convective–Radiative Hyperbolic Lumped Systems with Simultaneous Variation of Temperature-Dependent Specific Heat and Surface Emissivity by MsDTM and BPES

With the advent of temperatures near absolute zero, it is often claimed that at very low temperatures the effect of thermal wave propagation must be included by the hyperbolic heat conduction equation (HHCE). In this paper the non-linear convective–radiative HHCE is investigated. Opposite to common numerical analyses, analytical expressions are obtained for the temperature variations by the multi-step differential transformation method. Some conclusions about alteration of the specific heat of the material, temperature steeping, and Vernotte number have been formulated.     

Mesoscale finite element prediction of concrete failure

The present paper studies the failure of concrete from the mesoscopic point of view. Biphasic cubic concrete samples containing spherical aggregates embedded in a homogenized mortar have been simulated using standard finite element method. Linear elasticity and damage-plasticity hypotheses are considered for the aggregates and mortar, respectively. Various triaxial loading conditions are assumed for each sample to generate adequate discrete failure points within the stress space. In the next step, the approximated failure surfaces of specimens are constructed using the Delaunay triangulation technique. The effects of mesostructural features such as aggregate grading curve, aggregate volumetric share, and more importantly the controlling parameters of mortar’s damage-plasticity constitutive model have been investigated. Finally, the failure modes of some selected samples have been reported and discussed.     

Application of the differential transformation method and variational iteration method to large deformation of cantilever beams under point load

Large deflection of a cantilever beam subjected to a tip-concentrated load is governed by a non-linear differential equation. Since it is hard to find exact or closed-form solutions for this non-linear problem, this paper investigates the aforementioned problem via the differential transformation method (DTM) and the variational iteration method (VIM), which are well-known approximate analytical solutions. The mathematical formulation is yielded to a non-linear two-point boundary value problem. In this study, we compare the DTM and VIM results, with those of Adomian decomposition method (ADM) and the established numerical solution obtained by the Richardson extrapolation in order to verify the accuracy of the proposed methods. As an important result, it is depicted from tabulated data that the DTM results are more accurate in comparison with those obtained by the VIM and ADM, which is one of the objectives of this article. Moreover, the effects of dimensionless end point load, ??, on the slope of any point along the arc length and the dimensionless vertical and horizontal displacements are illustrated and explained. The results reveal that these methods are very effective and convenient in predicting the solution of such problems, and it is predicted that the DTM and VIM can find a wide application in new engineering problems.     

Novel solution for acceleration motion of a vertically falling spherical particle by HPM–Padé approximant

In this paper the acceleration motion of a vertically falling spherical particle in incompressible Newtonian media is investigated. The velocity is evaluated by using homotopy perturbation method (HPM) and Padé approximant which is an analytical solution technique. The current results are then compared with those derived from HPM and the established fourth order Runge–Kutta method in order to verify the accuracy of the proposed method. It is found that this method can achieve more suitable results in comparison to HPM.     

Application of multidivisional bi-level programming to coordinate pricing and inventory decisions in a multiproduct competitive supply chain

This study concerns the coordination of pricing and inventory decisions in a multiproduct two-stage supply chain that consists of one manufacturer and multiple retailers within a competitive environment. The retailers order some substitutable products from a common manufacturer. It is assumed that channel members have different market power. The purpose of this paper is to coordinate pricing and inventory decisions such that utility of all involved levels (manufacturer and retailers) is met. Hence, a nonlinear multidivisional bi-level programming model is developed. This model considers both retailers and manufacturer when deciding about the pricing and production volume (for manufacturer) or amount of purchase (for retailers). A hybrid of genetic algorithm (GA) and local search method is proposed to solve the nonlinear bi-level model. This model is reduced to a nonlinear programming by replacing the Karush–Kuhn–Tucker (KKT) conditions of followers to the lower level of the model. Then, the obtained single-level model is relaxed to a linear model to achieve an upper bound (UB). Finally, a numerical example is presented to analyze which parameters have more effect on the price, lot size and, consequently, on the profit. Results show that increasing the market scale parameter of the manufacturer increases the profit of the manufacturer, but the market scale parameter of retailers has no effect on the manufacturer’s profit, although it increases the retailers’ profit.     

The application of differential transformation method to nonlinear equations arising in heat transfer

In this paper two nonlinear heat transfer problems were solved by considering variable specific heat coefficient. The calculations are carried out by using differential transformation method (DTM) which is a semi-numerical-analytical solution technique. By using DTM, the nonlinear constrained governing equations are reduced to recurrence relations and related initial conditions are transformed into a set of algebraic equations. The principle of differential transformation is briefly introduced, and then applied for the aforementioned problems. The solutions are subsequently solved by a process of inverse transformation. The current results are then compared with those derived from the variational iteration method (VIM), homotopy perturbation method (HPM), perturbation method (PM) and the exact solutions in order to verify the accuracy of the proposed method. The findings reveal that the DTM can achieve more suitable results in predicting the solution of such problems.     

A new technique of splenic preservation: extraperitoneal transposition of the traumatized spleen

The lifelong risk of overwhelming infection after splenectomy is well recognized. Although children are at greater risk, adults are clearly vulnerable. This is an incentive to safely preserve the spleen in splenic injuries. Nonoperative management and use of different surgical techniques and synthetic materials to stop bleeding have been experienced and reported. They have the major advantage of spleen mass preservation and prevention of splenectomy complications: but also some disadvantages, for instance: prolonged hospital stay and subdiaphragmatic collection or delayed spleen rupture. This has prompted us for splenic salvation without any attempt to stop bleeding by transposition of spleen into an extraperitoneal cavity created surgically. During a 4 year period (from the end of 1989 to the fall of 1993) ten trauma patients were treated with this original technique. All of these patients had a definitive indication for emergency laparotomy. The procedure was successful in all patients without any unexpected complication.     

Exact Solution for Thermal Buckling of Functionally Graded Plates Resting on Elastic Foundations with Various Boundary Conditions

In this article, we investigate the buckling analysis of plates that are made of functionally graded materials (FGMs) resting on two-parameter Pasternak's foundations under thermal loads. Three different thermal loads were considered, i.e., uniform temperature rise (UTR), linear and non-linear temperature distributions (LTD and NTD) through the thickness. The mechanical and thermal properties of functionally graded material (FGM) vary continuously along the plate thickness according to a simple power law distribution. Employing an analytical approach, the five coupled governing stability equations, which are derived based on first-order shear deformation plate theory, are converted into two uncoupled partial differential equations (PDEs). Considering the Levy-type solution, these two PDEs are reduced to two ordinary differential equations (ODEs) with variable coefficients. Then, the ODEs are solved using an exact analytical solution, which is called the power series Frobenius method. The appropriate convergence study and comparison with previously published related articles was employed to verify the accuracy of the proposed method. After such verifications, the effects of parameters such as the plate aspect ratio, side-to-thickness ratio, gradient index, and elastic foundation stiffnesses on the critical buckling temperature difference are illustrated and explained. The critical buckling temperatures of functionally graded rectangular plates with six various boundary conditions are reported for the first time and can serve as benchmark results for researchers to validate their numerical and analytical methods in the future.     

Thermal Buckling Analysis of Piezoelectric Functionally Graded Plates with Temperature-Dependent Properties

In this study, the thermal buckling analysis of hybrid laminated plates made of two-layered functionally graded materials (FGMs) that are integrated with surface-bonded piezoelectric actuators referred to as (P/FGM)_s are investigated. Material properties for both substrate FGM layers and piezoelectric layers are temperature-dependent. Uniform temperature rise as a thermal load and constant applied actuator voltage are considered for this analysis. By definition of four new analytic functions, the five coupled governing stability equations, which are derived based on the first-order shear deformation plate theory, are converted into fourth-order and second-order decoupled partial differential equations (PDEs). Considering a Levy-type solution, these two PDEs are reduced to two ordinary differential equations. One of these equations is solved using an accurate analytical solution, which is named as power series Frobenius method. The effects of parameters, such as the plate aspect ratio, ratio of piezoelectric layer thickness to thickness of FGM layer, gradient index, actuator voltage, and the temperature dependency on the critical buckling temperature difference, are illustrated and explained. The critical buckling temperatures of (P/FGM)_s with six various boundary conditions are reported for the first time and can be served as benchmark results for researchers to validate their numerical and analytical methods in the future.