STRESSES IN VISCOELASTIC PLATE DRIED CONVECTIVELY

The deformations and drying-induced stresses in a saturated porous plate insulated on one side and dried convectively on the others were analysedPlate material is assumed to be elastic and viscoelastic. A rigorous solution of the problem is presented using Laplace transformations and the method of variable separation. The results are presented in the form of a series resulting from the solution of a Sturm-Liouville problem. The shrinkage stresses in the plate are caused by non-uniform distribution of the moisture content. The thermal stresses are not included as the consideration were confined to only constant rate drying period.     

INFLUENCE OF THE DRYING MEDIUM PARAMETERS ON DRYING INDUCED STRESSES

ABSTRACT

A thermomechanical model of drying of capillary-porous materials whose material constants depend on moisture content and temperature is presented in the paper. The finite element method is used for the solution of two-dimensional problem of convective drying of a prismatic bar. The moisture distributions, temperature distributions, drying induced strains and stresses for various drying medium parameters are determined. The effect of these parameters on moisture distribution and in particular on drying induced stresses is discussed.     

Calculation of Residual Thermal Stresses in Injection Molded Amorphous Polymers by the Finite Element Method

Abstract

The finite element method (FEM) is used to calculate the distribution of residual internal stresses in an injection molded plate-shaped polystyrene specimen. The first step of the calculating procedure is the determination of the temperature distributions in the plate and its variation with cooling time. The temperature distribution data are then used for the determination of the corresponding stress distribution. Also this latter step is accomplished using the FEM-technique. The residual stress distribution is obtained when the sample has been cooled to the temperature of the mold. The main result of the calculations is the finding that the surface layer of the plate is subject to compressive stresses, while the interior accommodates stresses of tensile type. The calculations relate to a polystyrene specimen. The results are shown to agree well with earlier data concerning internal stresses in injection molded objects. The possible influence of anisotropy and visco-elastic relaxation has been neglected. The method can be applied to other amorphous polymers and, after a slight modification, also to polymers of semicrystalline type.     

A Sharp Drying Front Model

Abstract

The drying of materials is often described by nonlinear diffusion equations. Up to now the only way to solve these equations is by numerical simulations. Recently an analytic solution has been proposed for the drying problem. Based on this solution a sharp drying front model is presented. Measured moisture profiles during drying and the drying curve of gypsum are compared with approximate models.     

A study of the structural integrity of graphite composite structure subjected to low velocity impact

An analysis for the transient deflections, bending strains, and interlaminar shear stresses in a simply supported laminated composite plate subject to low velocity impact has been obtained using a series solution of the plate governing equations. Results are presented showing the effect of plate geometry and impact location on damage mode. Computed stresses and strain are compared with impact test data to verify, the analysis.     

CONJUGATE ANALYSIS OF NATURAL CONVECTIVE DRYING OF BIOLOGICAL MATERIALS

ABSTRACT

This paper presents a numerical analysis of heat and mass transport during natural convective drying of an extruded com meal plate. The conjugate problem of drying and natural convection boundary layer Is modeled. The finite volume technique was used to discretize and solve the highly nonlinear system of coupled differential equations governing the transport inside the plate. The boundary layer solution was obtained by means of a finite difference software package that utilizes Runge-Kutta's 5th order method to solve the inherent transport equations. A methodology for evaluating the heat and mass transfer coefficients during the numerical simulation was developed and successfully implemented. The results showed that there is no analogy between heat and mass transfer coefficients for this type of problem.     

Stress analyses of composite tee joints at elevated temperature

Thermal–structural coupling nonlinear finite element analyses are conducted in this paper to determine three-dimensional stresses of a composite tee joint, which is formed when a right angled plate is adhesively bonded to a base plate at elevated temperature. The von-Mises stresses of the adhesive layer of the tee joint with three different laminate stacking sequences viz. unidirectional [0]₈, cross-ply [(0/90)_s]₂, and angle-ply [(+45/?45)_s]₂ laminates have been evaluated when the tee joint is subjected to an out-of-plane loading through the right angled plate in addition to an elevated temperature applied at the undersurface of the base plate. The effects of laminate stacking sequence and temperature on von-Mises stresses have been investigated in this paper. The effects of the coefficient of thermal expansion and thermal conduction of the adhesive layer on von-Mises stresses have also been studied. Conclusions about the stresses of the composite tee joint with different stacking sequence, different coefficient of thermal expansion, and different thermal conduction of the adhesive layer are drawn.     

Predicting residual stresses due to solidification in cast plastic plates

Abstract

Thermal processing is an economical and efficient way of manufacturing polymeric products. However, it suffers from an important side effect that may considerably affect product performance: during non-uniform cooling to room temperature, strains become ‘frozen in’ the material. These frozen in strains lead to undesirable distortions and residual stresses within the final product. This work is concerned with cast filled PMMA plates for domestic applications. In a typical casting process, the material is first polymerised at a high temperature and then cooled to the ambient temperature. After cooling, the plate has distorted to an extent dependent on the cooling conditions.

A method has been developed for quantitative prediction of the distortions and consequent residual stresses caused by non-uniform solidification. A ‘residual’ temperature field is introduced, which provides the relationship between the thermal history and frozen in strains. When applied as an actual temperature distribution, it results in distortions and residual stresses. Laboratory tests indicative of the actual casting process validated the frozen in strain model. Preheated plates were cooled in a controlled environment while temperatures were recorded at a number of locations on the plate surfaces. The measured temperature histories were then used in the numerical prediction of the residual temperature field. Experimental and numerically predicted distorted shapes agree very well.     

Optimal Control of the Secondary Drying Stage of Freeze Drying of Solutions in Vials Using Variational Calculus

Abstract:

The problem of operating freeze drying of pharmaceutical products in vials loaded on trays of freeze dryer to obtain a desired final bound water content in minimum time is formulated as an optimal control problem. Two different types of freeze dryer designs were considered. In the type I freeze dryer design, upper and lower plate temperatures were controlled together, while in the type II freeze dryer design, upper and lower plate temperatures were controlled independently. The heat input to the material being dried and the drying chamber pressure were considered as control variables. Only the scorch temperature was considered as a constraint on the system state variables during the secondary drying stage, because all the free water content (frozen water) is removed from the solid matrix during the primary drying stage of freeze drying. Necessary conditions of optimality for the secondary drying stage of freeze drying process in vials were derived and presented by using rigorous multidimensional unsteady-state mathematical models. The theoretical approach presented in this work was applied in the freeze drying of skim milk. Significant reductions in drying times of the secondary drying stage of the freeze drying process in vials were observed and more uniform bound water and temperature distributions in the material being dried were obtained compared to the conventional operational policies.     

A New Coupled Solution for Interfacial Stresses Analysis in a Repaired Beam with an Adhesively Bonded Prestressed FRP Plate

This paper focuses on a new coupling solution for determining the elastic interfacial shear and normal stresses in an adhesive joint between a strengthening plate and a simply supported beam. The mismatch of the curvatures in the beam and plate is considered by including both the effect of the adherend shear deformations and the prestressed laminates model. This new method leads to the coupling of governing differential equations for the interfacial shear and normal stresses. Most of the other solutions in the literature assume that the beam and plate have an equal curvature to uncouple this effect. In this paper, however, a solution is presented to calculate the interfacial stresses of beams strengthened with a prestressed composite plate having a new rigidity model coupled with the shear lag effect, which are neglected by the previous studies. It is found that the present method can predict accurately stresses in the interior and near the ends of the adhesive layer, where the stress fields can be significantly influenced by the edge effects. A parametric study was carried out to show how the stress concentration and distribution are influenced by the dimensions of the adherends and the material properties of the strengthened beam.     

Optimal Control of the Primary Drying Stage of Freeze Drying of Solutions in Vials Using Variational Calculus

Abstract

The problem of operating freeze drying of pharmaceutical products in vials placed in trays of a freeze dryer to remove free water (in frozen state) at a minimum time was formulated as an optimal control problem. Two different types of freeze dryer designs were considered. In type I freeze dryer design, upper and lower plate temperatures were controlled together, while in type II freeze dryer design, upper and lower plate temperatures were controlled independently. The heat input to the material being dried and the drying chamber pressure were considered as control variables. Constraints were placed on the system state variables by the melting and scorch temperatures during primary drying stage. Necessary conditions of optimality for the primary drying stage of freeze drying process in vials are derived and presented. Furthermore, an approach for constructing the optimal control policies that would minimize the drying time for the primary drying stage was given. In order to analyze optimal control policy for the primary drying stage of the freeze-drying process in vials, a rigorous multi-dimensional unsteady state mathematical model was used. The theoretical approach presented in this work was applied in the freeze drying of skim milk. Significant reductions in the drying times of primary drying stage of freeze drying process in vials were obtained, as compared to the drying times obtained from conventional operational policies.     

Murphree,Hausen, Vaporization,and Overall Efficiencies in Binary Distillation of Associated Systems

Abstract

In this paper a comparative study of different plate efficiencies models considering binary systems with association of one component in both phases is presented. The experiments were carried out in a laboratory column with 10 real bubble-cup plates for the benzene—acetic acid and toluene—acetic acid systems. The actual and ideal compositions at each plate are interpreted. The model of associated systems using the concentration-dependent liquid phase association constant was considered.     

EFFECT OF INTERMITTENT HEATING ON DRYING-INDUCED STRAIN-STRESS OF MOLDED CLAY

ABSTRACT

Parametric analyses of the strain-stress in the drying process are performed to study the influence of the intermittent drying on the behaviors of drying-induced strain-stress and deformation as well as the drying characteristic. The transient three-dimensional problem of strain-stress and heat and moisture transfer in a slab is solved simultaneously by the finite element method. The dimensionless parameters are introduced to generalize the problem in the conservation equations of heat and moisture transfer. The intermittent drying is modeled by applying periodically smaller and larger Biot numbers to the boundary conditions. The maximum tensile and compressive stresses fluctuate, and fall remarkably during the smaller Biot number period when a slab is heated intermittently. The peak stress of the fluctuation exceeds beyond the case in the continuous healing where the overall drying rate is almost equivalent to that in the intermittent beating, but the reduction of the stresses takes place rapidly in the low heating period.     

Study of Controlled Cyclic Distillation: II. Analytical Transient Solution and Asymptotic Plate Efficiencies

Abstract

The dynamic equations of the composition variables of a controlled cycling distillation column are solved to obtain the transient solutions for the vapor-flow period. These solutions are then used to establish asymptotic expressions for the compositions at the pseudo-steady-state condition of the cycling column. Analytical expressions for the asymptotic plate efficiencies in terms of the operating conditions, equilibrium data, and local point efficiencies are derived to show quantitatively the amount of improvement in the separating ability that can be achieved in an ideal cycling column. A method of numerical iterative solution for a nonlinear equilibrium relationship is demonstrated, and a simplified graphical method for calculating the number of stages required for a given separation is presented.     

Thermal residual stresses in adhesively bonded in-plane functionally graded clamped circular hollow plates

This study investigates the effects of in-plane compositional gradient exponent and direction on the thermal residual stress and deformations in adhesively bonded functionally graded clamped circular plates. The material composition was assumed to vary with a power law along an in-plane direction not through the plate thickness direction. The transient heat conduction and Navier equations in polar coordinates describing the two-dimensional thermo-elastic problem were discretized using finite-difference method, and the set of linear equations were solved using the pseudo-singular-value method. The material composition direction is designed as Ceramic-Metal (CM)–CM, CM–Metal-Ceramic (MC), MC–CM, and MC–MC for the inner and outer plates. The temperature decreased radially along the plates, but exhibited a sharp decrease across the adhesive layer. The compositional gradient exponent and direction affected evidently temperature levels and heat transfer period. The compressive radial and shear strains are more effective on the deformation in the adhesive layer and the plate regions near the plate–adhesive interfaces. The adhesive layer is subjected to considerable shear deformations. The equivalent strain and stresses are very low in a large region of the plates but exhibit sharp peaks on the plate regions near the plate–adhesive interfaces, and decrease towards the adhesive interfaces. These stress and strain peaks in the plates and adhesive layer are affected by the compositional gradient and direction. For an outer edge flux, the largest equivalent strain and stresses are observed in the CM–MC joint but the lowest levels occur in the MC–CM or secondly CM–CM joint. In addition, an inner edge flux results in the lowest and highest peak strains and stresses in the MC–CM and CM–MC joints, respectively. The MC–MC and CM–CM joints result in lower temperature, stress and strain levels around the adhesive layer and along the adhesive interfaces for outer and inner edge fluxes, respectively.     

Drying-Induced Stresses in Macaroni Dough

The mechanical effects like shrinkage and drying induced stresses arising during convective drying of macaroni dough are analyzed in this article. The aim of these studies is to test the sensitivity of macaroni dough on fracture formation caused by shrinkage during drying. The development of stresses was analyzed theoretically on the example of a thin plate placed on the impermeable metal plate, which simultaneously played the role of a waveguide for acoustic signals. The acoustic emission equipment with the sensor fixed to the metal plate enabled monitoring on-line the development of fractures occurring in the macaroni dough. Mechanical coefficient of this material were estimated experimentally. The studies have proved that an enhanced acoustic emission is observed at those instants when the stresses tended to their maximal values.     

Further Studies of the Gas Penetration Process in Gas‐Assisted Injection Molding

Abstract

Gas‐assisted injection molding is one of the innovation injection‐molding processes recently developed. The solution of gas penetration thickness interface is the key problem in the simulation of gas‐assisted injection molding, but also the puzzle. By applying the matching asymptotic expansion method, an analytical solution of the gas penetration interface is deduced. First, the governing equations and boundary conditions are transformed to be dimensionless. And then matching asymptotic expansion method is applied to solve the dimensionless equations, where capillary number Ca and Ca ^2/3 are used as perturbation parameters. Compared with experimental results, the presented mathematical model and solving method are proved to be correct.     

On the Effect of Time-Dependent Deformations on the Interface Behaviour of RC Beams Strengthened by FRP Plates

In this paper, the effect of time-dependent deformations (such as shrinkage and creep) on the interfacial stresses between a concrete beam and a fibre reinforced polymer plate is presented. The analysis given here involves a closed-form solution for such stresses and includes creep and shrinkage effects. The adherend shear deformations have been included in the present theoretical analysis by assuming a parabolic shear stress through the thickness of both concrete beam and fibre reinforced polymer panel. Contrary to some existing studies, the assumption that both the concrete beam and the fibre reinforced polymer panel have the same curvature is not used in this investigation. The influence of creep and shrinkage effect relative to the time of the casting and the time of the loading of the beams is taken into account. Numerical examples of a typical concrete beam strengthened with an externally bonded fibre reinforced polymer plate are discussed with the emphasis on the shear and normal stresses at the edge of the plate.     

Basic Equations Relating Separation Time to Relevant Operational Parameters in Chromatography

Abstract

Basic equations are derived to relate the chromatographic separation time to operational parameters, which are chosen to ensure that they can be experimentally measured. The most important of these parameters are the available pressure-drop across the column, the extracolumrrcontributions to band broadening, the plate height of the column itself, the parameters that determine the plate height, the column length, and the separation factor. The derivation is presented in such a way as to stress the assumptions often implicitly introduced in the theory.