Thickness Temperature Distribution Research Articles

Thermal protection properties of profiled timber with peat-vermiculite insulation

Today, the use of environmentally friendly materials is becoming increasingly important. The construction of energy-saving buildings with enclosing structures made of insulated profiled timber, is one of the most promising areas in low-rise construction.Materials having minimum negative impact on the environment during their operation, include new construction insulation materials based on peat-vermiculite granules. The paper studies the main physical properties of wooden exterior walls made of profiled timber, in which peat vermiculite is used as insulation, thermal conductivity of which ranges from 0.05 to 0.06 W/(m·K). For this purpose, numerical simulation is performed for the heat-mass transfer in wooden enclosing structures made of insulated timber with three different connector options.The temperature and heat flow distributions are obtained as a result of modeling stationary thermal conductivity processes in timber structures. It is shown that plywood connectors do not affect the thickness temperature distribution in wooden walls with peat-vermiculite insulation. An increase in thermal conductivity of insulation has no significant effect on the temperature difference along the connector axis or outside the region of its temperature influence.It is found that the thickness of the peat-vermiculite insulation layer should be at least 0.176 m to ensure the compliance with the main requirements for thermal protection properties of enclosing structures in the climatic conditions of Tomsk. The greatest heat loss with a minimum insulation thickness is observed for the wall made of profiled insulated timber with T-shaped connectors. A high-strength timber with the additional central lamella has the best thermal protection with the lowest insulation thickness.

Buckling behavior of composite and functionally graded material plates

In this work the formulation for linear buckling and for geometrically nonlinear analysis of laminated composite and functionally graded material (FGM) plates under mechanical uniaxial in-plane uniform loads, and thermal loads, is presented. An implemented finite element model based on a non-conforming triangular flat plate/shell element with three nodes and eight degrees of freedom per node, associated with a higher order shear deformation theory is used.The through the thickness variation of the material properties, discrete for laminated composite plates or continuous for FGM plates, as well as the through the thickness temperature distribution, originate a non-symmetry with respect to the middle-surface. Thus, in general, the occurrence of bifurcation-type buckling should be studied, and the transverse deflection at the centre of the plate could be a good indicator to anticipate this occurrence.The solutions of some illustrative examples involving different boundary conditions, composite lay-up, FGM variation of volume fractions, temperature distributions, material combinations, and boundary conditions are presented for benchmarking purposes, with emphasis for the plate transverse deflections. Linear solutions are compared with numerical alternative models. The occurrence of bifurcation-type buckling is discussed for several representative cases, the validity of the linear buckling solutions is addressed and nonlinear analyses have been performed for confirmation purposes.

Transient radiative-conductive heat transfer modeling in constructional semitransparent silica ceramics

The article deals with transient radiative – conductive heat transfer investigation in constructional silica ceramics with 10% of total porosity in 2D slab geometry. An empirical model, the so-called effective thermal conductivity (ETC) approximation, and rigorous radiative heat transfer (RCHT) problem solution are compared. Effective thermal conductivity coefficients were determined by both quasi-stationary and non-stationary sample heating and corresponding conductive heat transfer inverse problem solution. Rigorous RCHT calculations were based on radiative transfer equation solution. Spectral directional-hemispherical reflectances were used for scattering and absorption coefficients determination by an identification technique. Identification was based on direct problem solution by invariant embedding technique and parametric optimization. Mie theory and independent scattering approximation with regard to scatterers (pores) size distribution were used for mean scattering cosine estimation. It was shown that in the case of non-stationary temperature regime with rapid heating and cooling stages ETC models fail to predict through the thickness temperature distribution with absolute error less than 502013100 K. The absolute value of this error is strongly affected by the heating schedule. Moreover, calculations revealed several features of the heat flux through the unheated boundary that could not be taken into considerations by effective thermal conductivity approaches.

Static analysis of stepped functionally graded magneto-electro-elastic plates in thermal environment: A finite element study

In this article, a finite element (FE) formulation accounting for multiphysics response of multilayered magneto-electro-elastic (MEE) plates in the thermal environment has been presented. The equilibrium equations of motion are attained using the principle of total potential energy and coupled constitutive relations of MEE material. Maxwell’s equation of electrostatics and magnetostatics are used to model the electric and magnetic behavior. The influence of various through thickness temperature distributions on the static parameters of stepped functionally graded magneto-electro-elastic (SFG-MEE) plates is investigated. Further, an extra attention has been devoted to evaluate the effect of product properties (pyroelectric and pyromagnetic coupling), boundary conditions and aspect ratio on the direct (displacements, electric potential and magnetic potential) and derived quantities (stresses, electric displacement, and magnetic flux density) of the SFG-MEE plate. A comparative study is also carried out to analyse the effect of stacking sequence, boundary conditions, pyroeffects, length-to-width ratio and aspect ratios of the SFG-MEE plate. The credibility of the proposed FE model is verified with the results available in the literature. It is expected that the findings in this article may be useful for accurate design and analysis of MEE structures under the thermal environment.

A Combined Experimental and Modelling Approach towards an Optimized Heating Strategy in Thermoforming of Thermoplastics Sheets

Abstract Determining the operational settings for the heating equipment in thermoforming is still mainly done by trial and error as well as personal experience. Depending on the type of IR heating equipment, these settings can be the consumed electrical power or the desired temperature of the heating elements. In this study, a workflow is developed, applied and validated to characterize the IR heating equipment and to determine the optimal heating strategy. The workflow starts with an on-site equipment/machine characterization, which takes all machine and environment parameters into account. This approach results in the optimal heater setting and heating duration in order to obtain a through thickness temperature distribution which lies within a predefined forming range. The proposed methodology is universally applicable as it can deal with different types of sheet material and thicknesses. Moreover it can be applied to any type of IR heating element (halogen, metal foil, ceramic or quartz). Moreover, the methodology can easily be implemented in an industrial environment. Additionally, an estimate for the thermal efficiency of halogen heater equipment can be determined.

Static studies of stepped functionally graded magneto-electro-elastic beam subjected to different thermal loads

In this article, a three dimensional finite element (FE) formulation for a multilayered magneto-electro-elastic (MEE) beam in thermal environment is presented. The equilibrium equations of the system are attained using the principle of total potential energy and linear coupled constitutive equations of MEE material. The corresponding FE equations are derived and the numerical evaluation of stepped functionally graded (SFG) MEE beam is carried out. The influence of various in-plane and through thickness temperature distributions on the direct quantities (displacements and potentials) and derived quantities (stresses, electric displacement and magnetic flux density), across the thickness of SFG-MEE cantilever beam is analyzed. In addition, an attempt has been made to investigate the effect of stacking sequence, thermo-magnetic and thermo-electric coupling on the direct quantities of the SFG-MEE beam. Further, a comparative study is made to evaluate the variations of displacements, potentials, electric displacements, magnetic flux density and stresses at different regions of the beam. It is expected that the results presented in this article may be useful in the design and analysis of MEE smart structures and sensor applications.

Experimental and Computational Analysis of the Heating Step during Thermoforming of Thermoplastics

The present study addresses the difficulties in heating thermoplastic sheets for ther-moforming applications. In industrial environments, the sheets are heated in a contact free method by means of convective hot air ovens and infrared radiation. In this study the temperature evolution at the outer surface as well as the core of thermoplastic sheets as a function of time is measured by means of thermocouples. These measurements reveal significant through thickness temperature dif-ferences which need to be resolved before high quality products can be made. The temperature dif-ferences can be decreased by decreasing the radiative power. This is however not acceptable in in-dustry since it lowers the number of produced parts per unit of time.In order to gain insight in the time-temperature relationship during the heating phase, a finite differ-ence model is developed. The model clearly shows the constantly changing through thickness tem-perature distribution and can be used as a tool by the thermoforming industry to optimize the pro-duction process.

Systematic Evaluation of the Advantages of Static Shoulder FSW for Joining Aluminium

Static Shoulder Friction Stir Welding (SS-FSW) is a modification to conventional FSW that was originally developed to improve the weldability of titanium alloys by reducing through thickness temperature gradients. Surprisingly, to date, there have been no published systematic studies comparing SS-FSW to FSW for aluminium welding. This may be because the high conductivity of aluminium means the heat input produced by the shoulder is thought to be beneficial. In the work presented when welding a high strength 7050 aluminium alloy, even in a relatively thin 6 mm plate, it is shown that SS-FSW has several advantages; including a reduction in the heat input, a massive improvement in surface quality, and a more uniform through thickness temperature distribution, which leads to narrower welds with a reduced heat affected zone width and more homogeneous through thickness properties. The reasons for these benefits are discussed.

Residual Stress and Warpage Models for Complex Injection Molded Parts

Abstract In the postfilling stage of an injection molding process, thermal induced residual stress usually develops during the solidification of the melt with non-uniform through thickness temperature distribution. Furthermore, the packing pressure is applied through the gate, and will be different in different locations. Since the local melt pressure varies with time due to the change of melt viscosity, the material solidifies under different frozen-in pressure. The stress relaxation behavior of the plastic materials also complicates the stress field. This study uses a simple thermoviscoelastic model to calculate the residual stress developed in the postfilling stage and a elastic model to determine the warpage after demolding for three dimensional complex parts. Based on the calculation of the injection molding process, the temperature and pressure histories in the postfilling stage can be determined, and used to calculate the developed stress field. The model divides the thickness into two regions, liquid and solid phases. Residual stress calculation is applied in the solid region, while the liquid region is kept at the melt pressure without any strain. The resulted in-mold stress fields are used to calculate the part warpage after demolding.

AN ASSESSMENT OF MIXED AND CLASSICAL THEORIES FOR THE THERMAL STRESS ANALYSIS OF ORTHOTROPIC MULTILAYERED PLATES

This article compares theories formulated on the basis of the classical Principle of Virtual Displacements (PVD) to mixed theories formulated on the basis of the Reissner Mixed Variational Theorem (RMVT) to evaluate the thermal response of orthotropic laminated plates. So-called layer-wise (LW) and equivalent single-layer (ESL) modelings have been developed for both classical and mixed approaches (each layer is considered as a single plate for LW analysis, while the unknown variables are independent of the number of the constitutive layers for the ESL cases). Linear up-to fourth-order displacement and stress field cases have been implemented to derive thermomechanical governing equations, consistent with the used variational statements. All the theories have been presented in a unified manner by referring to findings recently presented by the author. The numerical investigation has been restricted to a simply supported plate loaded by harmonic distribution of in-plane temperature fields. Constant and linear through-the-thickness temperature distributions have been considered for which exact three-dimensional solutions are available. The results of in-plane and out-of-plane displacement and stress components are given in the form of tables and diagrams. The superiority of the mixed approach to the PVD formulation has been confirmed. Higher order, layer-wise expansions for the unknown variables are required for an accurate description of the thermomechanical response of thick multilayered plates. It has been found that the thickness temperature distributions T(z) have a significant influence on the accuracy of the considered theories.

Thermal analysis of FRP chimneys using consistent laminated shell element

Due to their high corrosion and chemical resistance, fiber reinforced plastic (FRP) materials are increasingly being used in the construction of industrial chimneys. The design of a chimney is governed by wind loads as well as thermal loads resulting from the differences among the ambient, the operating and the curing temperatures. This study involves an investigation for the thermal stresses induced in angle-ply laminated FRP chimneys, using an in-house developed laminated shell element model. The finite element model is verified by performing thermal analysis of a number of plate and shell problems and comparing the results to those available in the literature. An extensive parametric study is then conducted using the shell element model to identify the parameters which significantly affect thermal stresses induced in FRP chimneys. The study indicates that the thermal stresses are only affected by the inclination of the lamina plies, the percentage of fibers content and the through thickness temperature distribution. Analyses also show that localized cracks in the direction perpendicular to the fibers are expected to occur due to the thermal loads. Finally, thermal stress values that can be used in the design of FRP chimneys, when cracking is considered, are presented as function of the through thickness temperature distributions.

Curing Residual Stresses and Failure Analysis in Composite Cylinders

A method to predict the residual stress due to curing in thick or thin lami nated cylinders is presented, decoupling the stress analysis from the cure kinetics. The method employs a 3D elasticity solution, calculating in-plane and normal stresses. The results compare well with those obtained by a verified computer code (WINDTHICK), with a substantial savings in running time. Transient stresses during curing due to the non uniform through the thickness temperature distribution are also calculated. The risk of micro cracking and internal delaminations can then be evaluated.