Tube stresses due to in-plane thermal expansion of tubesheets in closely spaced double tubesheets

An approximate analysis of thermal stresses developed in heat exchanger tubing between closely spaced double tubesheets is presented. Tube loading is caused by in-plane differential thermal movement of the adjacent tubesheets. To obtain solutions valid for arbitrary spacing between the tubesheets, the effect of shear deformation is included. The effect of edge restraint such as peripheral flange bolting is also included. Typical results are presented to illustrate the interaction of bending and shear in the tubes.     

Analysis of Dynamic Characteristics of Rotating Circular Saw Subjected to Thermal Loading and Tensioning

An analysis is carried out to investigate the dynamic characteristics of a tensioned circular saw. The analytical model is a rotating annular disc, undergoing plastic strain at a given temperature. By using the plate bending theory, the governing equations for the in-plane behavior during rotation and under thermal load and plastic strain and those for the resulting out-of-plane behavior are derived. Then, the solution of in-plane forces is obtained and the modal analysis is carried out. The in-plane forces and natural frequencies are calculated numerically to investigate the effect of tensioning conditions on them, and to find suitable tensioning conditions.     

Thermal Stress Analysis for an Inclusion with Nonuniform Temperature Distribution in an Infinite Kirchhoff Plate

Abstract

An elliptic inclusion with prescribed polynomial eigenstrains in an infinite Kirchhoff plate is analyzed. The integral type general solutions for the in-plane and out-of-plane displacements on the mid-plane of the plate were derived. The integrals were simplified by using Green's function for the Kirchhoff plate. The integrals could be explicitly expressed by calculating two potential functions defined in this work. After some manipulation of Ferrers and Dyson's formula related to the integration of the harmonic potential for the three-dimensional ellipsoid, we evaluated the potential functions, which can be algebraically expressed by the I-integrals. The results were applied to the analysts of the thermal stress for an inclusion with non uniform temperature distribution that might be approximated by a polynomial. For mathematical convenience, we consider an inclusion with a linear temperature distribution. The expressions for the displacements were decomposed in order to separately investigate the effects of the constant and the first-order term of the temperature distribution. The elastic fields caused by an elliptic inhomogeneity with polynomial eigenstrains, which is called the inhomogeneous inclusion, were also determined by the equivalent eigenstrain method.     

THERMAL RESIDUAL STRESSES IN FILAMENT-WOUND CARBON-FIBER-REINFORCED COMPOSITES

Explicit algebraic expressions are first proposed to predict easily and precisely the thermal-expansion coefficients of unidirectional reinforced plastics. They are given as functions of the thermal and elastic properties of the constituent materials and of the fiber-volume fraction. They are derived by considering circular anisotropic fibers arranged in a hexagonal array in a matrix. Then, analytical expressions are derived for the thermal-expansion coefficients and curing stresses in filament-wound laminated composites under the assumption of elastic behavior and within the framework of laminated plate theory.

Experiments on carbon-fiber/epoxy composite cylinders reinforced by helical and circumferential windings show good agreement with the calculated values. The residual stresses induced by curing are found not to be negligible compared with the low tensile strength transverse to the fibers. Such algebraic expressions for thermal coefficients, together with those for elastic moduli and failure criterion proposed by one of the authors, seem to be of use in the tailored design of laminated composite structures in a closed form, which elucidate the effects of various sorts of constitutive parameters.     

Effects of nonlinear hygrothermomechanical loading on bending of FGM rectangular plates resting on two-parameter elastic foundation using four-unknown plate theory

In the present study, a simple four-unknown exponential shear deformation theory is developed for the bending of functionally graded material (FGM) rectangular plates resting on two-parameter elastic foundation and subjected to nonlinear hygrothermomechanical loading. The elastic properties, coefficient of thermal expansion, and coefficient of moisture expansion of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of material constituents. Unlike first-order and other higher-order plate theories, the present theory has four independent unknowns. The in-plane displacement field of the present theory uses exponential functions in terms of thickness co-ordinate for calculating out-of-plane shearing strains. The transverse displacement includes bending and shear components. The principle of virtual displacement is employed to derive the governing equations and associated boundary conditions. A Navier solution technique is employed to obtained an analytical solutions. The elastic foundation is modelled as two-parameter Winkler–Pasternak foundation. The numerical results obtained are compared with previously published results wherever possible to prove the efficacy and accuracy of the present theory. The effects of stiffness and gradient index of the foundation on the hygrothermomechanical responses of the plates are discussed.     

Thermomechanical Response of Variable Stiffness Composite Panels

Analysis of non-traditional Variable Stiffness (VS) laminates, obtained by steering the fiber orientation as a spatial function of location, have shown to improve buckling load carrying capacity of flat rectangular panels under axial compressive loads. In some cases the buckling load of simply supported panels doubled compared to the best conventional laminate with straight fibers. Two distinct cases of stiffness variation, one due to fiber orientation variation in the direction of the loading, and the other one perpendicular to the loading direction, were identified as possible contributors to the buckling load improvements. In the first case, the increase was attributed to the favorable distribution of the transverse in-plane stresses over the panel platform. In the second case, a higher degree of improvement was obtained due to the re-distribution of the applied in-plane loads. Experimental results, however, showed substantially higher levels of buckling load improvements compared with theoretical predictions. The additional improvement was determined to be due to residual stresses introduced during curing of the laminates. The present paper provides a simplified thermomechanical analysis of residual stress state of variable stiffness laminates. Systematic parametric analyses of both cases of fiber orientation variations show that, indeed much higher buckling loads could result from the residual stresses present in such laminates.     

A simplified approach for the thermoelastic large deflection in the thin clamped annular sector plate

The present article is concerned with analysis of large deflection of a heated thin annular sector plate with clamped edges under transient temperature distribution using Berger’s approximate methods. The prescribed surface temperature is at the top face of the plate whereas the bottom face is kept at zero temperature. In this study, the Laplace transform as well as the classical method have been used for the solution of heat conduction equation. The thermal moment is derived on the basis of temperature distribution, and its stresses are obtained using resultant bending moment and resultant forces per unit length. The calculations are obtained for the aluminium plate in the form of an infinite series involving Bessel functions, and the numerical results for temperature, deflection, resultant bending moments, and thermal stresses have been illustrated by graphs.     

Thermoelastic analysis of functionally graded porous beam

We present a thermoelastic analysis of functionally graded porous beams under in-plane thermal loading which is applied as uniform temperature distribution over the entire beam. The pore distributions are modeled by a power law and assumed to vary smoothly across the thickness of beam. We consider both saturated and unsaturated pores filled with fluid. The governing equations of porous beam are derived using the variational formulation based on the Timoshenko beam theory. We study the influence of pore’s material properties comparing the results to solutions of homogeneous beams.     

Limit loads for piping branch junctions under internal pressure and in-plane bending—Extended solutions

The authors have previously proposed plastic limit load solutions for thin-walled branch junctions under internal pressure and in-plane bending, based on finite element (FE) limit loads resulting from three-dimensional (3-D) FE limit analyses using elastic–perfectly plastic materials [Kim YJ, Lee KH, Park CY. Limit loads for thin-walled piping branch junctions under internal pressure and in-plane bending. Int J Press Vessels Piping 2006;83:645–53]. The solutions are valid for ratios of the branch-to-run pipe radius and thickness from 0.4 to 1.0, and for the mean radius-to-thickness ratio of the run pipe from 10.0 to 20.0. Moreover, the solutions considered the case of in-plane bending only on the branch pipe. This paper extends the previous solutions in two aspects. Firstly, plastic limit load solutions are given also for in-plane bending on the run pipe. Secondly, the validity of the proposed solutions is extended to ratios of the branch-to-run pipe radius and thickness from 0.0 to 1.0, and the mean radius-to-thickness ratio of the run pipe from 5.0 to 20.0. Comparisons with FE results show good agreement.     

Studies on gasketed flange joints under bending with anisotropic Hill plasticity model for gasket

The behavior of a gasketed flange joint under bending loads has been studied by three dimensional finite element analysis (FEA) and experiments. The in-plane and bending stiffness of spiral wound gaskets are considered using anisotropic Hill plasticity material model. The variation in bolt axial force of joints under bending load predicted by the finite element analysis compares well with the experimental results. The contact stress distribution obtained have significant variation in the pattern from the previous material models and consistent with the results of Bouzid [1] regarding flange rotation.     

分布拉杆转子动力学建模与分析

通过接触力学建立了分布拉杆转子轮盘间接触的等效弯曲刚度的表达式,进而分析了等效弯曲刚度随偏转角和拉紧力的变化规律;同时将等效弯曲刚度添加到拉杆转子模型中并进行数值仿真,进而得到分布拉杆转子临界转速随等效弯曲刚度的变化趋势。研究结果表明:等效弯曲刚度与转角间并不始终是线性关系,当转角达到某一值后,等效弯曲刚度随转角变化呈指数式变化;同时拉杆转子随拉紧力的增加,临界转速增加较多。     

Development of DKT Finite Element Formulation for Thermal Bending of Thin Plate

The finite element formulation for thermal bending analysis of a thin plate due to the temperature gradient through its thickness is presented. The formulation is developed for the Discrete Kirchhoff Triangle (DKT) element to analyze the plate bending behavior under the thermal loading. The finite element load vector is derived in closed-form expressions so that the numerical integration is not required. Solution accuracy of the developed DKT finite element is evaluated by several examples. Performance of the developed DKT finite element is also compared with the effective nonconforming triangular element (BCIZ element). Results show that the developed DKT finite element formulation provides high solution accuracy for analysis of plate bending problem under thermal loading.     

Thermal Residual Stresses in One-Directional Functionally Graded Plates Subjected to In-Plane Heat Flux

This study carries out the transient thermal residual stress analyses of functionally graded clamped plates for different in-plane material compositions and in-plane heat fluxes. The heat conduction and Navier equations representing the two-dimensional thermoelastic problem were discretized using the finite-difference method, and the set of linear equations were solved using the pseudo singular value method. Both in-plane temperature distributions and the heat transfer period were affected considerably by the compositional gradient. The type of in-plane heat flux had a minor effect on the temperature profile, but on the heat transfer period. The high stress levels appeared in the ceramic-rich regions. The normal and equivalent stresses exhibited a sharp change in the plates with ceramic-rich as well as metal-rich compositions, and the concentrated on a narrow ceramic layer. A smooth stress variation was achieved through the graded region with a balanced composition of ceramic and metal-phases, and the stress discontinuities disappeared. The in-plane shear stress was negligible. The equivalent stress exhibited a linear temporal variation for both constant and sinusoidal heat fluxes, but a nonlinear variation for the exponential heat flux. In case the heat flux is applied along the metal edge (metal-to-ceramic plate) instead of the ceramic edge, the displacement and stress components exhibited similar distributions to those of a ceramic-to-metal plate but in the opposite direction. As a result, the distribution of in-plane material composition affects only normal stress distributions, whereas the peak stress levels occur in the ceramic-rich regions. Since the normal stresses concentrate along a narrow ceramic layer for ceramic-rich or metal-rich compositions, a balanced in-plane material composition distribution of ceramic and metal would be useful to avoid probable local ceramic fracture or damage.     

Thermal Stress Analysis of Sandwich Structures

ABSTRACT

Significant thermal and interlaminar transverse stresses often occur in sandwich structures subjected to thermal loading due to the mismatch in thermal expansion of different materials in structures. A kind of 32-node, 3-layered shell element with relative degrees-of-freedom accompanied by a post-processing method is presented based on 3D FEM to accurately describe thermo-structures behavior and easily connected with brick elements. The present method is verified by a theoretical result. The thermal stress fields in a sandwich cylinder with a cutout with and without reinforcement are calculated by the method successfully. The results show that reinforcement may cause significant transverse thermal stresses, although it is beneficial to reducing in-plane stress.     

A comparison of plastic collapse and limit loads for single mitred pipe bends under in-plane bending

This paper presents a comparison of the plastic collapse loads from experimental in-plane bending tests on three 90° single un-reinforced mitred pipe bends, with the results from various 3D solid finite element models. The bending load applied reduced the bend angle and in turn, the resulting cross-sectional ovalisation led to a recognised weakening mechanism. In addition, at maximum load there was a reversal in stiffness, characteristic of buckling. This reversal in stiffness was accompanied by significant ovalisation and plasticity at the mitre intersection. Both the weakening mechanism and the post-buckling behaviour are only observable by testing or by including large displacement effects in the plastic finite element solution. A small displacement limit solution with an elastic-perfectly plastic material model overestimated the collapse load by more than 40% and could not reproduce the buckling behaviour.     

R&D of the ground-coupled heat pump technology in China

The ground-coupled heat pump (GCHP) systems have been identified as one of the best sustainable energy technologies for space heating and cooling in residential and commercial buildings. In this paper, research on and development of the GCHP technology in China are summarized. New models are presented for efficient thermal analysis of ground heat exchangers, of which one- and two-dimensional solid cylindrical source models and their analytical solutions are devised to deal with pile ground heat exchangers. Analytical solutions are also derived for vertical and inclined finite line source models as well as for a groundwater advection model. Explicit solutions of a quasi-three-dimensional model can be used to better evaluate the thermal resistance inside boreholes. Studies on hybrid GCHP systems and the thermal response test in China are also commented.     

R&D of the ground-coupled heat pump technology in China

The ground-coupled heat pump (GCHP) systems have been identified as one of the best sustainable energy technologies for space heating and cooling in residential and commercial buildings. In this paper, research on and development of the GCHP technology in China are summarized. New models are presented for efficient thermal analysis of ground heat exchangers, of which one- and two-dimensional solid cylindrical source models and their analytical solutions are devised to deal with pile ground heat exchangers. Analytical solutions are also derived for vertical and inclined finite line source models as well as for a groundwater advection model. Explicit solutions of a quasi-three-dimensional model can be used to better evaluate the thermal resistance inside boreholes. Studies on hybrid GCHP systems and the thermal response test in China are also commented.     

Thermal–structural analysis of large deployable space antenna under extreme heat loads

Large deployable space antennas may be exposed to severe thermal environments in future space missions; extreme heat loads will result in considerable thermal stresses and deformations which seriously affects the accuracy of the antenna's parabolic surface. In this study, thermal–structural finite element analysis of a deployable AstroMesh antenna under extreme heat loads was presented. Considering position and orientation with respect to the Sun and Earth, the antenna's temperature changing law under orbital heat fluxes was first evaluated to find the worst condition as loading point. Analyses for the antenna under different levels of extreme heat loads were then performed to obtain the temperature distributions utilizing an equivalent quarter antenna model. Based on the temperature calculation results and prestress designs, structural analyses were finally made to gain the resulting stresses and deformations. The analysis results show that the existing antenna may generate significant performance distortion under extreme thermal environments; so attentions for reliability and safety under such conditions should be taken seriously in future antenna works. Modeling and analysis method proposed in this article was validated to be contributive in antenna's thermal and precompensation designs.     

Quantifying wave and yaw effects on a scale tidal stream turbine

The behaviour of Tidal Stream Turbines (TST) in the dynamic flow field caused by waves and rotor misalignment to the incoming flow (yaw) is currently unclear. The dynamic loading applied to the turbine could drive the structural design of the power capture and support subsystems, device size and its proximity to the water surface and sea bed. In addition, the strongly bi-directional nature of the flow encountered at many tidal energy sites may lead to devices omitting yaw drives; accepting the additional dynamic loading associated with rotor misalignment and reduced power production in return for a reduction in device capital cost. Therefore it is imperative to quantify potential unsteady rotor loads so that the TST device design accommodates the inflow conditions and avoids an unacceptable increase in maintenance action or, more seriously, suffers sudden structural failure.The experiments presented in this paper were conducted using a 1:20th scale 3-bladed horizontal axis TST at a large towing tank facility. The turbine had the capability to measure rotor thrust and torque whilst one blade was instrumented to acquire blade root strain, azimuthal position and rotational speed all at high frequency. The maximum out-of-plane bending moment was found to be as much as 9.5 times the in-plane bending moment. A maximum loading range of 175% of the median out-of-plane bending moment and 100% of the median in-plane bending moment was observed for a turbine test case with zero rotor yaw, scaled wave height of 2 m and intrinsic wave period of 12.8 s.A new tidal turbine-specific Blade-Element Momentum (BEM) numerical model has been developed to account for wave motion and yawed flow effects. This model includes a new dynamic inflow correction which is shown to be in close agreement with the measured experimental loads. The gravitational component was significant to the experimental in-plane blade bending moment and was also included in the BEM model. Steady loading on an individual blade at positive yaw angles was found to be negligible in comparison to wave loading (for the range of experiments conducted), but becomes important for the turbine rotor as a whole, reducing power capture and rotor thrust. The inclusion of steady yaw effects (using the often-applied skewed axial inflow correction) in a BEM model should be neglected when waves are present or will result in poor load prediction reflected by increased loading amplitude in the 1P (once per revolution) phase.     

Elementary solutions for the propagation of ovalization along straight pipes and elbows

This paper presents an extension of the classical Von Karman's theory for the calculation of the flexibility factor of a pipe bend terminated by a straight pipe or a flange. The analysis is restricted to the linear elastic deformation behavior under in-plane bending, for elbows with specific geometric features. The propagation of ovalization is investigated both in the straight part and in the elbow. The results are presented in terms of global as well as local flexibility factors. They have been compared with computational results and other published theories.