Thermal Bending Moments Research Articles

Thermo-Mechanical Jitter in Slender Space Structures: A Simplified Modeling Approach

Thermally induced vibrations usually affect spacecraft equipped with light and slender appendages such as booms, antennas or solar panels. This phenomenon occurs when a thermal shock, resulting from the sudden cooling and warming phases at the entrance and exit from eclipses, triggers mechanical vibrations. The study proposed hereafter concerns the modeling and prediction of jitter of thermal origin in a long and thin plate with a sun-pointing attitude in geostationary orbit. The system’s temperature and dynamics are described by a set of equations expressing the two-way coupling between the thermal bending moment and the shape of the panel. The structure is discretized and reduced to a one-degree-of-freedom simplified model able to identify a mechanism of thermal pumping that could lead to instability. Finally, the results of the analysis are compared with those obtained with a more accurate FEM modelization.

Numerical and experimental studies on the thermodynamic characteristics of post-buckling separate plate in the clutch

Considering the influence of the contact and friction for buckling deformation, a comprehensive model is proposed to study the timing-varying thermodynamic characteristics of the clutch. The mathematical model is developed to calculate the contact status of the post-buckling separate plate, which is testified by the finite element method and bench experiments. The post-buckling plate undergoes a five-stage deformation, and the radial contact pressure finally forms ‘M/W′ shape during engagements. With the increasing buckling angle, the plate flattening threshold and pressure decay increase gradually; meanwhile, the radial temperature distribution is sculptured as ‘W′ shape, creating larger thermal stress and thermal bending moment. Thus, the surface morphology is changed by the wear which related to the pressure and thermal distribution.

Nonlinear Deformation Model for Analysis of Temperature Effects on Reinforced Concrete Beam Elements

The results of the study are aimed at developing a nonlinear strain model for reinforced concrete beam elements in the general case of force actions and temperature effects for different durations. As a rule, temperature effects on structures involve temperature drops, causing heterogeneity of mechanical and rheological properties of concrete and reinforcement. The article has approximating expressions needed to take into account the effects of temperature and heating time on the values of temperature-induced strain and mechanical and rheological properties of heavy concretes with C30–C60 strength classes. The properties of concrete and rebars are heterogeneous from top to bottom and across the width of the cross section. A physically nonlinear problem is solved using the method of elastic solutions combined with the method of stepwise increases in temperature and force loading. The cooling of a heated reinforced concrete element to normal temperature is considered a short-term effect. Strength criteria of portions of a concrete cross section, crack closure conditions, and the ability of cracked sections to take loads in compression amid a change in the sign of stresses are determined. The stress–strain state (SSS) analysis of reinforced concrete beams, made according to the proposed method, is compared with the experimental studies using (i) values of thermal bending moments in statically indeterminate structures, (ii) cracking forces, and (iii) values of deformations (elongations and curvatures) of the elements in the longitudinal axis. Good agreement between the calculated and experimental values of controllable criteria confirms the reliability of physical relationships (i) developed for heterogeneous reinforced concrete beam elements and (ii) applied to the complex cases of temperature and force effects.

A Thin Elastic Plate Model for Thermally Contracting Young Oceanic Lithosphere: Insights From Comparison With Modern Seafloor Observations

AbstractWe find at fast‐ and intermediate‐spreading seafloor that their ridge‐parallel bathymetric profiles between two neighboring fracture zones, excluding the part of the seafloor inward to fracture zone (FZ) valley, are predominantly upward concave. The temporal evolution of the bathymetric profiles from the lithosphere formed at the Chile Rise is characterized by (a) the rapid growth of the middle deflection to about 200 m relative to the ends for the first few millions of years and (b) a steady state afterward. We show that these characteristics and the upward‐concave sense of bending can be reasonably explained as the flexure of a thin elastic plate contracting thermally from the top while cooling. The best‐fitting model needs only about 10% of the thermal bending moment based on the half‐space cooling model and the free‐end assumption. Our model is consistent with the recent observations that oceanic lithosphere is cut open at a FZ valley, which disprove the previous assumption that ocean floor is bent down forming the valley walls.

On the use of negative thermal expansion engineered structures in flexural-mode solid-state thermoacoustics

Recent numerical studies have shown evidence of self-sustained oscillations in solids due to externally-applied spatial thermal gradients. In analogy with its acoustic counterpart in gases, this phenomenon was dubbed solid-state thermoacoustics (SSTA). Such heat-driven oscillation can give rise to either longitudinal or flexural motion, depending on the specific design of the system. Although an experimental proof of self-sustained motion in flexural-mode SSTA (F-SSTA) devices has yet to be produced, previous experimental studies pointed to the reduction of the effective damping as a clear indicator of the thermo-mechanical energy conversion process at the core of the F-SSTA mechanism. The F-SSTA theory suggested that negative thermal expansion (NTE), which is not a common property in natural materials, offers a remarkable opportunity to enhance the F-SSTA instability. The present study explores a design approach that leverages the unique features afforded by the solid state design in order to improve the overall performance of F-SSTA’s devices and reduce the technological gap to achieve, in a near future, a successful experimental validation. The proposed design approach leverages a hybrid bilayer beam concept where one of the two layers is designed to exhibit NTE properties. More specifically, the NTE layer is composed of a bi-material octet truss that contracts in the axial direction upon heating. This axial contraction is particularly beneficial to induce a strong thermal bending moment that ultimately enhances the F-SSTA instability. In addition, this work also furthers the conceptual understanding of the F-SSTA process by presenting an analytical perturbation energy budget developed on the basis of a simplified discrete model. These theoretical considerations provide new important insights in the energy conversion mechanism at the basis of the F-SSTA process, hence helping reducing the gap of knowledge towards a successful experimental realization of the F-SSTA effect. • Improved performance of F-SSTA systems via architectured NTE materials. • Identification of parameters controlling the flexural thermoacoustic instability. • A simplified analytical energy budget to understand the energy conversion mechanism.

Study on the influence of localised thermal load on collapse strength of stiffened panels under longitudinal compression

The purpose of the present study is to investigate the influences of localised thermal stress on the load carrying capacity of stiffened panels under in-plane compression. The thermal loads and bending moment caused by extreme water wave seldom occur at the same time, hence, which are applied on ship structures in two load steps separately in the finite element (FE) analysis. Firstly, the stress state and structural responses of the stiffened panels under localised thermal loads with different heating zone ranges are discussed. Subsequently, the collapse behaviours of the stiffened panels under in-plane compression are simulated, in which the residual thermal stress due to the thermal loads is also included. The influences of residual thermal stress, areas of heating zone and boundary conditions on the collapse behaviours are investigated. It is found that the thermal loads could cause biaxial stress state that can reduce the load carrying capacity of the stiffened panels, which should be considered in the development of assessment formula of residual ultimate strength for ship structure design.

Large deformation behavior of functionally graded porous curved beams in thermal environment

The in-plane thermoelastic response of curved beams made of porous materials with different types of functionally graded (FG) porosity is studied in this research contribution. Nonlinear governing equations are derived based on the first-order shear deformation theory along with the nonlinear Green strains. The nonlinear governing equations are solved by the aid of the Rayleigh–Ritz method along with the Newton–Raphson method. The modified rule-of-mixture is employed to derive the material properties of imperfect FG porous curved beams. Comprehensive parametric studies are conducted to explore the effects of volume fraction and various dispersion patterns of porosities, temperature field, and arch geometry as well as boundary conditions on the nonlinear equilibrium path and stability behavior of the FG porous curved beams. Results reveal that dispersion and volume fraction of porosities have a significant effect on the thermal stability path, maximum stress, and bending moment at the crown of the curved beams. Moreover, the influence of porosity dispersion and structural geometry on the central radial and in-plane displacement of the curved beams is evaluated. Results show that various boundary conditions make a considerable difference in the central radial displacements of the curved beams with the same porosity dispersion. Due to the absence of similar results in the specialized literature, this paper is likely to provide pertinent results that are instrumental toward a reliable design of FG porous curved beams in thermal environment.

ANLYTICAL SOLUTION OF THERMOELASTIC DAMPING IN RECTANGULAR MINDLIN MICRO PLATES

Analytical solution of thermoelastic damping for rectangular Mindlin micro plate with the four edges simply supported is presented for the first time. Based on the Mindlin plate theory and the one-way coupled heat conduct theory, governing differential equations for thermo-elastically coupled free vibration of the micro plate are formulated. Ignoring the in-plane variation of the temperature gradient, analytical solution of temperature field in terms of the kinematic parameters is obtained under the adiabatic boundary conditions at the top and bottom surfaces. Furthermore, the equations of structural vibration including the thermal bending moment are transformed into a fourth-order partial differential equation only in terms of the deflection. By using the mathematical similarity between the eigenvalue problems under the simply supported boundary conditions, analytical solution of the complex natural frequency of the Mindlin plate is expressed in terms of the frequency of isothermal Kirchhoff plate. Then the inverse quality factor which represents the level of the thermoelastic damping is obtained. Finally, the effects of the shear deformation, the material and the geometry parameters on the thermoelastic damping are examined in detail by the numerical results. The numerical results show that thermoelastic damping estimated by Mindlin plate theory is less than that by Kirchhoff plate theory. The difference between the values evaluated by the two plate theories becomes very significant near the critical thickness. Moreover, along with the increase of the side-to-thickness aspect ratio,the maximum of the thermoelastic damping in micro Mindlin plate increase monotonically, however, that of micro Kirchhoff plate keeps constant.

Analytical solution of heat conduction of a multilayered annular disk and associated thermal deflection and thermal stresses

In this article, a three dimensional multilayered annular disk with internal heat generation under unsteady temperature distribution is considered. Finite integral transform method is used to eliminate the partial derivatives with respect to r, while Fourier series and Fourier transform are used to deal with the variables and z, respectively. Exact solution for the temperature distribution is obtained. The thermal bending moments, thermal deflection and the resulting thermal stresses are obtained and analyzed. The results obtained in series form are numerically evaluated and analyzed by using graphical illustrations.

Stability of the Bernoulli–Euler Beam under the Action of a Moving Thermal Source

In this work, the problem of the propagation of a deflection wave in a Bernoulli–Euler beam during motion of the thermal source is solved, and the influence of the thermal bending moment and longitudinal force is analyzed. It has been established that the concentrated bending moment moving together with the heated region boundary determines the mode of the deflection wave, but cannot lead to a significant increase in its amplitude. It is shown that the average longitudinal compressive force increases linearly with time during uniform motion of the heating source. For the initial parameters, such as the source motion velocity and the temperature, the values enabling a loss of stability and a significant increase in deflection have been found.

Numerical study on thermal deformation behaviors of the single subassembly in sodium-cooled fast reactors based on Euler-Bernoulli beam theory

Due to the special geometry and compact arrangement of subassemblies in the sodium-cooled fast reactor, thermal deformation of the assemblies are easily triggered by uneven temperature distribution in the reactor core, which is negative for reactor safety. Therefore, it is necessary for researchers and engineers to conduct quantitative analysis towards thermal deformation behaviors of subassemblies, and furthermore, give reliable evaluation results on aftermath of the assembly thermal deformation. In the present study, thermal deformation analysis code FADAC, which was developed based on Euler-Bernoulli beam theory, was applied to make numerical investigation for thermal deformation behaviors of a single subassembly in sodium-cooled fast reactor. In order to preliminarily assess the capacity for thermal deformation, different temperature gradient conditions were considered and analyzed in detail for free bowing of the subassembly, furthermore, with the aid of numerical analysis for thermal axial forces and thermal bending moments, axial displacements and deflections were calculated finally. Besides, in order to predict the comprehensive results of the assembly deformation under both thermal load and mechanical load, restrained bowing were also analyzed for different temperature conditions. All of the simulation results were in good accordance with the experimental data. The present numerical research is of great significance to assembly deformation research in the sodium-cooled fast reactor, and will surely lay a solid foundation for deformation analysis towards multi-subassemblies.

An Analysis of Thermal-Bending Stresses in a Simply Supported Thin Elliptical Plate

In this paper, a transient thermal stress investigation on a simply supported thin elliptical plate during sectional heating with time-dependent temperature supply is considered. The solution of heat conduction equation with corresponding initial and boundary conditions is obtained by employing an integral transform approach. The governing equation solution for the small deflection theory is obtained and utilized to preserve the intensities of thermal bending moments, involving the Mathieu and modified functions and its derivatives. The deflection results show an approximately good agreement with the previously given results. It is also demonstrated that the temperature field in a circular solution could be resulted in a particular case of the present mathematical solution. The obtained numerical results utilizing computational implements are precise enough for practical purposes.

Analysis of the thermo-elastic vibration for axially moving Euler beam

The thermo-elastic vibration response of simple supported axially moving Euler beam is investigated. The differential equation of moving beam is established by recourse to Hamilton principle and the thermal effects is considered by introducing the equivalent thermal bending moment. A 2-D transient temperature field is calculated by the alternating-directional implicit (ADI) method and the equivalent thermal moment is calculated numerically. The dimensionless equation is discretized by Galerkin method and the modal analysis of gyroscopic system is used to calculate the forced vibration response. The time-history curve of the beam’s upper middle point is obtained for thermal or non-thermal situations.

Transient thermal stresses of annulus elliptical plate with mixed-type boundary conditions.

In this paper, we deal with transient thermal stress problem of an annulus elliptical plate subjected to internal heat source with mixed-type boundary conditions. The solution of conductivity equation and the corresponding initial and boundary conditions are obtained by employing anew integral transform technique.The governing equation for small deflection is found and utilized to find intensities of thermal bending moments and twisting moments, etc. involving Mathieu and modified functions and their derivatives. The analytical solution for the thermal stress components are obtained in terms of resultant forces and resultant moments, and same are illustrated graphically.

Heat source problem of thermoelasticity in an elliptic plate with thermal bending moments

ABSTRACTThe principal aim of this article is to investigate the thermoelastic problems on an elliptical plate in which interior heat sources are generated within the solid, with compounded effect due to sectional heating and boundary conditions of the Dirichlet type. The analysis is based on the small-deflection theory of the elliptical plate and performed in the elliptical coordinate system. In addition, the intensities of bending moments, twisting moments, etc., are formulated involving the Mathieu and modified functions and their derivatives. The analytical solution for the thermal stress components is obtained in terms of resultant forces and resultant moments.

Investigation on attitude disturbance control and vibration suppression for fuel-filled flexible spacecraft

This paper is mainly focused on the attitude dynamics and control of a fuel-filled flexible spacecraft subjected to the thermal payload during eclipse transitions. The flexible appendages are considered as Euler–Bernoulli beams, and the sloshing liquid is modeled as in two modes multi-spring-mass models; the governing equations of this coupled system are developed by using Hamilton’s principle. Numerical results show that the spacecraft attitude responses consist of a quasi-static displacement and superimposed vibration. Then, we design an adaptive sliding mode and use the Lyapunov approach control law to control the attitude disturbance and suppress the thermal jitter and liquid sloshing for the fuel filled flexible spacecraft subject to the thermal payload. Numerical results are presented to verify the efficiency of the hybrid control methods. The results show that the adaptive sliding mode method might be effective to handle the steady-state errors and the Lyapunov control algorithm would suppress the residual vibration. The attitude dynamics control and vibration suppression are investigated for a fuel-filled spacecraft with single solar panel subjected to thermal bending moment during eclipse transitions.

On thermal instability of delaminated composite plates

This paper examines the thermal instability of rectangular delaminated composite plates. A solution procedure is presented based on the third-order shear deformation theory by taking into consideration the von Karman geometrical nonlinearity. The proposed model is capable of analyzing both local buckling of the delaminated base laminate and sublaminate as well as the global buckling of the plate. The thermomechanical properties are temperature-dependent. The nonlinear equilibrium equations, derived by the minimum total potential energy principle, are solved by using the Ritz method along with the Newton–Raphson iterative procedure. Numerical results shed a light on the effects of embedded delamination, stacking sequences, and boundary conditions on the equilibrium path, thermal bifurcation points, buckling mode, in-plane displacement, normal/shear strain, and bending moment of the composite plates. It is found that the delamination leads to a substantial reduction in the thermal load-carrying capacity. Furthermore, depending on the boundary conditions and stacking sequence, the response of the perfect composite plates could be either of the bifurcation type or of the unique stable path.

Reduction of Thermal Stress Induced in a Steel Plate Strengthened by Bonded Aluminum-CFRP Composite

In steel members strengthened with carbon-fiber reinforced polymer (CFRP) plate, thermal stresses are introduced in the steel members, the CFRP plates and the adhesive layers when temperature changes because the linear thermal expansion coefficients of steel and CFRP are mismatched. Therefore, the thermal stress caused by temperature change has to be considered when designing the repair or strengthening of a steel member with CFRP plates. With this in mind, the authors proposed a technique to reduce thermal stress in steel members strengthened by CFRP plate on both side, which involves bonding aluminum alloy plates with CFRP plates. In this proposed method, the thermal stresses in steel member can be reduced so that there are negligible levels of stress when the cross sectional areas of CFRP and aluminum plates are designed to correspond the coefficient of thermal expansion of steel, even though the thermal stresses are introduced in the CFRP and aluminum plates. So far, a thermal bending moment was not considered in the proposed method, because the steel members strengthened by CFRP-aluminum laminated plate on top and bottom sides were assumed. However, if the proposed method is applied on one side of steel member, the thermal stress in the steel member might not be reduced completely by generated thermal bending moment. Therefore, to confirm the effectiveness of the proposed method for one-sided bonding, heat tests were conducted on a steel plate with a laminated plate bonded on one side. Additionally, to verify test results and calculate the shear and peel stresses in the adhesive layers, a numerical model that used Eigenvalue analysis was proposed and applied. The tests revealed that using the proposed method to create a two-layered laminated plate consisting of CFRP and aluminum plates could not reduce the thermal stress completely in a thin steel plate. However, it was found that the thermal stress in steel plate can be completely reduced, even in thin steel plate, when the proposed method is used to create a three-layered laminated plate consisting of one CFRP plate between two aluminum plates, which when composited has a thermal bending moment equal to zero.

Dynamic Analysis of Space Structure Deployment with Transient Thermal Load

Thermal load is non-ignorable in the design and analysis of high precision and reliable space deployable structures. A new approach based on flexible multibody system is presented in order to investigate the thermoelastic effect on the deployment of space structure. Dynamic equations of an Euler Bernoulli beam element with transient thermal load are derived in Absolute Nodal Coordinate Formulation. The temperature distribution in the beam section is assumed as linear, which is reasonable for slender beams. The resulting generalized thermoelastic forces can be decomposed into thermal axial force and thermal bending moments, which can cause tension/compression and bending of the beam respectively. The dynamic equations of the beam element are then assembled into a flexible multibody system. Deployment analysis of a space mechanism with transient thermal load is studied with the new approach. Simulation result shows that thermoelasticity could cause static deformation of the final configuration as well as affect the external driving forces.

Vibration analysis of horizontal self-weighted beams and cables with bending stiffness subjected to thermal loads

Abstract This paper aims at proposing an analytical model for the vibration analysis of horizontal beams that are self-weighted and thermally stressed. Geometrical nonlinearities are taken into account on the basis of large displacement and small rotation. Natural frequencies are obtained from a linearization of equilibrium equations. Thermal force and thermal bending moment are both included in the analysis. Torsional and axial springs are considered at beam ends, allowing various boundary conditions. A dimensionless analysis is performed leading to only four parameters, respectively, related to the self-weight, thermal force, thermal bending moment and torsional spring stiffness. It is shown that the proposed model can be efficiently used for cable problems with small sag-to-span ratios (typically 1 8 , as in Irvine's theory). For beam problems, the model is validated thanks to finite element solutions and a parametric study is conducted in order to highlight the combined effects of thermal loads and self-weight on natural frequencies. For cable problems, solutions are first compared with existing results in the literature obtained without thermal effects or bending stiffness. Good agreement is found. A parametric study combining the effects of sag-extensibility, thermal change and bending stiffness is finally given.