Thermal bending of thick rectangular plates

An analysis with a shear deformation capability for the thermal bending of thick rectangular plates is presented. Formulation of the problem, with appropriate thermal terms incorporated and applicable to the bending of moderately thick plates, has been carried out by using Reissner's plate bending theory. Representative plate bending problems have been considered for illustrating the procedure. Numerical results obtained indicate that thick plate solutions to thermal problems deviate from those of the classical theory in practically the same manner as with mechanical loading cases.     

Thermal stresses in an orthotropic rectangular plate with a rigid ribbonlike inclusion

On the basis of the complex variable method for determining the stationary two-dimensional thermal stresses, the thermal stresses in an orthotropic rectangular plate with a rigid ribbonlike inclusion under a steady state temperature field is considered. The solution is found by the analytic continuation argument and the modified mapping-collocation technique. Numerical results indicate a dependence of the orthotropic stress intensity factors on the thermal, elastic and geometrical constants over a certain parameter range     

Reduced and selective integration techniques in the finite element analysis of plates

Efforts to develop effective plate bending finite elements by reduced integration techniques are described. The basis for the development is a ‘thick’ plate theory in which transverse shear strains are accounted for. The variables in the theory are all kinematic, namely, displacements and independent rotations. As only C⁰ continuity is required, isoparametric elements may be employed, which result in several advantages over thin plate elements. It is shown that the avoidance of shear ‘locking’ may be facilitated by reduced integration techniques. Both uniform and selective schemes are considered. Conditions under which selective schemes are invariant are identified, and they are found to have an advantage over uniform schemes in the present situation. It is pointed out that the present elements are not subject to the difficulties encountered by thin plate theory elements, concerning boundary conditions. For example, the polygonal approximation of curved, simply-supported edges is convergent. Other topics discussed are the equivalence with mixed methods, rank deficiency, convergence criteria and useful mass ‘lumping’ schemes for dynamics. Numerical results for several thin plate problems indicate the high degree of accuracy attainable by the present elements.     

Transient thermal stresses in an orthotropic finite rectangular plate due to arbitrary surface heat-generations

The transient thermal stresses in an orthotropic finite rectangular plate due to arbitrary surface heat-generations on two edges are studied by means of the Airy stress function.The purposes of this paper are to present a method of determining the transient thermal stresses in an orthotropic rectangular plate with four edges of distinct thermal boundary condition of the third kind which exactly satisfy the traction-free conditions of shear stress over all boundaries including four corners of the plate, and to consider the effects of the anisotropies of material properties and the convective heat transfer on the upper and lower surfaces on the thermal stress distribution.     

A comparison of closed-form and finite-element solutions of thick laminated anisotropic rectangular plates

In this study the effects of reduced integration, mesh size, and element type (i.e. linear or quadratic) on the accuracy of a penalty-finite element based on the theory governing thick, laminated, anisotropic composite plates are investigated. In order to assess the accuracy of the present finite element, exact closed-form solutions are developed for cross-ply and antisymmetric angle-ply rectangular plates simply supported and subjected to sinusoidally distributed mechanical and/or thermal loadings, and free vibration.     

A finite element method for neutron transport. Part IV: A comparison of some finite element solutions of two group benchmark problems with conventional solutions

The one group finite element formulation of the neutron transport equation is adapted to treat multigroup shielding problems. The method is extended to eigenvalue problems by using a source iteration technique. The results for one-dimensional two group shielding problems show that the finite element method is fast and accurate; in the case of transport problems the solutions are free from the ray defects often found with discrete ordinate methods. Results for eigenvalue problems show that the method, when compared with discrete ordinate and collision probability methods and with diffusion theory in appropriate cases, is again fast and accurate. In the majority of cases, approximate values of the lowest eigenvalue when plotted against the reciprocal of the square number of nodes, lie very close to a straight line; consequently a very good estimate of the benchmark eigenvalue can often be found with coarse finite element methods. The results for two group problems have shown that the accuracy and speed achieved for the corresponding one group benchmark problems are maintained. These results and those of Part III, for the two-dimensional two region one group problems indicate that the finite element method is promising for the multigroup two dimensional problems. For both sets of results the finite element representation is used for the spatial dependence of the angular flux. The directional dependence of the angular flux is treated by expansions: either the Spherical Harmonics, the continuous representation; or Walsh Functions, the discrete representation. Walsh Functions do not appear to have any particular advantage over Spherical Harmonics. In the case of one dimension when the Spherical Harmonics reduce to Legendre functions, they are superior to Walsh Functions.     

Thermal stress singularities at tips of a Griffith crack in a finite rectangular plate

This paper is concerned with a method for calculating the thermal stresses in a finite rectangular plate with a Griffith crack under a steady state temperature field. In the analysis, based on the complex variable method for determining the stationary two-dimensional thermal stresses, the analytic continuation and the modified mapping-collocation methods are effectively employed. Numerical calculations for the strength of thermal stress singularity of the symmetric and the skew-symmetric types are carried out, and the results are shown in graphs.     

Thermal stresses in reactor constructions

Conditions for the appearance of thermal stresses in reactors are investigated; also their magnitude and the danger they create are estimated. The influence of the form of the heat-generating elements (HGE) on the temperature drop and magnitudes of thermal stresses is analyzed; recommendations are given with the aim of decreasing the harmful effect of thermal stresses.The methods from the theory of elasticity employed in the calculation of thermal stresses have significant limitations. In many cases when estimating the magnitude and degree of danger created by the thermal stresses, when combining such stresses with mechanical stresses, and also when seeking a way to decrease them, other effects such as fluidity, creep, initial breakdown, and microscopic processes must be taken into consideration.     

Thermal and mechanical stresses in nuclear reactor vessels

This paper is concerned with stress and deformation analysis of a circular cylindrical, thin, elastic shell, representing a nuclear reactor vessel, with an insulated cutout of arbitrary shape subjected to mechanical and thermal loads. The analysis is based on the method of superposition. The actual stresses in the shell may be considered as the sum of the following two parts:

1.

(a) Stresses caused by the given heat flow and mechanical loads in a similar shell without a hole (nominal stress solution);     

Thermal and gravity stresses in hyperboloidal cooling towers

Nuclear power plants usually require particularly large cooling towers, the design of which necessitates detailed analyses of the structural behavior under thermal and mechanical loadings.Thermal stresses are obtained in this paper for a reinforced hyperboloidal cooling tower for a wide range of foundation constants. The temperature field in the tower is assumed to be asymmetric with a linear variation through the thickness of the tower and an arbitrary variation along the height. The effects of the weight of the tower are included. The reinforcing material is assumed to have an equivalent orthotropic distribution along meridional and circumferential coordinate lines, and it is taken to be symmetrically located relative to the middle surface of the tower. The partial differential equations of equilibrium of the tower are based upon thin elastic shell theory and utilize the Love-Kirchhoff approximation. Fourier expansions in the circumferential variable are used to reduce these equations to ordinary differential equations in the meridional variable. Numerical solutions to the ordinary differential equations are obtained by the finite element subdomain collocation method.Numerical results are presented for thermal stresses in the Beaver Valley Station cooling tower for assumed temperature distributions on the inner and outer tower surfaces. The results show that the difference in temperature distributions on the inner and outer tower surfaces gives rise to significant thermal stresses in the tower. An example of a hot spot on a cylindrical shell is also presented. The analysis is particularly applicable to reinforced concrete cooling towers with hot spots.     

Thermal stresses in heterogeneous thick isotropic shells

The application of a thick shell theory in the design of nuclear pressure vessels is given. A derivation for thick shells of revolution with the inclusion effects of transverse shear stress and normal stress, in which the Young's modulus is considered dependent on temperature, is presented. The set of equations so obtained are solved by a numerical integration method. The example of a spherical shell is solved and the results compared with the case in which the Young's modulus is assumed to be constant. It is shown that under large temperature gradients through the thickness, the change in deflections and stresses can be significant, if the present derivation is used.     

Thermal stresses in the Space Shuttle Orbiter: Analysis versus test

Significant temperature differences occur between the internal structure and the outer skin of the Space Shuttle Orbiter as it returns from space. These temperature differences cause important thermal stresses. A finite element model containing thousands of degrees of freedom is used to predict these stresses. A ground test was performed to verify the prediction method. The analysis and test results compare favorably.     

Thermal transient and the temperature profile in a HELICA mock-up simulated by a new finite element homogenous model

This paper deals with a numerical approach for simulating the thermal and mechanical behaviour of pebble beds used as breeder and neutron multiplier in breeding blanket of nuclear fusion reactor. The model of the pebble beds is based on the results of a theoretical and experimental research activity performed by the Authors on ceramic pebble beds (lithium ortosilicate and lithium metatitanate). The results of this activity permitted to determine the effective thermal conductivity of the beds, versus the temperature and the axial pressure and to implement a homogenous model of pebble bed in a FEM code.This paper illustrates an application of the implemented model, considering pebble beds under several cycles of heating and cooling. The examined geometry corresponds to the HELICA mock-up tested by ENEA in the research centre Brasimone. The experimental tests performed on HELICA have been used as a benchmark problem in order to assess the different approaches for simulating pebble beds. In this paper, the simulations performed with two-dimensional models are illustrated. Moreover the numerical results are compared with the experimental ones. Finally, a discussion on results obtained by other authors involved in the benchmark is reported.     

Thermal stresses around circular holes in spherical shells

The thermal stress problem of a circular hole in a spherical shell of uniform thickness is solved by using a continuum approach. The influence of the hole is assumed to be confined to a small region around the opening. The thermal stress problem is converted as usual to an equivalent boundary value problem with forces specified around the cutout. The stresses and displacement are obtained for a linear variation of temperature across the thickness of the shell and presented in graphical form for ready use.     

Soil-structure interaction: Continuum or finite element?

A survey of both the continuum and the finite element approaches to the soil-structure interaction problem is made. The limitations and advantages of both methods are evaluated with an emphasis on the present state of the art. Some recommendations are made regarding the circumstances under which either approach should more appropriately be used.     

Finite deflection and postbuckling behavior of heated rectangular plates with temperature-dependent properties

Finite deflections and postbuckling behaviors of heated rectangular elastic plates are analyzed. Governing field equations and admissible boundary conditions are derived by variational principles for an elastic material with thermal effects. Temperature-dependent mechanical and thermal properties of plate are considered and their effect on the deflection is discussed. Numerical results are shown for two kinds of boundary conditions and temperature distributions.     

Thermal stresses in cylindrical shells based on improved theory

The thermal stresses in cylindrical shells subjected to local heating are studied by using the equations which include the effects of shear deformation. Developing the theory along lines identical to the Donnell-type formulation, the fundamental equation in terms of a single displacement containing the correction terms due to shear deformation and the thermal effects is found. The solutions for a finite cylindrical shell subjected to local heating are obtained using the Fourier transform method. The effects of the shear deformation on the thermal displacements and stresses are discussed by a comparison with the results due to the classical theory.     

Finite element analysis of thick annular and sector plates

A finite element displacement formulation based on Reissner's thick plate theory is presented for the bending analysis of annular and sector plates. An annular element and an annular sector element, associated with six and twenty degrees of freedom, respectively, are developed. One of the significant features of these elements, which include both bending and shear deformation effects and which conform with respect to all degrees of freedom considered, is the ability to satisfy exactly the condition of vanishing shear stress resultant along a free edge. Numerical results are presented for substantiating the proposed procedure.     

Predicting welding residual stresses in a dissimilar metal girth welded pipe using 3D finite element model with a simplified heat source

Dissimilar metal welds are commonly used in nuclear power plants to connect low alloy steel components and austenitic stainless steel piping systems. The integrity assessment and life estimation for such welded structures require consideration of residual stresses induced by manufacturing processes. Because the fabrication process of dissimilar metal weld joints is considerably complex, it is very difficult to accurately predict residual stresses. In this study, both numerical simulation technology and experimental method were used to investigate welding residual stress distribution in a dissimilar metal pipe joint with a medium diameter, which were performed by a multi-pass welding process. Firstly, an experimental mock-up was fabricated to measure the residual stress distributions on the inside and the outside surfaces. Then, a time-effective 3-D finite element model was developed to simulate welding residual stresses through using a simplified moving heat source. The simplified heat source method could complete the thermo-mechanical analysis in an acceptable time, and the simulation results generally matched the measured data near the weld zone. Through comparing the simulation results and the experimental measurements, we can infer that besides the multi-pass welding process other key manufacturing processes such as cladding, buttering and heat treatment should also be taken into account to accurately predict residual stresses in the whole range of the dissimilar metal pipe.