Discontinuity Stresses Research Articles

Analysis of discontinuity stress at shell and elliptical head juncture using theory of beam on elastic foundation

A thin-walled pressure vessels under internal pressure generates higher amount of stresses at shell-head juncture compared to membrane stress. These localized stresses are generated due to change in the shape of the meridian. The change in shape of the meridian is seen at the head and shell junction. The discontinuity in shape changes the direction of resultant stress. To predict the accurate stresses around the discontinuity region, bending of beam on an elastic foundation is used as part of the analytical analysis. Charts have been plotted of various stresses generated near juncture. The method is applied to pressure vessel with cylindrical shell and elliptical head. The theoretical results are then compared to the analytical results obtained from finite element analysis (FEA). In the present work, the discontinuity stresses have been evaluated analytically and the same is also compared with the finite element analysis results. It is found that the results of FE analysis closely agrees with the analytical results maximum percentage variation of 1.19.

Strength and stability of spherical-conical shell assemblies under external hydrostatic pressure

Abstract Thin shells are increasingly finding new applications under the sea. In this study, we consider a thin-walled shell-of-revolution assembly comprising a deep spherical shell dome (deeper than a hemisphere) axisymmetrically and tangentially joined to a steep-sided conical shell, the whole being a closed shell structure intended for stationary deployment beneath the surface of the sea in relatively shallow water. The closed shell structure, which might serve as an underwater observatory, is intended to operate at a constant depth, anchored to the seabed against flotation forces, with the thin steel shell walls being required to withstand the external hydrostatic pressure of the surrounding water. We use shell theory to investigate the discontinuity stresses that occur at the junction of the spherical shell and the conical shell, and employ FEM to explore the buckling behaviour of the thin shell. While discontinuity stresses are relatively small, they may influence the lower buckling modes of the shell, which are found to be largely confined to the region of the cone that is adjacent to the junction. Considerations are extended to a doubly-curved variant of the cone in the form of a paraboloid of revolution. As expected, double curvature enhances buckling capacity and also influences the mode shapes.

Material and residual stress considerations associated with the autofrettage of weld clad components

A fatigue-resistant cladding concept confirms the presence of compressive residual stresses in a cylinder weld clad with 17–4 PH stainless steel while tensile residual stresses exist in an Inconel 625 clad layer. In this study, autofrettage of an Inconel 625 thick-walled clad cylinder is investigated with modified residual stress distributions obtained indicating that tensile residual stresses throughout the clad layer are transformed to compressive in nature, discontinuity stresses at the clad/substrate interface are almost entirely eliminated and compressive residual stresses exist to a depth of around 18 mm. An alternative clad material, 17–4 PH stainless steel, is investigated resulting in compressive residual stresses in the clad layer without the need for autofrettage. The complexity of modelling a martensitic stainless steel is discussed and sensitivity studies undertaken to illustrate the influence of coefficient of thermal expansion on resulting residual stresses. Strain hardening effects and the assumption of an idealised interface are discussed. Contour method measurements prove that discontinuity stresses are reduced in reality due to alloying and diffusion effects, highlighting also the need for further characterisation of 17–4 PH. Additional considerations such as the weld clad profile and process parameters are briefly discussed.

Autofrettage of Weld Clad Components

A fatigue-resistant cladding concept confirms the presence of compressive residual stresses in a cylinder weld clad with 17-4 PH stainless steel while tensile residual stresses exist in an Inconel 625 clad layer. In this study, autofrettage of an Inconel 625 thick-walled clad cylinder is investigated with modified residual stress distributions obtained indicating that tensile residual stresses throughout the clad layer are transformed to compressive in nature, discontinuity stresses at the clad/substrate interface are almost entirely eliminated and compressive residual stresses exist to a depth of around 18mm. Strain hardening effects and the assumption of an idealized interface are discussed.

Review of Structural Assessment of Pipe Bends

This paper presents a review of technical reports available for the structural assessment of pipe bends. Compared with smooth bends, the volume of literature available for joint bents (mitres) is less and least explored in challenging applications, such as low temperature use. The issue that affects a pipe bend is discontinuity stresses and cross-section ovalisation. These lead to delay in the enlargement of non-linear analysis of pipe bends. The constrains of pipe work designers are thoroughly analyzed and discussed, together with the effects of loading and out-of-circularity. The scope for additional work on the effect of combined loading, and end effects, out of- circularity are high. Limit, collapse and disintegrate loads are not yet obtainable across the entire continuum of bends and loading parameters. Creep and optimization is least explored as far as pipe bends are concerned. The presence of unforeseen vibration is a common source of high-cycle weakness collapse in pipe work, resulting vibration-induced fatigue studies.

Evaluation of Speed Lowering of Primary Sodium Pump into Sodium Pool for 500 MWe PFBR Based on Creep Damage

Abstract In 500 MWe Prototype Fast Breeder Reactor (PFBR), the Primary Sodium Pump (PSP) contained in the primary circuit circulates sodium through the core. The PSP is supported on the roof slab. The space between the roof slab and sodium free surface is filled with argon. PSP will be lowered slowly, using a flask, into the main vessel (MV) after the completion of preheating and sodium filling of the main vessel. Pump inside the flask will be at ambient condition before lower ng into the sodium pool. While lowering PSP into MV sodium, one of the critical welds near the shell-flange junction at the discharge nozzle will experience thermal stress due to the hot shock offered by the sodium. The governing failure mode to ensure the structural integrity of the PSP is the creep damage developed in the weld near the junction of flange due to the discontinuity stresses that would be locked up the weld while lowering. This paper addresses the thermo-mechanical analysis carried out towards establishing the preheating temperature and speed of lowering the pump in the sodium pool. The PSP may be take in out for inspection/maintenance and lowered it back into the sodium pool around 5-10 times during the plant life. Based on this investigation, the PSP preheat temperature and lowering rate has been recommended.

Pipe-anchor discontinuity analysis utilizing power series solutions, Bessel functions, and Fourier series

One of the paradigmatic classes of problems that frequently arise in piping stress analysis discipline is the effect of local stresses created by supports and restraints attachments. Over the past 20 years, concerns have been identified by both regulatory agencies in the nuclear power industry and others in the process and chemicals industries concerning the effect of various stiff clamping arrangements on the expected life of the pipe and its various piping components. In many of the commonly utilized geometries and arrangements of pipe clamps, the elasticity problem becomes the axisymmetric stress and deformation determination in a hollow cylinder (pipe) subjected to the appropriate boundary conditions and respective loads per se. One of the geometries that serve as a pipe anchor is comprised of two pipe clamps that are bolted tightly to the pipe and affixed to a modified shoe-type arrangement. The shoe is employed for the purpose of providing an immovable base that can be easily attached either by bolting or welding to a structural steel pipe rack. Over the past 50 years, the computational tools available to the piping analyst have changed dramatically and thereby have caused the implementation of solutions to the basic problems of elasticity to change likewise. The need to obtain closed form elasticity solutions, however, has always been a driving force in engineering. The employment of symbolic calculus that is currently available through numerous software packages makes closed form solutions very economical. This paper briefly traces the solutions over the past 50 years to a variety of axisymmetric stress problems involving hollow circular cylinders employing a Fourier series representation. In the present example, a properly chosen Fourier series represent the mathematical simulation of the imposed axial displacements on the outside diametrical surface. A general solution technique is introduced for the axisymmetric discontinuity stresses resulting from an anchor restraint on a selected of pipe geometry. These solutions can be economically implemented on today's symbolic calculus software packages with no loss in solution accuracy when compared to often more expensive techniques such as the finite element method. Verification of the axisymmetric solution technique is illustrated by the comparison of results for the closed form solutions versus those approximated by the finite element technique. Extensions of the general axisymmetric solution technique to other geometries and applied loads are also discussed while the numerical and graphical results are tendered.

Design of a smart functionally graded thermopiezoelectric compositestructure

In this paper, a smart functionally graded piezoelectricstructure is analyzed. The smart structure consists of three layers: onelayer of metal, one layer of piezoelectric material (PZT) used as anactuator, and a graded metal/PZT layer between the metal layer and the PZTlayer. A finite element code is developed in the programming environmentMATLAB and FORTRAN, with each finite element having varied materialproperties through space coordinates. The results reveal that both thestress discontinuity and thermal deformation of the structure can becontrolled. By introducing a functionally graded layer between the PZTactuator layer and the metal beam layer, both stress discontinuity and theedge local stresses can be essentially reduced. The proposed method isexpected to be useful for functionally graded thermopiezoelectric compositestructures under operating environments where the thermal and piezoelecticeffects are important.

Finite element analysis of pressure vessel using beam on elastic foundation analysis

In this study, we first applied the variation principle to derive a new finite element method (FEM) based on the theory of beam on elastic foundation using line element. The derived FEM was then applied to solve, for the first time, the pressure vessel problems with uniform thickness. Our FEM results, obtained even by using only one line element, agreed exactly with the available closed-form solution, confirming the validity and computing efficiency of our finite element formulation. Moreover, we have applied our new FEM to solve pressure vessel problems with non-uniform thickness where no exact analytical solution is known to exist. The distributions of discontinuity stress in the cylindrical part were obtained. We found that shear force and bending moment were indeed discontinuous at the geometrically discontinuous juncture, due to the bending rigidity and elastic constant change by the non-uniform thickness. Finally, the case of discontinuity stresses in a bimetallic joint was also studied. The locations of maximum shear force and bending moment were found to be affected by the bending rigidity of the material.

Discontinuity stresses in orthotropic pressure vessels

Expressions for stresses and displacements in orthotropic cylindrical, ellipsoidal, toroidal and conical shells are derived. Discontinuity stresses in orthotropic cylindrical pressure vessels connected to flat, ellipsoidal, and toriconical heads are determined. Stress intensification factors are also calculated. In some cases, the variation of stress intensification factors with moduli ratio and aspect ratio is also investigated.

End reinforcement of composite cylinders for biaxial testing

A detailed theoretical investigation has been carried out into factors affecting external end reinforcement of GRP (glass-reinforced plastic) cylindrical specimens for biaxial tests using axisymmetric solid finite elements. The reinforcement method is intended as a general solution to a wide range of applied axial and hoop stresses in the third quadrant of the stress field. Among the parameters considered were the ratio of hoop-to-axial stress, material employed for reinforcement, thickness, length and taper angles of the reinforcement layers. The assessment of the effective control of high discontinuity stresses at the fixed ends by the end reinforcement was made with the help of the Tsai-Wu strain index distribution and decay length of the bending stresses. The paper also describes the preliminary experimental work to show the effectiveness of an external composite reinforcement method in controlling the strain distribution of GRP cylinders closed by rigid end flanges.

Discontinuity phenomena around the supports of stepwise-thickened spherical steel tanks. Part 2: Numerical examples and design recommendations

This paper is a continuation of the study (Zingoni & Pavlović, Int. J. Pres. Ves. & Piping, 53 (1993) 405-35 of discontinuity phenomena around the supports of locally thickened spherical steel tanks, where such thickening is achieved abruptly from either side of the support latitude. Herein, the theoretical results that were derived in the first part are applied to a representative practical example, from which typical design recommen- dations suggest themselves. Two main findings emerge from the present study. During the course of design, once the local stresses at the support itself have been adjusted to acceptable levels by stepwise thickness-enhancement on either side, the ensuing discontinuity stresses at the edges of the thickened width of the shell need not be a cause for concern, since they remain non-critical for the range of thickness-discontinuity ratios likely to be adopted in practice. Also, contrary to certain design practice, local shell thickening in the zone of the support need not be extended for the full effective range of the anticipated support bending disturbance.

Behavior of Pressure-Induced Discontinuity Stresses at Elevated Temperature

Abstract Conventional wisdom has been that discontinuity bending stresses at temperatures within the creep regime are self-limiting, and therefore secondary. A series of creep relaxation analyses were performed on typical discontinuities (junctions). The analyses show that, in general, discontinuity bending moment and stress due to pressure do not relax, but remain more or less constant with time. These stresses should therefore be evaluated as primary. A creep follow-up mechanism was identified that sustains the discontinuity stresses. The implications for design are discussed.

Theory and Design of Pressure Vessels

Pressure vessels. Stresses in pressure vessels. Stresses in flat plates. Discontinuity stresses in pressure vessels. Fracture control. Design-construction features. Fabrication, innovation, and economics. Buckling of vessels under external pressure. Index.

An elastic-plastic analysis of the integral tubesheet in U-tube heat exchangers—Towards an ASME code oriented approach

The tubesheet in a U-tube heat exchanger with integral shell and channel joints may develop high discontinuity stresses at these joints. Evaluation of the structural support provided by the shell and the channel to the tubesheet must consider the possibility of plastic hinges at the shell/tubesheet and channel/tubesheet joints. An incremental elastic-plastic analysis is herein presented which treats the formation of the plastic hinge in a systematic and conservative manner. A practical, somewhat more conservative, design procedure is also proposed for possible inclusion in the ASME Code, Section VIII Div. I rules.

The elbow centroid for hockey stick heat exchanger designs with hexagonal tube bundles

In nuclear component design it is the conservative (and usual) practice to assume that the center of gravity of 90° elbows lies on the centerline of the elbow. However, there is some logic for a more exact design with explicit safety factors, as opposed to safe assumptions. An exact design improves the accuracy in determining the overall vessel center of gravity, in assessing effects of seismically induced moments, in determining mechanical loads at vessel supports, and in calculating discontinuity stresses at elbow junctions.

Some singular aspects of three-dimensional transonic flow

a series of elastic concentration- factor values from 1.05 to 10 and for values of the Ramberg- Osgood .exponent from 5 to 200. The data for Figs. 1 and 2 were obtained from the tabular output of the program. Conclusions 1) Design relations have been developed for plastic discontinuity stresses using Neuber's equation and the Ramberg-Osgood analytic approximation of stress-strain properties. 2) The limiting value of the discontinuity stress in the developed relations is the Ramberg-Osgood end-value. The latter is the maximum value of stress for which the Ramberg- Osgood equation provides a satisfactory fit of experimental stress-strain data. The end-point of the equation has been identified using a non-dimensional strain parameter. The end- stress is obtained by computation. 3) The relative reduction of the stress concentration factor associated with plastic discontinuity stresses is independent of the elastic concentration factor. The reduction is mainly dependent on the maximum discontinuity stress and the Ramberg-Osgood exponent value. 4) Limiting values of the stress-concentration reduction factor occur when the discontinuity stress is at the Ramberg- Osgood end-value and the reference stress is elastic: a) If the end-value is the secant-yield stress, the plastic concentration factor is 83.7% of the elastic concentration factor for all values of the Ramberg-Osgood exponent and for all elastic values of the reference stress; or b) If the end value is greater than the secant-yield stress, the reduction value is a function of both the exponent and the end-stress. However, for given values of the two parameters, the limiting value of the reduction factor is constant for all elastic values of the reference stress.

Stress, buckling and vibration of hybrid bodies of revolution

The analysis is applicable to bodies of revolution composed of thin shell segments, thick segments and discrete rings. The thin shell segments are discretized by the finite difference energy method and the thick or solid segments are treated as assemblages of 8-node isoparametric quadrilateral finite elements of revolution. Suitable compatibility conditions are formulated through which these dissimilar segments are joined without introduction of large spurious discontinuity stresses. Plasticity and primary or secondary creep are included. Axisymmetric prebuckling displacements may be moderately large. The nonlinear axisymmetric problem is solved in two nested iteration loops at each load level or time step. In the inner loop the simultaneous nonlinear equations corresponding to a given tangent stiffness are solved by the Newton-Raphson method. In the outer loop the plastic and creep strains and tangent stiffness are calculated by a subincremental procedure. The linear response to nonaxisymmetric loading is obtained by superposition of Fourier harmonics. Many examples are given to demonstrate the scope of the computer program, BOSOR6, derived from the analysis and to illustrate certain stress concentration effects in shell-type structures which cannot adequately be treated with use of thin shell theory.

Nonlinear Effects on the Discontinuity Stresses in a Cylindrical Shell With a Flat Head Closure

The effect of large displacements on the flexural edge stresses in thin cylindrical shells with flat head closures subjected to axisymmetric loads is considered. Results are presented which show that neglecting this nonlinear effect leads to nonconservative results. However, it is shown that these effects can usually be safely neglected except for very thin shells or for shells with a low modulus of elasticity. Curves are given which illustrate this effect for selected shell parameters.

Optimum Design of Composite Multilayer Shell Structures

An improved method of structural optimization is presented which encompasses recent advances in nonlinear mathematical programming methods and methods of analysis for fibrous composite materials. The methodology is based on a transformation of an inequality constrained minimization problem into a sequence of unconstrained minimizations, by applying a penalty function formulation of the Fiacco-McCormick type. Advances include the formulation and solution of a composite shell design problem, including constraints on joint-discontinuity stresses and fibrous composite failure modes. The optimization method is first developed by considering a classic structural design application, the redundant three bar truss. Next, an application to a composite shell structure is demonstrated. Behavior constraints invoked for the shell include consideration of joint discontinuity stresses, shell buckling, deformation limits, and combined stress failure. The objective function is general enough to include both cost and weight criteria. Results for optimum sectional properties for the three bar truss, a composite pyrocarb cylinder and a carbon/aluminum cylinder joined with a composite hemisphere are obtained by this decision making technique.