The steam generators (SG) control the capacity factor of sodium cooled fast reactor plants and hence they are designed with high reliability. One of the strategies to enhance the reliability is to demonstrate leak before break (LBB) justification. LBB analysis is reported for 500 MWe sodium cooled fast reactor (SFR) in this paper. The material of construction is modified 9 Cr-1 Mo and the critical location is the shell nozzle junction. The initial surface crack is postulated at the critical locations at the shell nozzle junction. The critical crack length is computed by adopting the philosophy of CEGB-R6 procedure, for which J integral is computed by finite element method. For determining the detectable through-wall crack length, the crack opening area is also determined by finite element method. Finally, it is demonstrated that it is possible to justify leak before break argument for SFR SG with adequate margins. The required material properties are extracted from French Design Code RCC-MR-2002 and validated with tests on plates.

In this paper, a base isolator called a multiple direction optimized-friction pendulum system (Multiple DO-FPS) with numerous sliding interfaces is proposed. To understand the mechanical behavior of the Multiple DO-FPS isolator under multidirectional excitations, an analytical model called the multiple yield and bounding surfaces model is proposed. On the basis of the derived mathematical formulations for simulation of the characteristics of the Multiple DO-FPS isolation bearing, it is revealed that the natural period and damping effect of the Multiple DO-FPS isolator are a function of the sliding displacement and sliding direction. By virtue of the proposed model, the phenomena of the sliding motions of the Multiple DO-FPS isolator with numerous sliding interfaces subjected to multidirectional excitations can be understood in a simple manner. The analytical results indicate that the natural frequency and damping effect of the Multiple DO-FPS isolator with numerous concave sliding interfaces change continually during earthquakes and are controllable through appropriate designs.

This paper is aimed to study dynamic actuation of circular tubular shell structures coupled with distributed electrostrictive actuator segments. A mathematical model of the hybrid elastic/electrostrictive circular tubular shell, including the electrostrictive/elastic/control couplings, is derived. The generalized electrostrictive control actuation induced by an arbitrary electrostrictive actuator segment consists of three contributing components: the circumferential membrane control action, the longitudinal bending control action, and the circumferential bending control action. In particular, spatial modal actuation characteristics of the total actuation and the three contributing components corresponding to various design parameters (e.g., actuator thickness, shell radius, and thickness) are evaluated and compared with respect to actuator patch sizes. Analysis data suggest that the electrostrictive membrane control actuation dominates the overall control action in lower shell modes; however, the control moment becomes important in higher shell modes. Optimal placements of electrostrictive actuator segments on the circular tubular shell are identified. Modal filtering behaviors, due to cancellation of internal attenuation/amplification effects, occur when large-size actuators are used, rendering the actuation less effective.

We present a scheme that utilizes one elastic stress field (no iterations) to compute lower bound limit load multipliers of structures that collapse through gross (or localized) plasticity. A criterion to distinguish between these collapse modes is presented. For structures that collapse through gross plasticity, we demonstrate that the m′ multiplier proposed by Mura et al. (1965, Extended Theorems of Limit Analysis,” Q. Appl. Math., 23 (2), pp. 171–179) is a lower bound in the context of deformation theory. For structures that undergo plastic localization at collapse, we present a criterion that identifies (approximately) the subvolumes of the structure that participate in the collapse. Multiplier m ′ is computed over the selected subvolumes, denoted as m ' S , and demonstrated to be a lower bound multiplier in the context of deformation theory. We consider numerical examples of structures that collapse by localized or gross plasticity and show that our proposed multiplier is lower than the corresponding multiplier obtained through elastic–plastic analysis and the proposed multiplier is not overly conservative.

Our previous studies have shown that stress intensity factors (SIFs) are influenced considerably from the presence of the Bauschinger Effect (BE) in thick-walled pressurized cracked cylinders. For some types of pressure vessels, such as gun barrels, working in corrosive environment, in addition to acute temperature gradients and repetitive high-pressure impulses, erosions can be practically induced. Those erosions cause stress concentration at the bore, where cracks can readily initiate and propagate. In this study, the BE on the SIFs will be investigated for a crack emanating from an erosion’s deepest point in a multiply eroded autofrettaged, pressurized thick-walled cylinder. A commercial finite element package, ansys , was employed to perform this type of analysis. A two-dimensional model, analogous to the authors’ previous studies, has been adopted for this new investigation. Autofrettage with and without BE, based on von Mises yield criterion, is simulated by thermal loading and the SIFs are determined by the nodal displacement method. The SIFs are evaluated for a variety of relative crack lengths, a 0 /t = 0.01–0.45 emanating from the tip of the erosion of different geometries including (a) semicircular erosions of relative depths of 1%–10% of the cylinder’s wall thickness, t; (b) arc erosions for several dimensionless radii of curvature, r′/t = 0.05–0.4; and (c) semi-elliptical erosions with ellipticities of d/h = 0.5–1.5, and erosion span angle, α, from 6 deg to 360 deg. The effective SIFs for relatively short cracks are found to be increased by the presence of the erosion and further increased due to the BE, which may result in a significant decrease in the vessel’s fatigue life. Deep cracks are found to be almost unaffected by the erosion, but are considerably affected by BE.

In spite of the fact that coke drums are subjected to cyclic thermal and mechanical loads, generally, they are not designed for cyclic loads. Thus, their operational life is much shorter than other pressure equipment in refineries. Due to information developed from surveys, it was determined that the major typical location of failure due to thermal fatigue in coke drums is the shell-to-skirt junction area. This paper focuses on temperature and stress characteristics and also the thermal fatigue life of the junction area. The main objective of this paper was to explore effect of the switching temperature on thermal fatigue life of the junction area. Four coke drums, currently in service have been considered in the analyses, named drums A, B, C, and D, identical in dimensions and with an operating cycle period of 48 h. Operational temperatures and strains have been measured and collected every minute. The number of measured cycles of coke drum A, B, C, and D were 52, 53, 53, and 54 cycles, respectively. Thus, a total of 212 cycles have been analyzed. The operational temperatures and strains were examined. Finite Element Method (FEM) analyses have been performed on the selected cycles in order to find the most severe location in the junction area. The strain history and FEM results were used to assess thermal fatigue life. The thermal fatigue lives were calculated based on low cycle fatigue properties using engineering steels for high temperature components issued by National Institute for Materials Sciences (NIMS) in Japan. The number of cycle to fracture versus switching temperature for the coke drums was then plotted. The curve best fitting criteria was then used to develop an equation relating the number of cycle to fracture as a function of switching temperature. The results show that the switching temperature strongly affects the number of cycle to fracture. These results can be used to provide the necessary information to operate coke drums safely in order to extend their useful lives.

The hydrostatic test of integrated multilayer clamping high pressure vessel is performed from 15.7 MPa to 56.52 MPa (1.8 times of the design pressure). The measured stress values have deviation from the Lamè equation (maximum error 34%). The inner wall stress is low while the outer wall stress is high. The layered vessel mechanics model is deduced to analyze the deviation. The inner shell is an external pressure vessel and the outer shell is the internal pressure vessel. The contact of the inner shell and the outer shell generates preload stress. The multilayer structure parameter is a universal nondimensional parameter to calculate the preload stress of layered vessel, and the corrected theory values have smaller error in high pressure (less than 10%). The super hydrostatic test alters the preload stress distribution and the gaps between layers.

This work explores the possibilities of using functionally graded material (FGM) layers to reduce normal and shear stress gradients due to internal pressure and thermal loadings at the interface of a two-layered wall pressure vessel. The two walls are made of an internal thin metallic layer (titanium used as a liner to avoid a chemical/physical reaction between the gas and the external layer) and an external thick layer (carbon fiber used as a structural restraint). Two main geometrical elements are investigated: a cylindrical shell and a spherical panel. The shell analysis has been made by referring to mixed layerwise theories, which lead to a three-dimensional description of the stress/strain fields in the thickness shell direction; results related to the first order shear deformation theory are given for comparison purposes. It has been concluded that it is convenient to use FGM layers to reduce shear and normal stress gradients at the interfaces. Furthermore, the FGM layers lead to benefits as far as buckling load is concerned; lower values of in-plane shear and longitudinal compressive stresses are, in fact, obtained with respect to a pure two-layered wall.

Mechanical damage in transportation pipelines is a threat to their structural integrity. Failure in oil and gas pipelines is catastrophic as it leads to personal fatalities, injuries, property damage, loss of production, and environmental pollution. Therefore, this issue is of extreme importance to pipeline operators, government and regulatory agencies, and local communities. As mechanical damage can occur during the course of pipeline life due to many reasons, appropriate tools and procedures for assessment of severity is necessary. There are many parameters that affect the severity of the mechanical damage related to the pipe geometry and material properties, the defect geometry and boundary conditions, and the pipe state of strain and stress. The main objective of this paper is to investigate the effect of geometry, material, and pressure variability on strain and stress fields in dented pipelines under static and cyclic pressure loading using probabilistic analysis. Most of the published literature focuses on the strain at the maximum depth for evaluation, which is not always sufficient to evaluate the severity of a certain case. The validation and calibration of the base deterministic model was based on full-instrumented full-scale tests conducted by Pipeline Research Council International as part of their active program to fully characterize mechanical damage. A total of 100 cases randomly generated using Monte Carlo simulation are analyzed in the probabilistic model. The statistical distribution of output parameters and correlation between output and input variables is presented. Moreover, regression analysis is conducted to derive mathematical formulas of the output variables in terms of practically measured variables. The results can be used directly into strain based assessment. Moreover, they can be coupled with fracture mechanics to assess cracks for which the state of stress must be known in the location of crack tip, not necessarily found in the dent peak. Furthermore, probabilities derived from the statistical distribution can be used in risk assessment.

A plate structure of a triangular truss core sandwiched by two panels is treated as an equivalent homogeneous laminated plate by obtaining equivalent anisotropic elastic constants. The equivalent elastic constants are obtained by considering generalized Hook’s law of a three dimensional elastic body with no a priori assumption and the equilibrium of a segment deformed by bending moments. To verify the accuracy of the equivalent elastic constants, a linear static analysis of sandwiched aluminum plates subjected to lateral pressure is carried out. The results of the finite element analysis applied to the equivalent laminated plates are compared with those of a NASTRAN analysis of the original structural layouts. The results are also compared with a closed-form solution, which simplifies the sandwiched plate as a homogeneous orthotropic thick plate continuum ( Lok and Cheng, 2000, “Elastic Stiffness Properties and Behavior of Truss-Core Sandwich Panel,” J. Struct. Eng., 126(5), pp. 552–559 ). As the maximum deflections of three analyses agreed closely, one has assurance that the method of the homogeneous plate with equivalent elastic constants is valid and useful.

Structural integrity of an in-service component containing damage such as corrosion and thermal hot spot has to be evaluated regularly so as to certify the acceptance and safety of continued service of the component. In this paper, limit load solutions of a damaged conical shell, particularly local wall thinning and thermal hot spot, is investigated. The derived solutions are based on identifying the regions in the damaged component that directly participate in the plastic action (kinematically active). The concepts of reference volume and decay length are employed to identify the kinematically active regions in the damaged conical shell. The different solutions proposed in this paper are compared with the elastic-plastic finite element analysis. The results indicate that proposed solutions can be used with acceptable accuracy to make integrity assessment decisions.

Fracture toughness tests were conducted for carbon composite scarf joints with and without carbon nanotube (CNT) reinforcement in order to study the effect of CNT on enhancing the fracture toughness of the scarf joint interface. Both mode I (i.e., opening mode) and mode II (i.e., shear mode) fracture tests were undertaken with and without CNT applied locally at the joint interface. During the study, the image correlation technique was used to examine the fracture mechanisms altered by the introduction of CNT. The experimental study showed that CNT increased the fracture toughness of the composite interface significantly, especially for the mode II fracture, with altering the fracture mechanism. On the other hand, there was no significant change on mode I fracture caused by CNT reinforcement. The enhancement of mode II fracture toughness was considered to result from the mechanical interlocking between polymers and CNT at the scarf joint interface.

Thin cylindrical shells used in engineering applications are often susceptible to failure by elastic buckling. Most experimental and theoretical research on shell buckling relates only to simple and relatively uniform stress states, but many practical load cases involve stresses that vary significantly throughout the structure. The buckling strength of an imperfect shell under relatively uniform compressive stresses is often much lower than that under locally high stresses, so the lack of information and the need for conservatism have led standards and guides to indicate that the designer should use the buckling stress for a uniform stress state even when the peak stress is rather local. However, this concept leads to the use of much thicker walls than is necessary to resist buckling, so many knowledgeable designers use very simple ideas to produce safe but unverified designs. Unfortunately, very few scientific studies of shell buckling under locally elevated compressive stresses have ever been undertaken. The most critical case is that of the cylinder in which locally high axial compressive stresses develop extending over an area that may be comparable with the characteristic size of a buckle. This paper explores the buckling strength of an elastic cylinder in which a locally high axial membrane stress state is produced far from the boundaries (which can elevate the buckling strength further) and adjacent to a serious geometric imperfection. Care is taken to ensure that the stress state is as simple as possible, with local bending and the effects of internal pressurization eliminated. The study includes explorations of different geometries, different localizations of the loading, and different imperfection amplitudes. The results show an interesting distinction between narrower and wider zones of elevated stresses. The study is a necessary precursor to the development of a complete design rule for shell buckling strength under conditions of locally varying axial compressive stress.

The present paper investigates structural response and buckling of long unstiffened thin-walled cylindrical steel shells, subjected to bending moments, with particular emphasis on stability design. The cylinder response is characterized by cross-sectional ovalization, followed by buckling (bifurcation instability), which occurs on the compression side of the cylinder wall. Using a nonlinear finite element technique, the bifurcation moment is calculated, the post-buckling response is determined, and the imperfection sensitivity with respect to the governing buckling mode is examined. The results show that the buckling moment capacity is affected by cross-sectional ovalization. It is also shown that buckling of bent elastic long cylinders can be described quite accurately through a simple analytical model that considers the ovalized prebuckling configuration and results in very useful closed-form expressions. Using this analytical solution, the incorporation of the ovalization effects in the design of thin-walled cylinders under bending is thoroughly examined and discussed, considering the framework of the provisions of the new European Standard EN1993-1-6.

The load carrying capacity of a component or structure with varying material properties (inhomogeneous) is investigated using various lower- and upper-bound limit load multipliers in the context of variational principles. In order to evaluate the different limit load multipliers, the elastic modulus adjustment procedure is used to obtain statically admissible stress and kinematically admissible strain fields. The proposed upper and lower bound limit load estimates are compared with the results obtained from inelastic finite element analysis for two- and three-dimensional geometries.

An important issue in engineering application of the “design by analysis” approach in pressure vessel design is how to decompose an overall stress field obtained by finite element analysis into different stress categories defined in the ASME B&PV Codes III and VIII-2. In many pressure vessel structures, it is difficult to obtain P L + P b due to the lack of information about primary bending stress. In this paper, a simple approach to derive the primary bending stress from the finite element analysis was proposed with application examples and verifications. According to the relationship of the bending stress and applied loads or the relationship of the bending stress and displacement agreement, it is possible to identify loads causing primary bending stress for typical pressure vessel structures. By applying the load inducing primary bending stress alone and necessary superposition, the primary bending stress and corresponding stress intensity P L + P b can be determined for vessel design, especially for axisymmetric problems.

This paper describes the results of vibration tests using a 1/10 reduced scale model of large-scale cylindrical water storage tanks to clarify their dynamic behavior under seismic excitation. The thin sidewall of the tanks is not so rigid that the vibration modes (sloshing and bulging) induced by earthquake can affect the distribution of their liquid pressure and seismic load. It is, therefore, important for the seismic design of water storage tanks to consider such elastic deformation theoretically and experimentally. In this study, vibration tests by shaking table are conducted using a reduced scale tank model partially filled with water to investigate the dynamic fluid pressure behavior and seismic-proof safety of the tanks. A small sinusoidal excitation test, large amplitude sinusoidal excitation test and seismic excitation test are conducted. The measured values are compared with the calculated ones by some conventional seismic design methods. The results reveal that the distribution shape and magnitude of the dynamic fluid pressure are different between under positive and negative pressures and depend on the magnitude of input acceleration. Further examination concludes that the oval-type vibration, which is a high-order vibration mode, occurring on the sidewall of the tanks affects the distribution shape and magnitude of dynamic fluid pressure. However, it is demonstrated that the vibration does not act as a seismic load in the conventional evaluation of seismic-proof safety.

Experimental and analytical investigations into crack tip opening displacement (CTOD) were conducted to demonstrate the relationship between BS7448-CTOD and ASTM E1290-CTOD. The CTOD test results showed that ASTM-CTOD was occasionally much lower than BS-CTOD both in single edge notch bend specimens and in compact tension (C(T)) specimens for low-strength structural steels, and this tended to be more remarkable in C(T) specimens. In addition, the analytical results of simplified elastic-plastic fracture parameter calculation using the Electric Power Research Institute scheme demonstrated that the ratio of ASTM-CTOD to BS-CTOD was not constant but varied according to CTOD changes. Material factors such as the yield stress, the strain hardening exponent, specimen size and configurations influenced the CTOD ratio, and low strain hardening exponents in the Ramberg–Osgood relation and C(T) specimen configuration significantly decreased the CTOD ratio. An equation that transforms BS-CTOD into ASTM-CTOD is proposed in this study. This equation gives a good estimate of ASTM-CTOD from BS-CTOD.

An improved version of the analytical solutions by Xue, Hwang and co-workers (1991, “Some Results on Analytical Solution of Cylindrical Shells With Large Opening,” ASME J. Pressure Vessel Technol., 113, 297–307 ; 1991, “The Stress Analysis of Cylindrical Shells With Rigid Inclusions Having a Large Ratio of Radii,” SMiRT 11 Transactions F, F05/2, 85–90 ; 1995, “The Thin Theoretical Solution for Cylindrical Shells With Large Openings,” Acta Mech. Sin., 27(4), pp. 482–488 ; 1995, “Stresses at the Intersection of Two Cylindrical Shells,” Nucl. Eng. Des., 154, 231–238 ; 1996, “A Reinforcement Design Method Based on Analysis of Large Openings in Cylindrical Pressure Vessels,” ASME J. Pressure Vessel Technol., 118, 502–506 ; 1999, “Analytical Solution for Cylindrical Thin Shells With Normally Intersecting Nozzles Due to External Moments on the Ends of Shells,” Sci. China, Ser. A: Math., Phys., Astron., 42(3), 293–304 ; 2000, “Stress Analysis of Cylindrical Shells With Nozzles Due to External Run Pipe Moments,” J. Strain Anal. Eng. Des., 35, 159–170 ; 2004, “Analytical Solution of Two Intersecting Cylindrical Shells Subjected to Transverse Moment on Nozzle,” Int. J. Solids Struct., 41(24–25), 6949–6962 ; 2005, “A Thin Shell Theoretical Solution for Two Intersecting Cylindrical Shells Due to External Branch Pipe Moments,” ASME J. Pressure Vessel Technol., 127(4), 357–368 ; 2005, “Theoretical Stress Analysis of Two Intersecting Cylindrical Shells Subjected to External Loads Transmitted Through Branch Pipes,” Int. J. Solids Struct., 42, 3299–3319) for two normally intersecting cylindrical shells is presented, and the applicable ranges of the theoretical solutions are successfully extended from d / D ≤ 0.8 and λ = d / ( D T ) 1 / 2 ≤ 8 to d / D ≤ 0.9 and λ ≤ 12 . The thin shell theoretical solution is obtained by solving a complex boundary value problem for a pair of fourth-order complex-valued partial differential equations (exact Morley equations ( Morley, 1959, “An Improvement on Donnell’s Approximation for Thin Walled Circular Cylinders,” Q. J. Mech. Appl. Math. 12, 89–91 ; Simmonds, 1966, “A Set of Simple, Accurate Equations for Circular Cylindrical Elastic Shells,” Int. J. Solids Struct., 2, 525–541 )) for the shell and the nozzle. The accuracy of results is improved by some additional terms to the expressions for resultant forces and moments in terms of complex-valued displacement-stress function. The theoretical stress concentration factors due to internal pressure obtained by the improved expressions are in agreement with previously published test results. The theoretical results discussed and presented herein are in sufficient agreement with those obtained from three dimensional finite element analyses for all the seven load cases, i.e., internal pressure and six external branch pipe load components involving three orthogonal forces and the respective three orthogonal moments.

Evaluation of creep-fatigue damage has been carried out for the hot gas duct (HGD) structure in the nuclear hydrogen development and demonstration (NHDD) plant. The core outlet and inlet temperature of the NHDD plant are 950 ° C and 490 ° C , respectively. Case studies on high temperature design codes of the draft code case for Alloy 617, ASME boiler and pressure vessel code section III subsection NH (ASME-NH), and RCC-MR were carried out for the inner tube of the HGD for the candidate materials of Alloy 617 and Alloy 800H. Technical issues in application of the draft code case to a high temperature structure are discussed for the Alloy 617 material. Code comparison between the ASME-NH and RCC-MR for Alloy 800H has been carried out. The candidate material of the outer pressure boundary (cross vessel) of the HGD is Mod.9Cr-1Mo steel. The damage evaluation, according to the ASME-NH and RCC-MR for the cross vessel of Mod.9Cr-1Mo steel, has been conducted and their results were compared.