Comparison of analytical predictions and experimental results for a 1:8-scale steel containment model pressurized to failure

The analyses used to predict the behavior of a 1:8-scale model of a steel LWR containment building to static overpressurization are described and results are presented. Finite strain, large displacement, and nonlinear material properties were accounted for using finite element methods. Three-dimensional models were needed to analyze the penetrations, which included operable equipment hatches, personnel lock representations, and a constrained pipe. It was concluded that the scale model would fail due to leakage caused by large deformations of the equipment hatch sleeves.     

Pretest predictions for the response of a 1:8 scale steel LWR containment building model to static overpressurization

The analyses used to predict the behavior of a 1:8-scale model of a steel LWR containment building to static overpressurization are described and results are presented. Finite strain, large displacement, and nonlinear material properties were accounted for using finite element methods. Three-dimensional models were needed to analyze the penetrations, which included operable equipment hatches, personnel lock representations, and a constrained pipe. It was concluded that the scale model would fail due to leakage caused by large deformations of the equipment hatch sleeves.     

Recent results on the evaluation of the overpressure response of concrete and steel containments

Analytical studies have been performed for the evaluation of the ultimate load capacity of concrete containment structures. In addition, analyses of steel containment models were carried out to validate computer codes for the analysis of steel containment structures. This paper reports on some of the results of these analyses, dealing first with the global ultimate load behavior of typical prestressed and reinforced concrete containment structures. The results of these analyses are described, with particular attention given to identifying local effects and failure mechanisms of concrete containment structures. On the basis of the global analysis results, local effects analyses were carried out which show clear evidence of large strain concentrations in the liner. The utility of the ABAQUS-EPGEN code is also demonstrated for three steel containment small-scale models tested by Sandia National Laboratory. The basic geometry of the models consisted of a thin cylindrical shell with a hemispherical dome. One of the models included ring stiffeners in the cylinder, and the other model included penetrations without ring stiffeners. The results of these calculations are presented without test data comparisons.     

Stability of stiffened plates using high precision finite elements

High precision finite elements for both thin plate and stiffener are developed in this paper to analyse the stability of thin plates subjected to arbitrary membrane loading with arbitrarily oriented stiffeners. Application of these elements to some complex stability problems show high accuracy even with a relatively coarse finite element mesh. For all the problems considered the predicted critical loads are accurate upper bounds.     

Forced vibrations of a shell inside a narrow water annulus

The response of a shell to pulsating pressure in a narrow water-filled annulus is determined. The analysis is patterned after Penzes, according to which the imposed pump pressure over a portion of the outer periphery of the water annulus is replaced by an equivalent body force of appropriate thickness. While the amplitude of the response is smaller than that obtained by Penzes by a factor of about 8, the mode shapes agree closely with his results.     

Dynamic response of a clamped/ring-stiffened circular cylindrical shell under non-axisymmetric loading

In order to investigate the structural integrity of light water reactors in case of a blowdown accident the reactor core barrel is modeled as a linear-elastic thin walled circular cylindrical shell, clamped at the upper end and ring-stiffened at the lower end. A computer code CYLDY2 has been developed for analysis of the dynamic respinse of such shells. In this paper the mathematical model on which the code CYLDY2 is based is described in some detail. The transient shell deformations are represented by sets of orthogonal modal functions and the appropriate amplitudes are determined by variational principles. Test calculations confirm that the spatial resolution provided by CYLDY2 is satisfactory even for peak types of loadings having a peak width smaller than 1/10 of the cylinder length and that the computer time is by one or two orders of magnitude smaller than the computer time required for application of well known finite element codes.     

Structural analysis of a three-dimensional perforated plate by the finite element method with test correlation

An application of the finite element method to a three-dimensional perforated plate structure is presented using a nested modeling technique. Stresses calculated by a general three-dimensional finite element computer program were compared with those obtained from a model test. The structure considered in this analysis is a plenum cover of a pressurized water reactor internal which is a circular perforated plate stiffened with welded cross ribs. This type of structure is common in reactor internals. The nested model analyses consist of two finite element models; one is for the overall structure model and the other for an isolated portion of the structure with refined grid system for more accurate stress calculation. The first model was analyzed to obtain the nodal displacements under the applied loads. Then the second model was run using the displacement boundary conditions obtained from the first model analysis. A fully instrumented Plexiglas model test was conducted to verify this method. Comparison between the test results and the calculated stresses from the second model analysis showed good agreement.     

Analytic study of the steel liner near the equipment hatch in a 1:4 scale containment model

A containment scale-model test, performed at Sandia National Laboratories, was loaded by overpressurization and the first leak was concluded to be caused by tears in the steel liner found near the equipment hatch. These tears were located in the vicinity of the vertical fold in between the general curved part and the embossment (vertical bend line). A 3D finite element analysis of the region near the equipment hatch, shows that high localized strains will develop in the vicinity of the bend line. It is shown that the liner separates from the concrete wall near the bend line when the containment expands. The tensioned liner will be in contact with the surface of the concrete wall in general, but near the vertical bend line the liner tends to be straightened out. This flexural behaviour cause high strains in the weld located in the bend line. The actual peak strain level is depending on the detailed geometry in the bend line and the failure strain level of a welded biaxial stressed zone is difficult to define. However, the analysis presented in this paper shows that the flexural behaviour in the bend line most likely contributed to the liner tears found in the scale-model test. A general conclusion from the study presented in this paper is that, the non-linear plastic behaviour of the liner is very sensitive to the detailed design and the interaction between the liner and the concrete.     

Stresses in ellipsoidal pressure vessel heads with noncentral nozzle

The objective of this paper is further investigation of the shell intersection problem. The shell theory and finite element method are used for stress analysis of nozzle connections in ellipsoidal heads of the pressure vessels. Ellipsoidal heads having attached nozzles considerably displaced from the head axis are mainly considered. The features of the numerical procedure, structural modeling of nozzle-head shell intersections and SAIS special-purpose computer program are discussed. The results of stress analysis and parametric study of an ellipsoidal vessel head with a noncentral nozzle under internal pressure loading are presented.     

Seismic proof test of a reinforced concrete containment vessel (RCCV): Part 2: Results of shaking table tests

A 1/8-scale model was constructed of a reinforced concrete containment vessel (RCCV) used in the latest advanced boiling water reactors (ABWR). Shaking table tests were conducted on it with input motions corresponding to or exceeding a design earthquake assumed for a real Nuclear Power Plant.The objectives of the tests were to verify the structural integrity and the leak-proof functional soundness of the RCCV subjected to design earthquakes, and to determine the ultimate strength and seismic margin by an excitation that led to the model's collapse. The model, the test sequence and the pressure and leak test results were addressed in Part 1. The shaking table test method, the input motions and the test results, including the transition of the model's stiffness, natural frequencies and damping factors and the effects of vertical input motions and internal pressure on the model's characteristics and behavior, the load-deformation, the ultimate strength, the failure mode of the reinforced concrete portion and the liner plate are described here. The seismic safety margin that was evaluated by the energy input during the failure test to a design basis earthquake will be described in Part 3. The analytical results of simulation using the multi-lumped mass model will be described in Part 4.     

Seismic proof test of a reinforced concrete containment vessel (RCCV): Part 2: Results of shaking table tests

A 1/8-scale model was constructed of a reinforced concrete containment vessel (RCCV) used in the latest advanced boiling water reactors (ABWR). Shaking table tests were conducted on it with input motions corresponding to or exceeding a design earthquake assumed for a real Nuclear Power Plant.The objectives of the tests were to verify the structural integrity and the leak-proof functional soundness of the RCCV subjected to design earthquakes, and to determine the ultimate strength and seismic margin by an excitation that led to the model's collapse. The model, the test sequence and the pressure and leak test results were addressed in Part 1. The shaking table test method, the input motions and the test results, including the transition of the model's stiffness, natural frequencies and damping factors and the effects of vertical input motions and internal pressure on the model's characteristics and behavior, the load–deformation, the ultimate strength, the failure mode of the reinforced concrete portion and the liner plate are described here. The seismic safety margin that was evaluated by the energy input during the failure test to a design basis earthquake will be described in Part 3. The analytical results of simulation using the multi-lumped mass model will be described in Part 4.     

核电厂设备闸门外压极限承载特性研究

采用有限元分析方法对设备闸门外压极限承载特性进行研究。在ANSYS程序中建立参数化计算模型，通过非线性屈曲分析得到设备闸门封头的外压极限载荷。计算结果与经验公式结果相近，验证了有限元分析方法的可靠有效性。对影响外压极限承载特性的设计参数进行了敏感性研究，总结出其影响变化规律。优化设计示例表明该研究方法具有实用性，可为设备闸门的结构设计提供优化方案。      

Analyses of Pool Swell Tests by Two-Dimensional Hydrodynamic Computer Code

A two-dimensional hydrodynamic computer code SOLA-VOF was examined on the analytical capability for dynamic loads by pool swell in the MARK-I type BWR suppression chamber under LBLOCA (Large Break Loss of Coolant Accident) conditions. Two pool swell tests, (LLL 1/5-scale and EPRI 1/12-scale tests) were selected for this purpose and analyzed by the SOLA-VOF code modified with incorporation of a simple downcomer flow model. In these analyses, it was necessary to take account of three-dimensional effect of pool swell behavior along the chamber axis by use of a method such as spatially weighting function experimentally determined, because a simple two-dimensional calculation by the SOLA-VOF code gave too much conservative evaluation for the impact load on the ring header. Applications of this method gave a good agreement between the calculation and measurement. The vertical loads on the suppression chamber wall were well analyzed by this code. It might be because the local pressure difference caused by the nonuniform pool swelling disappeared owing to pressure integration on the surface of suppression chamber wall.     

核电厂设备闸门外压极限承载特性研究

The ultimate bearing characteristics of the equipment hatch under the external pressure was studied by the finite element analysis method. The parametric calculation model was established in ANSYS, and the external pressure ultimate load of the equipment gate head was obtained by nonlinear buckling analysis. The calculated results were similar to those of the empirical formula, which verified the reliability and effectiveness of the finite element analysis method. The sensitivity of the design parameters affecting the ultimate bearing characteristics of the external pressure was studied, and the changing law of the influence was summarized. The example of the optimization design showed the practicability of the research method and could provide the optimization scheme for the structural design of the equipment hatch.     

Homogeneous eigenfunction method applied to the elasticity problem of a pressure vessel with a hemispherical head

A semi-analytical three-dimensional method is applied to the axisymmetric problem of elastic stress analysis of a shell intersection consisting of a pressure vessel with a hemispherical head. The method uses the homogeneous eigenfunction technique of formulating general solutions to the governing equations and the numerical boundary-point-least-squares procedure of satisfying the continuity conditions on the vessel-head interface. A comparison is made with a previous shell theory solution and the present method is assessed for suitability for more complex intersection problems.     

Further three-dimensional stress analysis of an intersection of a cylindrical shell with a plate

The theory presented previously for the three-dimensional state of stress in a plate-cylindrical shell intersection under axisymmetric loading is generalized to include non-axisymmetric loading cases. Non-axisymmetric variations are taken into account by expansion of loads and stresses in a Fourier series in the circumferential direction. The geometry of the intersection is partitioned into three parts: cylindrical shell, plate, and ring. Computational schemes are developed for displacements and stresses in each of the three parts, for each term of the circumferential series, using eigenfunction expansions. Continuity between parts is enforced using the boundary-point-least-squares technique. Numerical results presented are restricted to the case of axisymmetric loadings applied on the cylindrical shell, representing the first term of the circumferential series. A discussion is presented of the stability of the computational procedure and a comparison is given of theoretical results with experimental data.     

铍环焊接残余应力的中子衍射测试与有限元分析

利用稳态堆上的中子衍射应力谱仪开展了铍环激光焊接后的残余应力测试。先进行铍材中子衍射应力测试的参数及其优化研究,在固定堆功率、衍射晶面和规范体积的条件下,选取测试时间分别为600s和6 000s进行铍环上同一点的中子衍射峰的重复性测试,结果表明,后者测试铍材应变的统计误差仅为前者的1/3,其标准偏差约为1.10×10-5。取后者测试时间作为优化参数,对铍环焊缝附近轴向应变和环向应变方向的中子衍射峰进行测试,获得两个方向的残余应变分布,进一步计算出焊接残余应力分布。对铍环激光焊接过程的温度场和应力场进行三维有限元数值模拟,将有限元计算得到的铍环焊缝附近中间壁厚处的残余应力和应变与中子衍射测试结果进行对比,结果表明二者分布规律较为一致。     

Correlation of test and FEA results for elbows subjected to out-of-plane loading

The objective of this study is to validate a finite element analysis (FEA) simulation methodology to predict the out-of-plane behavior of piping elbows. Two out-of-plane elbow experiments and the corresponding FEA shell and elbow element models are presented. For load–displacements results, all the FEA predictions showed excellent agreement with measured experimental results, and for load–strain behavior, the shell FEA model results correlated quite well with the experimental results.     

Numerical prediction of added mass and damping for a cylinder oscillating in confined incompressible gas–liquid two-phase mixture

This paper is concerned with the numerical analysis of the added mass and damping of a circular cylinder, which oscillates in an air–water bubbly mixture enclosed by a concentric shell. The mixture is assumed to be incompressible. This is because the oscillation frequency of the cylinder is low in this study, and accordingly the pressure change around the cylinder is not so large. An incompressible two-fluid model is solved by the finite element method, proposed by the author in a prior paper, to calculate the bubbly flow around the oscillating cylinder. The analysis reveals the effects of the diameter ratio of the cylinder to the shell, the air volumetric fraction and the bubble diameter. It also clarifies that the increase of damping ratio in the bubbly mixture is attributable to the phase lag of the drag force acting on the cylinder behind the cylinder displacement.     

Shell finite element of reinforced concrete for internal pressure analysis of nuclear containment building

This paper describes a 9-node degenerated shell finite element (FE), an analysis program developed for ultimate pressure capacity evaluation and nonlinear analysis of a nuclear containment building. The shell FE developed adopts the Reissner-Mindlin (RM) assumptions to consider the degenerated shell solidification technique and the degree of transverse shear strain occurring in the structure. The material model of the concrete determines the level of the concrete stress and strain by using the equivalent stress-equivalent strain relationship. When a crack occurs in the concrete, the material behavior is expressed through the tension stiffening model that takes adhesive stress into account and through the shear transfer mechanism and compressive strength reduction model of the crack plane. In addition, the failure envelope proposed by Niwa is adopted as the crack occurrence criteria for the compression-tension region, and the failure envelope proposed by Yamada is used for the tension-tension region. The performance of the program developed is verified through various numerical examples. The analysis based on the application of the shell FE developed from the results of verified examples produced results similar to the experiment or other analysis results.