Simplified Inelastic Analysis Research Articles

Elastic core concept for modified Bree problems considering in-phase and out-of-phase loading conditions

The elastic core concept developed from the Bree problem can be used for structural integrity evaluation of high temperature components, such as creep ratcheting and creep fatigue. The simplified inelastic analysis method of the ASME 2013 III-1 NH Code adopts the idea of core stress, which protects against creep rupture and collapse of the structure by limiting the accumulated inelastic strain. Currently, the formulas of core stress and evaluation diagram of effective creep stress parameter for Tests B-1 and B-3 adopted by the APPENDIX NH-T are developed from the classical loading Bree problem, however, the related concepts and evaluation diagrams of modified Bree problems considering generalized loading conditions have not been reported. This paper first reviews the development history of the elastic core concept and its corresponding analysis methods. Based on the modified Bree problems considering in-phase and out-of-phase loading developed by Bradford, the corresponding formulas of the core stress in the non-plastic ratcheting zone are completely proposed, and the corresponding evaluation diagrams of effective creep stress parameters are constructed for the first time. By comparing the core stress formulas and effective creep stress parameter diagrams under three loading cases, the conservatism and applicability of the classical core stress method are discussed. In addition, the differences and relations between two creep ratcheting assessment methods applicable to transient and sustained thermal load conditions respectively are clarified. The new results and conclusions presented in this paper can deepen the understanding of structural response under complex loading conditions, and provide guidance for shakedown analysis and creep ratcheting assessment of high-temperature components.

A Review on Strut and Tie Methods

Strut and tie method (STM) provides simplified solutions to complicated design problems. It was an evolutionary discovery which lead to an improved understanding of shear and flexural deformations of the structures. STM is applicable to the regions of the structure where beam theory is not valid. Numerous studies were conducted in this field, and various modifications are being attached to the conventional STM. Indeterminate models replaced determinate models, and nonlinear analysis replaced linear elastic analysis. New ideas like automatic generation of models based on optimisation techniques, simplified inelastic analysis using secant stiffness method and 3-dimensional analysis were also introduced. This paper summarises some of these studies and discusses their merits and limitations. Some suggestions to simplify these complicated methods are also included.

A JSME Code Case on Piping Seismic Design Based on Inelastic Response Analysis and Strain-Based Fatigue Criteria

Abstract A Code Case in the framework of the Nuclear Codes and Standards of Japan Society of Mechanical Engineers (JSME) has been published to incorporate seismic design evaluation methodologies for piping systems by detailed inelastic response analysis and strain-based fatigue criteria as an alternative design rule to the current rule, in order to provide a more rational seismic design evaluation by taking directly the response reduction due to plasticity energy absorption into account. The Code Case provides two strain-based criteria: one is a limit to maximum amplitude of equivalent strain amplitude derived from detailed analysis and the other is a limit to the fatigue usage factor also based on the equivalent strain amplitude. Some discussions are provided on the adequacy of additional damping in the simplified inelastic analysis and the safety margin and reliability of fatigue evaluation by the detailed inelastic response analysis provided in the Code Case.

弾塑性応答を考慮した配管系の耐震安全性評価

A Code Case in the framework of JSME Nuclear Codes and Standards is currently being developed to incorporate seismic design evaluation of piping by detailed elastic-plastic response analysis and strain-based fatigue criteria as an alternative design rule to the current rule, in order to provide a more rational seismic design evaluation. The Code Case provides two strain-based criteria; one is a limit to maximum amplitude of equivalent strain amplitude derived from detailed analysis and the other is a limit to the fatigue usage factor also based on the equivalent strain amplitude. The Code Case also provides an evaluation method by simplified inelastic analysis with an additional damping taking the response reduction due to plasticity into account. Some discussions are made on the adequacy of additional damping in the simplified inelastic analysis and the safety margin and reliability of fatigue evaluation by the detailed elastic-plastic response analysis provided in the Code Case.

Optimal fatigue analysis of structures during complex loadings

A new framework for high cycle fatigue analysis of metallic structures under complex multi-parameter loadings was here developed. This allows to reduce the analysis on a 2-D window with a characterized one-parameter cyclic loading thanks to an equivalence rule relative to damage between any two loadings. The simplified inelastic analysis introduced by J. Zarka [J. Zarka et al. 1990. A new approach in inelastic analysis of structures. CADLM] was used to find the limit state of the structure. A new design rules for fatigue analysis by utilizing automatic learning systems was successfully performed. A database was built by coupling numerical simulations and experimental results on several welded specimens which are considered as a general structure in the proposed approach. This could be possible by the introduction of an intelligent description of a general fatigue case based on the actual theories and models. A software, FATPRO [M.I. Systems, FatPro, available at http://www.mzintsys.com/our_products_fatpro.html], based on this work has been developed at MZ Intelligent Systems.

Simplified inelastic seismic analysis of base‐isolated structures using the N2 method

AbstractIn the paper a simplified nonlinear method has been applied to the analysis of base‐isolated structures. In the first part, a three‐linear idealization of the capacity curve is proposed. The initial stiffness is defined based on the first yielding point in the superstructure, whereas the secondary slope depends on the failure mechanism of the superstructure. A consequence is a much more pronounced secondary slope, which does not correspond to the presumptions used in the originally proposed N2 method. A parametric nonlinear dynamic study of single degree of freedom systems with different hardening slopes and damping has been performed for an ensemble of seven EC8 spectrum‐compatible artificial accelerograms. It was concluded that, in the long‐period range, the equal displacement rule could be assumed also for the proposed systems with non‐zero post‐yield stiffness. In the second part, the proposed idealization was used for the analysis of isolated RC frame buildings that were isolated with different (lead) rubber‐bearing isolation systems. The stiffness of the isolators was selected for three different protection levels and for three different ground motion intensities, which have resulted in elastic as well as moderately and fully damaged superstructure performance levels. Three different lateral load distributions were investigated. It was observed that a triangular distribution, with an additional force at the base, works best in the majority of practical cases. It was concluded that the N2 method can, in general, provide a reasonably accurate prediction of the actual top displacement, as well as of the expected damage to the superstructure. Copyright © 2009 John Wiley & Sons, Ltd.

참조응력법에 입각한 T-배관 국부 크리프 파단 평가를 위한 응력해석 사례연구

To investigate applicability of the reference stress approach as simplified inelastic stress analysis to estimate local creep rupture, detailed finite element stress analyses of a T-piece pipe with different inner pressure and system loading levels are performed. The reference stresses are obtained from the finite element (FE) limit analysis based on elastic-perfectly-plastic materials, from which the local reference stress for creep rupture is determined from R5. The resulting inelastic stresses are compared with elastic stresses resulting from linear elastic FE calculations. Furthermore they are also compared with the stresses from full elastic-creep FE analyses. It shows that the stresses estimated from the reference stress approach compare well with those from full elastic-creep FE analysis, which are significantly lower than the elastic stress results. Considering time and efforts for full inelastic creep analysis of structures, the reference stress approach is shown to be a powerful tool for creep rupture estimates and also to reduce conservatism of elastic stress analysis significantly.

Simplified dynamic inelastic analysis of tall buildings

Since the Kobe and Northridge earthquakes, static inelastic analysis has become an accepted and simple method for the seismic evaluation of high-rise buildings. In this method, the lateral load is monotonically increased with the same profile to find the ultimate capacity of the structure. Pushover analysis, however, has a limitation in the evaluation of a higher-mode dominant structure: for this reason, inelastic time history is used to compensate. In engineering practice, using inelastic time history analysis to evaluate the inelastic capacity of a building is impractical for tall buildings owing to the amount of computational time required and the difficulties in interpreting results. Therefore, a simplified inelastic analysis method is required for practical application. In the present paper, a simplified dynamic inelastic analysis (SDIA) method using elastic and inelastic response spectrums is introduced as a way to perform an inelastic analysis of a structure. The relative accuracy and efficiency of SDIA are explored by comparing the results with those of time history analysis software, DRAIN-2DX. The results of SDIA and DRAIN-2DX are almost identical, while with SDIA the computational time is dramatically reduced and time-consuming efforts interpreting results are saved.

Higher modes in simplified inelastic seismic analysis of single column bent viaducts

The influence of the higher modes and their consideration in the pushover analysis of reinforced concrete single column bent viaducts with different degree of irregularity is discussed. Typical multimode pushover-based methods (modal pushover analysis, modal adaptive non-linear static procedure and incremental response spectrum analysis) are addressed and compared with a single mode procedure (N2) and inelastic time history analysis. If in the transverse direction the substructure of the viaduct is flexible in comparison with the superstructure, the influence of higher modes is small (the structure is regular) and single mode procedure works well. This typically occurs when the columns are high or considerably damaged. Conversely, for the analysis of irregular structures having short and slightly damaged columns, the multimode methods are needed. In most cases, all the analysed multimode pushover-based methods have given the results comparable with time history analysis, with the exception of cases where torsional sensitivity is varying during the response. All the methods have limitations (discussed in detail in the paper), which should be fully recognized by the user. Copyright © 2005 John Wiley & Sons, Ltd.

Application of Simplified Inelastic Analysis Procedures Using Equivalent Linearization for Piping System Subjected to Shaking Table Test

Application of Simplified Inelastic Analysis Procedures Using Equivalent Linearization for Piping System Subjected to Shaking Table Test

Strain Concentration at Structural Discontinuities and Its Prediction Based on Characteristics of Compliance Change in Structures

Elevated temperature structural design codes pay attention to strain concentration at structural discontinuities due to creep and plasticity, since it causes an increase in creep-fatigue damage of materials. One of the difficulties in predicting strain concentration is its dependence on the magnitude of loading, the constitutive equations, and the duration of loading. In this study, the author investigated the fundamental mechanism of strain concentration and its main factors. The results revealed that strain concentration is caused by strain redistribution between elastic and inelastic regions, which can be quantified by the characteristics of structural compliance. The characteristics of structural compliance are controlled by elastic region in structures and are insensitive to constitutive equations. It means that inelastic analysis can be easily applied to obtain compliance characteristics. By utilizing this fact, a simplified inelastic analysis method was proposed based on the characteristics of compliance change for the prediction of strain concentration.

3322 繰返し負荷を受ける高温構造物の簡易非弾性解析手法

3322 繰返し負荷を受ける高温構造物の簡易非弾性解析手法

Strain Concentration at Structural Discontinuities and its Prediction based on Characteristics of Compliance Change in Structures.

Elevated temperature structural design codes pay attention to strain concentration at structural discontinuities due to creep and plasticity, since it causes to enlarge creep-fatigue damage of materials. One of the difficulties to predict strain concentration is its dependency on loading, constitutive equations, and relaxation time. This study investigated fundamental mechanism of strain concentration and its main factors. The results revealed that strain concentration was caused from strain redistribution between elastic and inelastic regions, which can be quantified by the characteristics of structural compliance. Characteristic of compliance is controlled by elastic region in structures and is insensitive to constitutive equations. It means that inelastic analysis is easily applied to get compliance characteristics. Paying attention to this fact, simplified inelastic analysis method was proposed based on characteristics of compliance change for prediction of strain concentration.

High Level Dynamic Testing and Analytical Correlations for a Small Bore Piping System

High-level dynamic testing of a prototypic insulated small bore diameter pipe system is described. The pipe system was supported by a minimum number of supports, with several combinations of supports and support locations tested. Load input consisted of a dynamic multifrequency time history and sinusoidal loading at increasing acceleration levels until gross deformation of the system occurred. Very high level pipe damping was exhibited when plastic response occurred. Post-test analyses were performed to assess the structural loading and response of the pipe system under the dynamic load input. Several elastic and elasto-plastic analysis failure prediction methods were used, along with simplified inelastic analysis.

Simplified analysis and design for elevated temperature components of Monju

The Japanese Prototype Fast Breeder Reactor Monju is now at a stage of submitting applications to the government for getting Construction Permission. Detailed structural design of components is now in progress. As well understood, a number of components of Monju have to be subjected to elevated temperature design. For this need, Power Reactor and Nuclear Fuel Development Corp. has developed “Elevated Temperature Structural Design Guide for Class 1 Components of Prototype Fast Breeder Reactor” (ETSDG). It is now incorporated into “Construction Code for Prototype Breeder Reactor”. The basic concept of ETSDG is originated from ASME Boiler and Pressure Vessel Code Section III, Case Interpretation N-47, ETSDG prepares some extended simplified inelastic analysis methods in addition to the basic concept of N-47. This extension is necessary to make easy the complicated inelastic analyses. The simplified methods have been developed through many case studies with detailed inelastic analyses, elastic analyses and experimental verifications.

Structural Analysis of an LMFBR Shield Assembly Duct Under Thermo-Mechanical and Seismic Loads

This paper describes the stress analysis performed to assess structural adequacy of the Clinch River Breeder Reactor (CRBR) core removable shield assemblies. Removable shield assemblies are located in the peripheral region of the core (between blanket assemblies and the fixed radial shield), and are subjected to severe cross-sectional thermal gradients and seismic loads requiring a relatively complex duct load pad design. For cost-effectiveness, the analysis was conducted in two stages. First, an elasto-plastic seismic stress analysis was performed using a detailed nonlinear finite element model (with gaps) of the load pad configuration. Next, in order to determine the total strain accumulation and the creep-fatigue damage the maximum seismic stresses combined with the “worst” thermal stresses from a single assembly model were used to perform a simplified inelastic analysis using two sets of material properties to bound the changing material conditions during reactor operation. This work demonstrated the necessity and applicability of the two simplified analysis techniques in elevated temperature structural design, i.e., the treatment of time-dependent degradation of material properties due to temperature and nuclear irradiation, and the use of time-independent finite element stress analysis results to perform a simplified creep-fatigue analysis.

Experimental and theoretical investigation of creep rupture of model structures.

The creep rupture experiments were performed on a spherical shell with a radial nozzle under cyclic loading conditions, to investigate the creep rupture behavior of structures and the validity of inelastic analysis. Inconel 617 was employed as a test material and the tests were performed at 950°C. The following two methods were used to predict the rupture life of specimens. One is a finite element method. The general purpose program MARC and an in-house special purpose program for axisymmetric shells were used for calculation. The linear creep fatigue interaction rule was applied for rupture life prediction. The other is a simplified inelastic analysis method for creep rupture of structures. The collapse load and corresponding stress field obtained by the finite element computer program were employed in the simplified methods. Experimental results were compared with the calculated values. It was confirmed that the detailed and the simplified inelastic analysis methods gave reasonable prediction.

A Simplified Method for Elastic-Plastic-Creep Structural Analysis

A simplified inelastic analysis computer program (ANSYMP) was developed for predicting the stress-strain history at the critical location of a thermomechanically cycled structure from an elastic solution. The program uses an iterative and incremental procedure to estimate the plastic strains from the material stress-strain properties and a plasticity hardening model. Creep effects can be calculated on the basis of stress relaxation at constant strain, creep at constant stress or a combination of stress relaxation and creep accumulation. The simplified method was exercised on a number of problems involving uniaxial and multiaxial loading, isothermal and nonisothermal conditions, dwell times at various points in the cycles, different materials, and kinematic hardening. Good agreement was found between these analytical results and nonlinear finite element solutions for these problems. The simplified analysis program used less than 1 percent of the CPU time required for a nonlinear finite element analysis.

Simplified Inelastic Analysis in Helical Coil Heat Exchanger Design

A simplified, inelastic analysis of helical coil tubing for high-temperature applications is described. Elastically calculated operating stresses are compared with inelastic estimates of allowable cyclic creep/fatigue stresses. The technique of simplifying and analyzing the operating cycles to determine acceptable creep damage levels has general application. The allowable stresses represent the greatest uncertainty in the method, and tests are required to improve their accuracy. A method of utilizing short-time test data to determine allowable stresses for reactor lifetimes of 30 to 40 years is proposed.

On a simplified inelastic analysis of structures

In this paper two main problems are considered: the derivation of cyclic constitutive relations during inelastic regime where hardening, softening and creep can occur, and the development of the eventual periodical state in the structure during cyclic thermodynamical loadings. We give a very simple and practical framework to solve these problems in one unique manner. Its essential feature consists in the introduction of a family of internal parameters which characterize local inelastic mechanisms and the family of transformed internal parameters which are linearly linked to the previous ones through a symmetrical non-negative matrix and are indeed the opposite of the associated residual stresses. Thanks to that, the treatment of the local plastic or viscoplastic yield conditions can be easily made from only the classical simple purely elastic (or viscoelastic) analysis. This property allows important results during cyclic loadings: conditions for elastic shakedown, plastic shakedown, ratcheting and bounds for the limiting state. Several examples are given in the text.