Inelastic Analysis Methods 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.

An advanced computational method for nonlinear inelastic thermo-mechanical analysis of spatial steel frames in fires

A novel advanced computational method incorporating the stability functions and the distributed plasticity model into the fiber beam-column element is proposed for the first time to predict the nonlinear inelastic thermo-mechanical behavior of spatial steel frames in fires. The space spread of plasticity is captured by tracing the uniaxial temperature-stress–strain relation of each fiber on sections at integration points. The element stiffness matrix is integrated via the Gauss-Lobatto numerical integration scheme. The nonlinear material behavior is captured by adopting the distributed plasticity model with the force-based interpolation function whereas the geometric nonlinearity of P-δ and P-Δ effects are considered by using the stability functions and a geometric matrix, respectively. The shear deformation and residual stresses which normally exist in steel frames are also considered. For the implementation, a nonlinear thermal incremental-iterative solution scheme based on the Newton-Raphson and Gaussian Elimination algorithm is also developed to address the nonlinear problems due to thermal expansion and material degradation. By taking advantage of the computational benefits of stability functions and the force-based interpolation function, the proposed method offers a novel computational framework for nonlinear structural analysis in a fire with excellent computational efficiency. The reliability and accuracy of the proposed program are verified by comparing the obtained results with results from test data, existing studies, and Abaqus. In addition, the computational performance of the proposed numerical program is about 10 times more effective than the Abaqus commercial software, thus would offer an extremely valuable tool for practical fire resistance designs.

Second-order arbitrarily-located-refined plastic hinge model for high-strength steel frame design

A second-order inelastic analysis method is developed for welded high-strength steel (i.e., Q460GJ steel in this study) frames with box-sections and H-sections. Due to the great differences in the distribution of the residual stresses between welded Q460GJ steel and mild steel, traditional tangent modulus and stiffness degradation function are unsuitable for the design of welded 460GJ steel members and structures. This paper proposes a new beam–column element using the stability functions which allows refined plastic hinges to form in an arbitrary location along the member. With the considering of the effects of residual stresses in Q460GJ steel sections, new tangent modulus formulae and stiffness degradation functions are proposed for the welded Q460GJ steel members and structures. Existing experimental results of welded Q460GJ steel columns under axial and eccentric compression are introduced to verify the reasonability and accuracy of the proposed method. Based on the theoretical model, a computation program is developed for the analysis of steel frames with welded Q460GJ steel section and the analyzed results agree well with the finite element results. The proposed analysis is shown to be an efficient tool ready to be implemented into the design practice.

Proposal of an Interlaminar Fatigue Life Evaluation Method for CFRP Based on Inelastic Two-Scale Analysis

In this paper, a prediction method for interlaminar fatigue life of carbon fiber-reinforced plastic (CFRP) is proposed based on an inelastic two-scale analysis method combined with the Coffin-Manson law. For this, the flatwise tension test of a CFRP is simulated using the two-scale analysis method, and the distributions of microscopic viscoplastic strain occurring at resin parts in micro-structures (unit cells) are examined. Then, the maximum value of microscopic viscoplastic strain is applied to the Coffin-Manson law for the resin to predict interlaminar fatigue life of the CFRP.

Shaking Table Tests to Validate Inelastic Seismic Analysis Method Applicable to Nuclear Metal Components

The main purpose of this study is to perform shaking table tests to validate the inelastic seismic analysis method applicable to pressure-retaining metal components in nuclear power plants (NPPs). To do this, the test mockup was designed and fabricated to be able to describe the hot leg surge line nozzle with a piping system, which is known to be one of the seismically fragile components in nuclear steam supply systems (NSSS). The used input motions are the displacement time histories corresponding to the design floor response spectrum at an elevation of 136 ft in the in-structure building in NPPs. Two earthquake levels are used in this study. One is the design-basis safe shutdown earthquake level (SSE, PGA = 0.3 g) and the other is the beyond-design-basis earthquake level (BDBE, PGA = 0.6 g), which is linearly scaled from the SSE level. To measure the inelastic strain responses, five strain gauges were attached at the expected critical locations in the target nozzle, and three accelerometers were installed at the shaking table and piping system to measure the dynamic responses. From the results of the shaking table tests, it was found that the plastic strain response at the target nozzle and the acceleration response at the piping system were not amplified by as much as two times the input earthquake level because the plastic behavior in the piping system significantly contributed to energy dissipation during the seismic events. To simulate the test results, elastoplastic seismic analyses with the well-known Chaboche kinematic hardening model and the Voce isotropic hardening model for Type 316 stainless steel were carried out, and the results of the principal strain and the acceleration responses were compared with the test results. From the comparison, it was found that the inelastic seismic analysis method can give very reasonable results when the earthquake level is large enough to invoke plastic behavior in nuclear metal components.

Nonlinear inelastic analysis of semi-rigid steel frames with circular concrete-filled steel tubular columns

A reliable and effective method for the nonlinear inelastic analysis of frames using circular concrete-filled steel tubular (CFST) columns is developed in this paper. In the proposed method, the CFST columns and steel beams of the frame are modeled by using a fiber beam-column element that accounts for the nonlinear behaviors of both geometry and materials of the structure. The cross-sections of the elements are discretized into many small fibers and the stiffness matrix of the beam-column element is integrated through the Gauss-Labatto integration. The semi-rigid connections are modeled by using a zero-length element model where the nonlinear relationship of moment and rotation is formulated using a three-parameter power model. The accuracy and efficiency of the proposed method for modeling CFST columns are validated first by comparing the numerical results with multiple experimental results. Two CFST structures including the circular CFST column cantilever and the full-scale portal CFST frame with a variety of beam-to-column connections are then analyzed and verified with finite element models implemented in ABAQUS. The obtained results showed that the proposed method is highly accurate and can be utilized as an extremely useful tool for the nonlinear inelastic analysis of the CFST structures.

Structural steel design using second-order inelastic analysis with strain limits

Steel framed structures are affected, to greater or lesser extent, by (i) geometrical nonlinearity associated with the change in geometry of the structure under load and (ii) material nonlinearity related to the onset and spread of plasticity. In traditional design approaches, the design forces and moments within structural members are usually determined from simplified structural analyses (e.g. first or second-order elastic analysis), after which member design checks are performed to assess the strength and stability of the individual members. The extent to which the strength and deformation capacity of cross-sections is affected by local buckling is typically assessed through the concept of cross-section classification. For example, only compact (Class 1) cross-sections are considered to possess sufficient rotation capacity for plastic hinges to develop and for inelastic analysis methods to be used. This approach results in step-wise capacity predictions and is considered to be overly simplistic. Since the structural analysis of steel framed structures is typically performed using beam finite elements, which are unable to explicitly capture local buckling, a more sophisticated treatment of the available deformation capacity is required if inelastic analysis methods are to be used for all cross-section classes. A novel method of design by advanced inelastic analysis has recently been developed (Gardner et al., 2019a; Fieber et al., 2019a, 2018a, 2018b [1–4]), in which strain limits are employed to represent the effects of local buckling in beam finite element models and thereby control the spread of plasticity and level of force/moment redistribution within a structure. It is thus possible to use a consistent advanced analysis framework to design structures composed of cross-sections of any class. In the present paper, application of the proposed design method to continuous beams and planar frames is illustrated and assessed. Ultimate load capacity predictions are compared against results obtained from benchmark shell finite element models that explicitly capture local buckling and to conventional steel design. It is found that the proposed method predicts safe-sided ultimate capacities that are consistently more accurate than current design methods, particularly for structures benefiting from strain hardening and for structures composed of non-compact cross-sections where inelastic redistribution is typically ignored.

Seismic performance of reinforced concrete structures with pushover analysis

A building that looks strong enough might possibly collapse due to the earthquake load. Earthquake resistant design is generally based on an analysis of elastic structures that are given a load factor to simulate ultimate conditions. When an earthquake occurs, the collapse behavior of a building structure is inelastic. Evaluations that can estimate the inelastic condition of buildings during an earthquake are analyzed using pushover analysis. Pushover analysis is the nonlinear static load of the structural collapse behavior of an earthquake, while the performance point is the magnitude of the maximum displacement of the structure during a earthquake. The inelastic structure analysis and evaluation method used computer application SAP 2000. Evaluation results of structural performance levels according to Applied Technology Council 40 (ATC-40) on the X and Y direction structure, the maximum total drift and total inelastic drift maximum values in the X and Y directions included in the Immediate Occupancy (IO) level category (maximum drift value of a building structure 0.00047 < 0.005).

Inelastic Ultimate Load Analysis of Steel Frames Considering Lateral Torsional Buckling Under Distributed Loads

Contemporary structural design approaches necessitates ways to determine realistic behavior of structures. For this purpose, inelastic ultimate load analysis methods are used widely since strength and stability of whole structure can be represented. In this study, a numerical method is proposed for determining inelastic ultimate load capacity of steel frames considering lateral torsional buckling behavior under distributed loads. In the analyses, inelastic material behavior, second-order effects and residual stresses of the structural frame system and its members are taken into account. Additionally, lateral torsional buckling behavior is considered in the analysis using finite difference method and it is used for determining the structural load carrying capacity of steel frames. Consequently, the problem associated with flexural capacity decreases due to lateral torsional buckling is precisely considered in the load increment steps of inelastic ultimate load analysis. In order to validate the proposed method, numerical examples from the literature are calculated considering the proposed method, AISC 360-16 design specification equations and approaches from the literature. Results of the numerical examples show that lateral torsional buckling is a key issue in determining structural load carrying capacity. Thus, proposed analysis method is shown to be an efficient and consistent tool for inelastic ultimate load analysis.

Towards reliable design-by-analysis for divertor plasma facing components – Guidelines for inelastic assessment (part 1: Unirradiated)

Guidelines are presented for the recommended method of assessing by analysis the structural integrity of divertor plasma facing components (PFCs) under high heat flux (HHF) loads. The objective is to enable analysis to provide greater supporting evidence for PFC qualification (which for ITER is currently achieved by test alone) and to provide reasonable estimates of irradiated PFC performance where component test data is limited or non-existent. Typically, PFCs comprise tungsten armour, CuCrZr heat-sink and copper interlayer. For more reliable assessment of this type of construction, two shortfalls in existing elastic analysis methods have been addressed. Firstly, the scope of assessment rules has been extended to cover armour failure (e.g. by deep cracking) and secondly the accuracy of analysis is increased by using inelastic analysis methods to address complexities created by PFC’s multi-material block like construction. These complexities arise mainly from the dissimilar yield strengths and thermal expansion coefficients of the component materials. This paper details the proposed “low temperature” design code rules in the guidelines, which are based on a combination of existing inelastic code rules plus a set of methodologies devised specifically for PFC structures. The failure mechanisms of exhaustion of ductility, fast-fracture, fatigue and ratcheting are addressed, and the process of assessment is demonstrated by means of an example analysis on an ITER-like monoblock component in its unirradiated condition. In two follow- up papers, creep rules and methods for estimating the HHF structural integrity of an irradiated component using sparse irradiated materials data are presented. In the unirradiated condition it is shown that fatigue and armour cracking performance dominate predicted structural integrity, but when irradiated, exhaustion of ductility is expected to be more prevalent. It is argued that with these more rigorous assessment methods, a significant step has been made towards developing reliable design-by-analysis methods for predicting the expected HHF structural integrity performance of divertor PFC designs.

Development and verification of an inelastic two-scale analysis method for composites using finite element analysis software

Development and verification of an inelastic two-scale analysis method for composites using finite element analysis software

Application of inelastic response spectrum analysis method to seismic response analysis of piping systems

Application of inelastic response spectrum analysis method to seismic response analysis of piping systems

A second-order flexibility-based model for steel frames of tapered members

The paper presents a new computer method for nonlinear inelastic analysis of steel frames consisting with members with non-uniform cross-sections. A novel second-order flexibility-based element has been developed. The behaviour model accounts for material inelasticity due to combined bending and axial force, element geometrical nonlinear effects in conjunction with initial geometric imperfections using only one element per structural member. The proposed element formulation combines the power series approach to obtain the general solution of the second-order bending moments with the Maxwell-Mohr method to compute the force-displacement relationship of the general continuously non-prismatic Timoshenko-Euler beam-column element. The method ensures also that the plastic strength interaction requirements are always satisfied in the plastic hinges developed at the ends of the member or within the member length. The second-order elasto-plastic tangent stiffness matrix and equivalent nodal loads vector of non-uniform 2D steel members with semi-rigid connections is developed and the proposed nonlinear analysis formulation has been implemented in a computer program. In order to verify the efficiency and accuracy of the proposed approach, several benchmark problems have been studied and the results prove the performance of the proposed method.

Practical nonlinear inelastic analysis method of composite steel-concrete beams with partial composite action

This paper presents an efficient computer method for nonlinear inelastic analysis of composite steel-concrete beams with partial composite action. The proposed formulation is intended to model the combined effects of partial composite action and distributed plasticity using only one 2-noded beam-column element per structural member. Based on elasto-plastic cross-sectional analyses the behaviour model is able to take into account the effects of partial composite action between the concrete slab and the steel beam. Gradual yielding throughout the cross-section is described through basic equilibrium, compatibility, material and shear connection nonlinear constitutive equations. Tangent flexural and axial rigidity of the cross-section are derived and then using the flexibility approach the elasto-plastic tangent stiffness matrix and equivalent nodal loads vector of the beam-column element including the shear deformability of the partially connected composite beam has been developed. The proposed nonlinear analysis formulation has been implemented in a general nonlinear static purpose computer program, NEFCAD. Advanced finite element simulations have been conducted by using the specialized software for nonlinear analysis of structures, ABAQUS. Several computational examples are given to validate the accuracy and efficiency of the proposed method by comparing the results predicted by NEFCAD with those given by the ABAQUS software and other results retrieved from the open literature.

Estimation of Plastic and Creep Strain Development of SAC Solder under Cyclic Loading by Using Stepped Ramp Waves

The fatigue tests under both loading conditions of the Fast-Slow and the Slow-Fast were conducted to discuss validity of an inelastic strain analysis method which was proposed previously. The development behaviors of plastic and creep strains during the tests were analyzed by employing the stepped ramp wave (SW) loading. Using the analysis results, the difference of the development behaviors of plastic and creep strains between the Fast-Slow condition and the Slow-Fast condition was clarified. Then, the fatigue failure surfaces obtained from the tests were observed by using SEM to clarify the difference of the fracture surface between the Fast-Slow condition and the Slow-Fast condition. By correlating the aspect of fracture surface with the development behavior of plastic and creep strain, the validity of the proposed inelastic strain analysis method was discussed.

Seismic Assessment of Reinforced Concrete Frameworks through Advanced Pushover Analysis and Nonlinear Response of a SDOF Oscillator

This paper presents an integrated system for advanced structural analysis and seismic performance evaluation of 2D reinforced concrete frameworks. The advanced non-linear inelastic static analysis employed herein uses the accuracy of the fibre elements approach for large deflection inelastic frame analysis and address its efficiency and modelling shortcomings both to element level, through the use of only one element to model each physical member of the frame, and to cross-sectional level through the use of path integral approach for numerical integration of the cross-sectional nonlinear characteristics. Evaluation of the seismic performance is achieved with an approach that uses nonlinear time-history analysis (NTHA) of a single degree-of-freedom (SDOF) oscillator. The inelastic ductility and displacement demand is determined directly from accelerograms, without graphical or numerical approximations. Several computational examples are given to validate the effectiveness of the proposed method, the reliability and time saving of the code. The influence of the accuracy of the second-order nonlinear inelastic analysis methods involved in the modelling of the selected RC frame in conjunction with the distributions of the pushover lateral loads is pointed out. The proposed procedure is developed in the framework of Eurocode 8 design methodology, as reliable tool ready to be implemented into everyday design practice for advanced analysis, pushover analysis, and seismic performance evaluation of RC frame structures.

Nonlinear inelastic time-history analysis of three-dimensional semi-rigid steel frames

This paper presents a simple, effective numerical procedure based on the beam–column method by using the based-displacement finite element method for nonlinear inelastic time-history analysis of three-dimensional semi-rigid steel frames. The nonlinear geometry effects are considered by using stability functions and the geometric stiffness matrix. The inelasticity of material is considered by the gradual yielding of plastic hinges. A space zero-length multi-spring element is proposed to simulate the nonlinear cyclic behavior of steel connections through the independent hardening model. The Hilber–Hughes–Taylor method combined with the Newton–Raphson balance iterative algorithm is adopted to solve the nonlinear equations of motion. The results of nonlinear responses for steel frames with fully rigid and linear semi-rigid connections compare well with those of previous studies and commercial SAP2000 software. Moreover, the results of steel frames with semi-rigid connections shown in this paper can be used to calibrate similar frames in future studies.

平織積層板のマクロ/メゾ/ミクロ非弾性解析手法の開発と実験的評価

In this study, macro/meso/micro inelastic analysis method for plain-woven laminates is developed based on a homogenization theory for nonlinear time-dependent composites. For this, a three-scale modeling of plain-woven laminates is performed by considering a plain-woven laminate as a macrostructure, fiber bundles (yarns) and a matrix in the laminate as a mesostructure, and fibers and a matrix in the yarns as a microstructure. Then, a macroscopic constitutive equation of the laminate is derived by dually applying the homogenization theory for nonlinear time-dependent composites to not only the meso/micro scale but also the macro/meso scale. Using the present analysis method, the elastic-viscoplastic analysis of a plain-woven glass fiber/epoxy laminate subjected to on and off-axis loading is performed. Moreover, the analysis results are compared with the experimental data. It is shown that the present analysis method successfully takes into account the effects of inelastic properties of the epoxy not only around the fiber bundles but also inside of the fiber bundles. It is also shown that the results of analysis are in good agreement with experimental data.

Role of local slenderness in the rotation capacity of structural steel members

The objective of this paper is to demonstrate how element (e.g., flange) local slenderness may be used to predict element strain capacity, and in turn, the element strain capacity may be used to predict member rotational capacity in structural steel members. Member plastic hinge rotation capacity has an important role in the design of steel structures, and while implicit understanding of the rotation capacity has sufficed in the past, as inelastic direct analysis methods are adopted in conventional as well as seismic design more explicit treatments are needed. Accordingly, a comprehensive series of material and geometric shell finite element collapse analyses are performed in ABAQUS on component elements (plates). The finite element analysis confirms the hypothesis that local slenderness of an element is intimately connected to the element's strain capacity. Utilizing element strain capacity to determine member rotational ductility demonstrates the importance of additional factors, such as depth-to-length and shape factor of the member in predicting the rotational capacity. The proposed method assumes Euler–Bernoulli beam theory, ignores interaction between local and lateral–torsional buckling, and presumes the flange (not the web) controls the section strain capacity. The analyses are compared to existing code provisions for both conventional and seismic design and recommendations for potential improvements are made.

A computer method for nonlinear inelastic analysis of 3D composite steel–concrete frame structures

This paper presents an efficient computer method for nonlinear inelastic analysis of three-dimensional composite steel–concrete frameworks. The proposed formulation is intended to model the geometrically nonlinear inelastic behaviour of composite frame elements using only one element per physical member. The behaviour model accounts for material inelasticity due to combined bi-axial bending and axial force, gradual yielding is described through basic equilibrium, compatibility and material nonlinear constitutive equations. In this way, the states of strain, stress and yield stress are monitored explicitly during each step of the analysis, the arbitrary cross-sectional shape, various stress–strain relationships for concrete and steel and the effect of material imperfections such as residual stresses are accurately included in the analysis. Tangent flexural rigidity of cross-section is derived and then using the flexibility approach the elasto-plastic tangent stiffness matrix and equivalent nodal loads vector of 3-D beam-column element is developed. The method ensures also that the ultimate strength capacity of the cross-section is nowhere exceeded once a full plastified section develops. The proposed nonlinear analysis formulation has been implemented in a general nonlinear static purpose computer program. Several computational examples are given to validate the effectiveness of the proposed method and the reliability of the code to approach large-scale spatial frame structures.