Elastic Modulus Reduction Method Research Articles

Structural analysis and optimization of steel truss bridge based on finite element method

In view of the defects of the current mainstream structural safety analysis method of Truss bridge, the safety analysis method at the component level should be further developed. Therefore, it is necessary to carry out the overall safety analysis and structural optimization at the structural level. Based on the concrete data of the actual steel truss beam bridge, this paper uses ABAQUS and MIDAS finite element software to model the truss structure. First of all, the static analysis is carried out, and then the structural analysis and optimization of the steel truss beam bridge is carried out with the elastic modulus reduction method. Based on the linear elastic finite element method, the bearing state of each component is solved, and the ultimate bearing capacity of the whole structure is calculated iteratively. Thus, the limitation of incremental nonlinear finite element method is overcome, and higher calculation accuracy and efficiency are realized.

Elastic modulus reduction method for stable bearing capacity analysis of dumbbell-shaped CFST arches

The elastic modulus adjustment procedures (EMAPs) can achieve much higher efficiency than incremental nonlinear finite element method (INFEM), however it could not take into account the stability effect on structures. In this paper, the elastic modulus reduction method (EMRM) was presented to estimate the stable bearing capacity of dumbbell-shaped concrete filled steel tube (CFST) arch. Firstly, the homogeneous generalized yield function (HGYF) was developed for dumbbell-shaped CFST members under combined action of axial force and bending moment by means of the fiber model technique, which was employed to determine the stable bearing capacity of these members. Secondly, the HGYF was adopted to define the element bearing ratio so that the EMRM was proposed for evaluating the stable bearing capacity of the dumbbell-shaped CFST arch by strategically reducing the elastic modulus of the highly stressed elements. Finally, results from the INFEM and test data of 3 dumbbell-shaped CFST arches and 30 dumbbell-shaped CFST members were adopted as examples to validate the proposed EMRM and the HGYF, which shows that the stability has a significant influence on the CFST arches and the proposed EMRM achieves higher accuracy and efficiency than the INFEM.

The elastic modulus reduction method for upper bound limit analysis of pressure vessels incorporating material strain hardening effect

Pressure vessel is a kind of special equipment which is involved in various industries. Once it is damaged, it will cause great loss to people’s life and property. The traditional elastic modulus reduction method for upper bound limit analysis of pressure vessels adopts the elastic-perfectly plastic material model. This method will result in waste of materials without considering the material strain hardening effect. So the material strain hardening effect is introduced into upper bound limit analysis. Firstly, the equivalent yield strength considering material strain hardening effect is established. Then, the formula of limit load multiplier which is expressed by the equivalent yield strength is derived based on the upper bound theorem. Combined with the strategy for elastic modulus adjustment, the elastic modulus reduction method for upper bound limit analysis of pressure vessels incorporating material strain hardening effect is constructed. The limitation of the elastic-perfectly plastic model for the upper bound analysis method is eliminated by the method proposed in this paper. The result calculated by this method is closer to the true limit load of pressure vessels.

Data for ultimate bearing capacity of concrete-filled steel tubular members and arches by the elastic modulus reduction method.

Homogeneous generalized yield function is adopted in this article to calculate the ultimate bearing capacity of 93 concrete-filled steel tubular components with detailed test data, and the ratios of the ultimate bearing capacity calculated to the tested are presented. Moreover, the incremental nonlinear finite element method and elastic modulus reduction method are adopted to evaluate the ultimate bearing capacity of 11 concrete-filled steel tubular arches, 7 among which with detailed test data. The component data cover those under different loading conditions, material strength and geometric parameters, and the arch data include those under different loading conditions and rise to span ratios. The data provided are useful to investigate the strength of CFST members and arches and to demonstrate the validation of other numerical methods. The current data are considered as a complementary for the main work “Linear elastic iteration technique for ultimate bearing capacity of circular CFST arches” [1].

Model-Free Method for Damage Localization of Grid Structure

A model-free damage identification method for grid structures based on displacement difference is proposed. The inherent relationship between the displacement difference and the position of structural damage was deduced in detail by the Sherman–Morrison–Woodbury formula, and the basic principle of damage localization of the grid structure was obtained. That is, except for the tensile and compressive deformations of the damaged elements, the deformations of other elements were small, and only rigid body displacements occurred before and after the structural damage. According to this rule, a method for identifying the position of the damage was proposed for the space grid structure by using the rate of change of length for each element. Taking a space grid structure with a large number of elements as an example, the elastic modulus reduction method was used to simulate the damage to the elements, and the static and dynamic test parameters were simulated respectively to obtain the difference in displacement before and after the structural damage. The rate of change of length of each element was calculated based on the obtained displacement difference, and data noise was added to the simulation. The results indicated that the element with the larger length change rate in the structure was the most likely to be damaged, and the damaged element can be accurately evaluated even in the presence of noise in data.

An experimental methodology to characterise post-necking behaviour and quantify ductile damage accumulation in isotropic materials

The development of ductile damage, that occurs beyond the point of necking in a tensile test, can be difficult to quantify. An experimental methodology has been developed to accurately characterise the post-necking deformation response of a material through continuous monitoring of the specimens shape up until rupture. By studying the evolution of the neck geometry, the correct values of the local stress and strain have been determined in samples of grade 304L stainless steel and C110 copper. Notched bar specimens of various notch acuities were examined enabling the effects of stress triaxiality on ductile fracture to be determined. The methodology developed has provided a robust framework for macroscopic measurements of ductile damage during the necking process. To characterise the material degradation process, the elastic modulus reduction method was employed on hourglass-shaped specimens of the same materials. Stiffness degradation was measured using a small gauge extensometer during uninterrupted tensile tests with partial elastic unloadings. A metallographic study was conducted on progressively damaged specimens in order to validate the macroscopic damage measurements. A new non-linear ductile damage accumulation law has been developed and calibrated, which provides an advanced representation of the experimental results, and a significant improvement compared to linear accumulation models frequently employed. This realistic modelling approach considers the degradation of the material when it has undergone severe plastic deformation, and provides a more accurate representation of the near failure behaviour by considering the effects of stress triaxiality. The methodology provides accurate data for damage model development and calibration, to improve the predictions of remnant life from ductile damage in engineering components.

Elastic Modulus Reduction Method Based Ultimate Bearing Capacity Analysis of CFST Truss Arch

In order to evaluate the application of elastic modulus reduction method on the ultimate bearing capacity analysis of CFST truss arch, the elastic modulus reduction method was compared with the test data and the increment nonlinear finite element method. Firstly, the element bearing ratio was defined according to the homogeneous generalized yield function, and the principle of deformation energy conservation was adopted to derive the elastic modulus adjustment strategy, based on which the modulus reduction method was developed for the ultimate bearing capacity analysis of CFST structures. Then, combined with the incorporated strength capacity technique, the section strength was modified to consider the structural constant load effect. Finally, the ultimate bearing capacity of a CFST truss girder and 136m span truss arch was obtained on the basis of the proposed method, and the results were compared with the test data and the incremental nonlinear finite element method. The results show that the elastic modulus reduction method can achieve high calculation accuracy and wide application for the ultimate bearing capacity analysis of CFST truss arch.

Failure path-independent methodology for structural damage evolution and failure mode analysis of framed structures

Traditional methods for structural damage evolution and failure mode analysis usually depend on specific failure path analysis, which is inefficient and time-consuming to implement for complex structures. In this paper, an efficient failure path-independent methodology for structural damage evolution and failure mode analysis of framed structures is proposed based on the elastic modulus reduction method. The element bearing ratio, uniformity of element bearing ratio and reference element bearing ratio are defined in terms of the homogeneous generalized yield function of spatial beam element, while a dynamic criterion is presented to identify the highly stressed elements. Subsequently, a self-adaptive strategy of elastic modulus adjustment is developed to reduce the elastic moduli of the highly stressed elements for simulation of structural damage evolution. Finally, the reduction rate of elastic moduli of the highly stressed elements is presented to determine the failed sections among the failure elements in the last iteration, based on which the potential failure mode is identified. The applicability, computational accuracy and efficiency of the proposed methodology are validated by comparing with the elasto-plastic methods through two numerical examples.

A failure-path independent method for analysis of structural system reliability

In order to overcome the disadvantages of traditional system reliability methods in the identification of significant failure modes and calculation of joint failure probability, a failure-path independent method is presented for structural system reliability analysis by combining the elastic modulus reduction method and the stochastic finite element method (SFEM). The stochastic responses by the SFEM were employed to define the element bearing ratio and the reference EBR, based on which an efficient dynamic criterion was developed for identification of highly stressed elements. The stochastic elastic modulus reduction method was proposed for simulation of internal force redistribution and damage evolution based on the principle of deformation energy conservation. The significant failure modes of structural system were identified according to the elastic modulus of the highly stressed elements in the limit state, while structural system reliability was calculated based on the joint failure probability of multi-failure modes. Investigation demonstrated the advantages of the proposed method over the traditional system reliability methods and its high accuracy and efficiency.

Limit Analyisis of Frame Structure Based on the Elastic Modulus Reduction Method

An efficient linear elastic iterative finite element method, namely, the elastic modulus reduction method is introduced to calculate limit load of frame structure. The elastic modulus reduction method defines the element bearing ratio on the basis of the generalized yield criterion and the strain energy equilibrium principle. Because the bending moment is the main factor inducing the frame structure damage, the element bearing ratio only considering the bending moment yield is proposed. Numerical examples demonstrate the applicability and precision of the elastic modulus reduction method for limit analysis of frame structures.

Homogeneous generalized yield criterion based elastic modulus reduction method for limit analysis of thin-walled structures with angle steel

A homogeneous generalized yield criterion (HGYC) expressed by piecewise polynomial is given for angle section. The element bearing ratio (EBR), reference EBR, and uniformity of EBR are defined in term of the HGYC. Then, a HGYC based elastic modulus reduction method for limit analysis of thin-walled structures with angle steel is presented based on the modulus adjustment strategy established on the EBR and the conservation criterion of energy. The method proposed can overcome the disadvantage of the conventional elastic modulus adjustment procedure where the nonhomogeneous generalized yield criterion is employed and the proportional loading condition is not satisfied.

Meshless techniques in estimation of C* integral using elastic modulus reduction approach

In this paper, an elastic modulus reduction (EMR) method is used for the estimation of the creep fracture mechanics parameter C*. The method makes use of uniaxial creep material properties and an appropriate definition of the limiting stresses ahead of the crack tip. Several standard test specimens are selected for analysis. First, the limit load calculations are performed for specimens using the EMR approach and then the C* integral is estimated using the reference stress method. For the limit load analysis of the cracked bodies, a special meshless code has been developed. The results obtained for both limit loads and C* integral are compared with the literature. It is shown that for the present geometries good agreement can be achieved.

Elastic Modulus Reduction Method Based Limit Analysis of Steel Lined Reinforced Concrete Penstocks Containing Flaws

In the context of ultimate bearing capacity of steel lined reinforced concrete penstock (SLRCP) containing flaws, the use of the elastic modulus reduction method (EMRM) in conjunction with curve beam based internal force calculation is presented. The corrosion models for steel bar and lining are introduced from the literature. The SLRCP is considered bearing load together with lining and reinforced concrete, and its internal force is determined based on a simplified curve beam model. The element bearing ratio of SLRCP is given through the internal force and sectional strength, and is employed by the EMRM. The change of ultimate bearing capacity of some typical SLRCP within their operating life is then evaluated.

Element Bearing Ratio Based Integral Safety Evaluation of Penstocks

Though it had been employed for limit analysis and integral safety assessment of pressure pipe and vessel, most of the elastic modulus adjustment procedures were applicable to simple structures because their load multiplier was mainly determined by stress. In this paper, a series of element bearing ratio (EBR) based load multiplier algorithms are given, in which the influence of both stress and material on limit load are included. The EBR based load multiplier algorithms are investigated, and two efficient algorithms are suggested. Then the two algorithms combined with the elastic modulus adjustment procedure of elastic modulus reduction method are applied to limit analysis and integral safety assessment of penstocks.

System Reliability Evaluation Based on Stochastic Limit Analysis

It is quite difficult to estimate system reliability of complex structures which involve lots of potential failure modes. A novel method for system reliability analysis of frame structure was proposed based on stochastic limit analysis. Stochastic limit load was firstly calculated based on the elastic modulus reduction method (EMRM) by taking the uncertainty of structural resistance into account. Once the limit state equation was established by the stochastic limit load, the system reliability index can be calculated by the first-order reliability method (FORM) efficiently. Numerical example illustrates the efficiency and accuracy of the proposed method by comparing with the traditional failure mode analysis approaches.

Safety Evaluation of Branch Pipe in Hydropower Station Using Elastic Modulus Reduction Method

The high pressure branch pipe in hydropower station (BPHS) is usually composed by different materials in different parts and has complicated geometric configurations. The accurate and efficient methods for safety evaluation of the BPHS are still desirable. By introducing the element bearing ratio (EBR), generalized yield criterion as well as the reference volume concept, the elastic modulus reduction method (EMRM) is improved and applied to determine both the upper and lower bounds on limit loads of the BPHS. The global safety factor (GSF) is defined as the ratio of limit load to design load. The safety performance of the BPHS is assessed by comparing the GSF resulted from the EMRM with its allowable value specified in code. The efficiency and precision of the proposed method for safety evaluation of the BPHS are demonstrated through numerical examples in this paper. The results show that the proposed method is more suitable for safety evaluation and design optimization of the BPHS, compared with the elastic stress analysis method (ESAM) based on stress categorization which might underestimate the safety performance of the BPHS.

System reliability analysis of spatial variance frames based on random field and stochastic elastic modulus reduction method

This paper presents the stochastic elastic modulus reduction method for system reliability analysis of spatial variance frames based on the perturbation stochastic finite element method (PSFEM) and the local average of a random field. The stochastic responses and reliability index of each element of a structural frame are characterized by the PSFEM and the first-order second-moment method, to properly handle the correlation structures and scale of fluctuation of random fields. A strategy of elastic modulus adjustment for the estimation of system reliability is developed to determine the range and magnitude of elastic modulus reduction, by taking the element reliability index as a governing parameter. The collapse mechanism and system reliability index of a stochastic framed structure are determined through iterative computations of the PSFEM. Compared with the failure mode approaches in traditional system reliability analysis, the proposed method avoids two major difficulties, namely the identification of significant failure modes and estimation of the joint probability of failure modes. The influences of the correlation structure and scale of fluctuation of the random field upon system reliability are investigated to demonstrate the accuracy and computational efficiency of the proposed methodology in system reliability analysis of spatial variance frames.

Limit Bearing Capacity Analysis of Structure System with Different Types of Element Using Elastic Modulus Reduction Method

Limit bearing capacity analysis of structure system with different types of element (SSDE) is difficult to elastic modulus adjustment procedures. In this paper, elastic modulus reduction method (EMRM) is introduced for evaluation of the limit bearing capacity of SSDE, using the element bearing ratio (EBR) as the governing parameter. As a dimensionless quantity, the EBR can be used to measure the bearing state of every element, and the scheme of reducing elastic modulus can be expressed using a uniform equation for different types of element. When the structure system destroys, all elements will tend to reach their own strength. The algorithm is then extended to the plastic limit analysis of SSDE. Numerical examples are employed to demonstrate the applicability, accuracy and efficiency of the method.

Study on the Strategy of Elastic Modulus Adjustment of the Elastic Modulus Reduction Method for Limit Analysis of Structures Containing Flaws

As a limit analysis method lately presented, the elastic modulus reduction method (EMRM) has the advantages of simplicity and high efficiency. In this paper, the strategy of elastic modulus adjustment of the EMRM is studied in order to extend the method applicable to the limit analysis of structures containing flaws (SCF). Two new algorithms of the reference element bearing ratio, reference element bearing ratio based on reference stress (REBS) and reference element bearing ratio based on integral element bearing ratio gradient (REBG), are proposed. Numerical examples show that the problems of instability and non-convergence in iterative process of limit analysis of SCF are improved, when the REBS or REBG is used in the strategy of elastic modulus adjustment of the EMRM.

Elastic modulus reduction method for limit analysis considering initial constant and proportional loadings

The paper proposes an efficient linear elastic iterative finite element method, namely, the elastic modulus reduction method (EMRM) to calculate lower-bound limit loads of frame structures under combined action of initial constant and proportional loads. The initial constant loads are scaled down by the limit load achieved in the last step of iterations and regarded as the pseudo-proportional loads (PPLs) on the assumption that the PPLs increase along with the proportional loads and their final values should be equal to the initial constant loads when structure gets to the plastic limit state. Meanwhile, the elastic modulus reduction method (EMRM) is developed by defining the element bearing ratio (EBR) on the basis of the generalized yield criterion and the strain energy equilibrium principle (SEEP). Numerical examples demonstrate the applicability and precision of the proposed method for limit analysis of frame structures under combined action of initial constant and proportional loads.