Elastic Modulus Adjustment Procedures Research Articles

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.

Quickly analyze the limit load of thinning defect elbows with elastic modulus adjustment method

In the process of production and service of pressure pipeline, local thinning defects may occur due to dielectric corrosion, manufacturing defects and other reasons. These defects reduce the carrying capacity of the pipeline and lead to leakage and rupture of the pipeline. Therefore, the integrity assessment of components and structures is required. Traditionally, the inelastic finite element method (FEM) is highly dependent on the specification of adequate mesh density and an assurance of numerically stable solutions. However, in engineering design, independent validation methods, such as Elastic Modulus Adjustment Procedures (EMAP), provide fast and stable solutions at relatively low cost. On the basis of elastic finite element analysis (FEA), the upper and lower bounds of limit load can be obtained by specifying the variations of elastic modulus in EMAP method. In this paper, an elastic modulus adjustment parameter k, which can improve the convergence of EMAP, is used to achieve stable convergence in the application of elbow with double defects. The EMAP method is also proved to be more efficient than the inelastic finite element analysis (FEA). Furthermore, the effect of defect size and distribution on the limit load of the elbow is studied.

Ratcheting boundary of pressurized pipe under reversed bending

Ratcheting boundary is firstly determined by experiment, elastic-plastic finite element analysis combined with C-TDF and linear matching method, which is compared with ASME/KTA and RCC-MR. Moreover, based on elastic modulus adjustment procedure, a novel method is proposed to predict the ratcheting boundary for a pressurized pipe subjected to constant internal pressure and cyclic bending loading. Comparison of ratcheting boundary of elbow pipe determined by the proposed method, elastic-plastic finite element analysis combined with C-TDF and linear matching method, which indicates that the predicted results of the proposed method are in well agreement with those of linear matching method.

Incorporated Strength Capacity Technique for Limit Load Evaluation of Trusses and Framed Structures under Constant Loading

AbstractTo overcome the difficulties encountered by the elastic modulus adjustment procedures applied to the ultimate bearing capacity analysis of framed structures under combined action of both constant and varying live loads, an efficient incorporated strength capacity technique is proposed in this work. A new structural analysis model is developed with totally different distributions of loads and resistance from the original model by incorporating the constant load effects into the sectional strength capacity of components in framed structures. The element bearing ratio (EBR) is defined according to the modified structural model on the basis of the generalized yield function of spatial beam element. The uniformity of the EBR is presented in terms of the EBR distribution characteristics, on the basis of which the reference EBR (REBR) is defined as a dynamic threshold to identify the highly stressed elements with the EBR greater than the REBR. Subsequently, an adaptive strategy of elastic modulus adjustm...

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.

Limit Load Evaluation Using the mα-Tangent Multiplier in Conjunction With Elastic Modulus Adjustment Procedure

In this paper, the mα-tangent multiplier is used in conjunction with the elastic modulus adjustment procedure (EMAP) for limit load determination. This technique is applied to a number of mechanical components possessing different kinematic redundancies. By specifying spatial variations in the elastic modulus, numerous sets of statically admissible and kinematically admissible stress and strain distributions are generated, and limit loads for practical components are then determined using the mα-tangent method. The procedure ensures sufficiently accurate limit loads within a reasonable number of iterations. Results are compared with the inelastic finite element results and are found to be in satisfactory agreement.

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.

Comparison of Elastic and Plastic Reference Volume Approaches

For finding out reliable limit load multipliers in pressure vessel components or structures using simplified limit load methods, proper estimation of reference volume is important. In this paper, two empirical methods namely elastic reference volume method (ERVM) and plastic reference volume method (PRVM) for reference volume correction are presented and compared. These reference volume correction concepts are used in combination with mα-tangent method and elastic modulus adjustment procedure to achieve converged limit load multiplier solution. These multipliers are compared with nonlinear finite element analysis results and are found to be lower bounded. Elastic reference volume method is the simplest method for reference volume correction when compared to plastic reference volume method.

Efficient Elastic Modulus Adjustment Procedure for Limit Analysis of Spatial Frame Structure

An efficient elastic modulus adjustment procedure to evaluate lower-bound ultimate bearing capacity of spatial frame structures was proposed based on the strain energy equilibrium principle. Four strategies to determine the elastic modulus adjustment factor were developed based on the fixed strain method (FSM), circular arc method (CAM), strain energy conservation law (SECL) and strain energy equilibrium principle (SEEP). The precisions and convergent properties of above four strategies were quantitatively investigated through two numerical examples. The results show that the efficiency and accuracy of the SEEP are of most acceptable.

Efficient Elastic Modulus Adjustment Procedure for Limit Analysis of Spatial Frame Structure

An efficient elastic modulus adjustment procedure to evaluate lower-bound ultimate bearing capacity of spatial frame structures was proposed based on the strain energy equilibrium principle. Four strategies to determine the elastic modulus adjustment factor were developed based on the fixed strain method (FSM), circular arc method (CAM), strain energy conservation law (SECL) and strain energy equilibrium principle (SEEP). The precisions and convergent properties of above four strategies were quantitatively investigated through two numerical examples. The results show that the efficiency and accuracy of the SEEP are of most acceptable.

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.

Variational and Classical Methods for Limit Load Analysis of Inhomogeneous Media

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.

Limit loads of ship structure components using the elastic modulus adjustment procedure (EMAP)

In this paper, the m α -tangent method is implemented in conjunction with elastic modulus adjustment procedure (EMAP) and an algorithm has been proposed for limit load estimation. This technique is applied to a number of ship structure components possessing different kinematic redundancies. Specifying spatial variations in the elastic modulus, numerous sets of statically admissible and kinematically admissible stress and strain distributions are generated, and both lower and upper bound limit load multipliers are obtained. Utilizing the lower and upper bound multipliers, accurate limit loads of ship structure components are then determined using the m α -tangent method. Results are compared with the inelastic finite element results and the available analytical solutions.

Ratchet Boundary Determination Using a Noncyclic Method

A simple and systematic procedure is proposed for shakedown analysis using a combination of linear and nonlinear finite element analysis (FEA). The method can identify the boundary between the shakedown and ratcheting domains directly and does not require a cyclic analysis (noncyclic). The proposed method performs an elastic-plastic FEA to determine the reduction in load carrying capacity due to the cyclic secondary loads. An elastic modulus adjustment procedure is then used to generate statically admissible stress distributions and kinematically admissible strain distributions under the applied primary loads. By modifying the local elastic moduli it is possible to obtain inelastic-like stress redistribution. The method is demonstrated with a “two-bar structure” model based on analytical routine. The analysis is then applied to some typical shakedown problems including the “classical Bree problem,” the “bimaterial cylinder,” and the “plate with a hole subjected to radial temperature gradient.”

Local Limit-Load Analysis Using the mβ Method

Abstract Several upper-bound limit-load multipliers based on elastic modulus adjustment procedures converge to the lowest upper-bound value after several linear elastic iterations. However, pressure component design requires the use of lower-bound multipliers. Local limit loads are obtained in this paper by invoking the concept of “reference volume” in conjunction with the mβ multiplier method. The lower-bound limit loads obtained compare well to inelastic finite element analysis results for several pressure component configurations.

Limit Load Analysis of Cracked Components Using the Reference Volume Method

Cracks and flaws occur in mechanical components and structures, and can lead to catastrophic failures. Therefore, integrity assessment of components with defects is carried out. This paper describes the Elastic Modulus Adjustment Procedures (EMAP) employed herein to determine the limit load of components with cracks or crack-like flaw. On the basis of linear elastic Finite Element Analysis (FEA), by specifying spatial variations in the elastic modulus, numerous sets of statically admissible and kinematically admissible distributions can be generated, to obtain lower and upper bounds limit loads. Due to the expected local plastic collapse, the reference volume concept is applied to identify the kinematically active and dead zones in the component. The Reference Volume Method is shown to yield a more accurate prediction of local limit loads. The limit load values are then compared with results obtained from inelastic FEA. The procedures are applied to a practical component with crack in order to verify their effectiveness in analyzing crack geometries. The analysis is then directed to geometries containing multiple cracks and three-dimensional defect in pressurized components.

Elastic modulus adjustment procedures—Improved convergence schemes

Elastic modulus adjustment procedures (EMAP) have been employed to determine limit loads of pressure components. On the basis of linear elastic finite element analysis (FEA) with non-hardening elastic properties, i.e. by specifying spatial variations in the elastic modulus, numerous sets of statically admissible stress and kinematically admissible strain distributions can be generated, and both lower and upper bounds on limit loads can be obtained. Some methods such as the classical, r-node and the m α methods provide limit loads on the basis of partly-converged distributions, whereas the accuracy of linear matching procedures rely on fully converged distributions. In this paper, a criterion for establishing the degree of convergence of EMAP is developed, and a simple procedure for achieving improved convergence is described. The procedure is applied to some practical pressure component configurations.

Limit Load Analysis of Pipe Bend Using the R-Node Method

The r-node method has been developed earlier as a technique to find the limit load using the Elastic Modulus Adjustment Procedures. It utilizes the systematic redistribution of the stress to find the load-controlled locations in a component to estimate the collapse load. In this paper, the method is shown to be applicable for multiple loads. A simple cantilever beam is analyzed using the redistribution-node (r-node) method subjected to both bending force and moment. The results compare well with the closed-form solution of the problem. The method is then used to estimate the limit load for an elbow subjected to in-plane and out-of-plane moment. The results compare well with the elastic-plastic analysis.

Limit Load of Anisotropic Components Using the M-Beta Multiplier Method

The mβ-multiplier method is based on Mura’s extended variational theorems in plasticity, and has been applied previously to isotropic components containing notches and cracks. Lower bound limit loads rapidly converge to inelastic analysis results when the method is used in conjunction with elastic modulus adjustment procedures. In this paper, the mβ-multiplier method is applied to pressure components exhibiting anisotropy. Specifically, the method is applied to the limit load determination of a heat exchanger tubesheet, wherein the tubesheet is modeled as an equivalent solid plate with anisotropic properties. Results are presented for a finite element model where plasticity is represented with Hill’s yield criterion, and a model using a fourth order yield criterion that accounts for compressibility of the tubesheet.

Lower Bound Limit Load Determination: The mβ-Multiplier Method

The existing lower bound limit load determination methods, that are based on linear elastic analysis such as the classical and mα-multiplier methods, have a dependence on the maximum equivalent stress. These methods are therefore sensitive to localized plastic action, which occurs in components with thin or slender construction, or those containing notches and cracks. Sensitivity manifests itself as relatively poor lower bounds during the initial elastic iterations of the elastic modulus adjustment procedures, or oscillatory behavior of the multiplier during successive elastic iterations leading to limited accuracy. The mβ-multiplier method proposed in this paper starts out with Mura’s inequality that relates the upper bound to the exact multiplier by making use of the “integral mean of yield.” The formulation relies on a “reference parameter” that is obtained from considering a distribution of stress rather than a single maximum equivalent stress. As a result, good limit load estimates have been obtained for several pressure component configurations.