Pseudo-elastic Analysis Research Articles

Pseudo-Elastic Analysis with Permanent Set in Carbon-Filled Rubber

Via cyclic loading and unloading tests of natural/styrene-butadiene rubber (NSBR) blends at room temperature, the effects of the stretching, rate, temperature, and volume fraction of carbon black in the filled rubber on a permanent set (residual strain) were studied. The results showed that increasing the stretching, rate, and volume fraction of carbon black and reducing the temperature yielded greater residual strain. The uniaxial tensile behaviors of composites with the Mullins effect and residual strain were simulated using the ABAQUS software according to the aforementioned data. An Ogden-type constitutive model was derived, and the theory of pseudo-elasticity proposed by Ogden and Roxburgh was used in the model. It was found that the theory of pseudo-elasticity and the Ogden constitutive model are applicable to this composite, and if combined with plastic deformation, the models are more accurate for calculating the residual strain after unloading.

Elastic-Plastic Analysis Under Proportional and Non-Proportional Loading Paths Using Deformation Plasticity Theory

An estimation of elastic-plastic stresses and strains is presented for mechanical components, using pseudo elastic analysis based on the deformation theory of plasticity. Analysis of two applications, one under proportional loading and other under non-proportional loading paths using pseudo elastic finite element method, is presented. A rectangular plate with a hole under tension loading and a rectangular plate fixed at one end under bending-tension non-proportional loading are considered for analysis. Pseudo Elastic finite element analysis for proportional loading uses elastic solutions and varies material properties for elements in plastic zone to estimate elastic-plastic solution. A finite element code is developed based on pseudo elastic analysis method. An attempt is made to extend pseudo elastic analysis to analyze bending-tension non-proportional loading problem. Both applications in consideration are assumed to be of Von Mises material and follow isotropic hardening rule with elastic-linear hardening material model. Non-linear analysis of the plate with a hole under proportional tensile loading and that of rectangular plate under bending-tension non-proportional loading are performed in ANSYS and results are compared for validation and are observed to be in good agreement with present analysis.

Pseudo Elastic Analysis of Carbon Reinforced Natural/Styrene-Butadiene Blend Rubber (NSBR) with Ogden Constitutive Model

In this paper, experimental results that illustrate stress softening in carbon filled natural/styrene-butadiene blend rubber (NSBR) together with Mullins effect are introduced firstly. Then, based on these data, the Ogden constitutive model is derived. The theory of pseudo-elasticity is used in the model. It is found that theory of pseudo-elasticity and Ogden constitutive model is applicable in this composite.

A Parallel Elastoplastic Reanalysis Based on GPU Platform

An efficient parallel elastoplastic reanalysis method is suggested. The main backbone of the suggested method is based on combined approximation (CA) reanalysis. GPU parallel computation is used to accelerate assembling the stiffness matrix. Assembling process is divided into the offline part for strain matrix and online part for element stiffness matrix, which makes the structure of the program more reasonable and efficient. Pseudo elastic analysis is introduced and extended to load increment method to make the CA method more feasible. The numerical examples show that the suggested method can improve the efficiency of elastoplastic analysis significantly and the accuracy of results can also be ensured.

Fatigue Stress Evaluation at Shell-to-Bottom Joint With Double Plastic Hinge in Elevated Temperature Steel Tanks on Concrete Ring Walls

The shell-to-bottom joint of hydrocarbon storage tanks is a critical location which may experience fatigue cracking and requires evaluation of the local cyclic stresses especially in the case of elevated temperature tanks. The fill/draw down cycle of the stored liquid causes low cycle fatigue near this joint and hence a fatigue evaluation is recommended. The peak alternating stress at this location, used to enter the fatigue curves is currently determined using a pseudo-elastic analysis that represents strain range due to inelastic deformations. API 650 employs beam on elastic foundation theory for this analysis. This theory is being used for tanks resting fully on earthen foundation as well as those on concrete ring wall. This paper studies the validity of using this theory for tanks with concrete ring wall foundation which are much more rigid compared to earthen foundations. Some of the difficulties in the current practice are highlighted. An alternative to the current model is presented for the determination of stresses in such tanks. The results are validated using finite element analysis. The results show that the current practice needs to be revised or rejustified in an alternative manner.

Creep and shrinkage analysis of curved composite beams with partial interaction

This paper investigates the time-dependent creep and shrinkage behaviour of horizontally curved steel–concrete composite beams, including the partial interaction existing between the concrete deck and the steel girder. The flexibility of the shear connection in the radial direction, as well as in the tangential direction at the steel and concrete interface, are taken into account in the proposed formulation. The creep and shrinkage effects of the concrete deck including concrete aging effects are considered by using the analytic Age-adjusted Effective Modulus Method (AEMM). This method is efficient in converting the creep analysis into pseudo-elastic analysis. The accuracy and efficiency of the proposed approach is validated by comparing its results with available experimental results reported in the literature and those based on a more sophisticated but computationally less efficient ABAQUS shell finite element model. The effects of initial curvature and partial interaction on the time-dependent behaviour of curved composite beams under serviceability conditions are also elucidated and the slip effect due to warping is examined.

Creep and shrinkage of HPC in prebended composite structures. Part II: in situ case study

A prefabricated, prebended and prestressed railway bridge deck was instrumented in June 2000 with strain gauges and vibrating wire extensometers. It is a kind of structure in which large time-dependent stress redistributions between steel and concrete are expected to occur. The purpose of this paper is to report on the comparison between strains recorded in situ on an instrumented bridge deck of this kind up to four years after its construction with values computed within the framework of four different time-dependent analyses: (a) a pseudo-elastic analysis with variable modular ratios for concrete used for the design of these bridge decks; (b) a step-by-step method applying the principle of superposition; (c) a step-by-step method incorporating a recovery function; and (d) an original modelling method. This final analysis is presented in Part 1 of this paper, which is based on the evolution of three fundamental local parameters: the temperature, the degree of advancement of reaction of hydration and the water content in concrete.

PSEUDO-ELASTIC ANALYSIS OF ELASTIC–PLASTIC CRACK TIP FIELDS USING ELEMENT-FREE GALERKIN METHOD

A methodology for the characterization of asymptotic elastoplastic crack tip stress fields is presented by coupling the pseudo-elastic analysis with the element-free Galerkin method (EFGM). An iterative linear elastic analysis using EFGM is carried out for the determination of elastic–plastic crack tip stress fields by treating material parameters as spatial field variables. Effective material parameters are used to describe the constitutive behavior of the continuum and are defined by using the Hencky's total deformation theory of plasticity. The effective material parameters are updated in an iterative manner based on strain controlled projection method using experimental uniaxial tension test curve. The effectiveness of the method is illustrated by predicting the stress fields near the crack tip region of a square plate subjected to asymptotic linear elastic displacement field on the outer boundary of the plate. Different geometries subjected to mode-I and mode-II loadings are considered for the present study. The material model considered in these problems is Ramberg–Osgood model with different hardening exponent values. The predictions of the asymptotic elastic–plastic stress fields near the crack tip are compared with the results of nonlinear finite element analysis and also with the HRR singular stress fields and found to be in good agreement. J-integral values which characterize the amplitude of HRR stress field are also evaluated for the considered geometries and are found to close matching with the EPRI estimation scheme.

Innovative Composite Precast Prestressed Precambered U-Shaped Concrete Deck for Belgium’s High Speed Railway Trains

During the past decade, an innovative composite precast, prestressed U-shaped bridge deck has been developed for use in the construction of the high speed railway system in Belgium. This deck is also used for replacing the old structural steel bridges that are being phased out. This article presents a method of analysis to measure the creep and shrinkage effects on the long-term behavior of the decks. The authors first review the origins and basic principles of this hybrid beam, then discuss their implementation. They note that, while these bridge decks have performed according to expectations, some variability has been observed between the measured and computed camber just after the transfer of prestressing. To explain the observed variability in camber, a multivariable statistical analysis was conducted on 42 bridge decks; results are reported in this paper. Variables studied include age of concrete at release, compressive strength, influence of curing temperatures, steel tensile stress versus strength, steel compressive stress versus strength, and bending moment. The most significant variables to explain camber measurement discrepancies at prestress transfer are the maximum tensile stress-to-yield strength ratio in the steel girders at prebending, and the steel girder type. In an instrumented bridge deck, the authors found that the computed strain values derived from an approximate, pseudo-elastic analysis with imposed modular ratios are quite different from the measured strains, especially 2 1/2 years after construction. The authors conclude that, in general, the step-by-step method is a more precise evaluator of the time-dependent redistribution of strains between steel and concrete than the age-adjusted effective modulus method.

Analysis of the variability of deflection of a prestressed composite bridge deck

Nearly 400 composite railway bridge decks of a new kind belonging to the trough type with U-shaped cross section have been constructed in Belgium over the last fifteen years. The construction of these bridge decks is rather complex with the preflexion of precambered steel girders, the prestressing of a concrete slab and the addition of a 2nd phase concrete. Until now, they have been designed with a classical computation method using a pseudo-elastic analysis with modular ratios. Globally, they perform according to the expectations but variability has been observed between the measured and the computed camber of these bridge decks just after the transfer of prestressing and also at long-term. A statistical analysis of the variability of the relative difference between the measured camber and the computed camber is made for a sample of 36 bridge decks using no less than 10 variables. The most significant variables to explain this variability at prestressing are the ratio between the maximum tensile stress reached in the steel girders during the preflexion and the yield strength and the type of steel girder. For the same sample, the long-term camber under permanent loading is computed by two methods and compared with measurements taken one or two years after the construction. The camber computed by the step-by-step method shows a better agreement with the measured camber than the camber computed by the classical method. The purpose of the paper is to report on the statistical analysis which was used to determine the most significant parameters to consider in the modeling in order to improve the prediction of the behaviour of these composite railway bridge decks.

Comportement différé du béton dans un pont ferroviaire mixte et précontraint

ABSTRACT A simply supported bridge deck of a new type with trough shaped cross section has been instrumented with strain gages and vibrating wire extensometers in June 2000 in order to assess its time-dependent behaviour. Additionally, creep and shrinkage tests on the C60 concrete used in this bridge deck are carried out in our laboratory. This paper reports on the comparison between creep and shrinkage measurements on the concrete samples and the predicted values by the more recent models. Then, bridge deck strain measurements are compared with predicted values by two pseudo—elastic analysis methods: the first one uses simply a variable modulus of elasticity whereas the second one applies the age adjusted effective modulus method.

Pseudo-elastic analysis of axial beltline flaws

Pseudo-elastic analysis of axial beltline flaws

Plastic Collapse of Steep Conical Shells under Axial Compression

Analysis and experimental results are presented for two axisymmetric plastic collapse modes in steep, truncated conical shells under axial compression. The two collapse modes are strongly dependent on cone height and the boundary conditions. One collapse mode, which consists of flaring of the large end of the cone, can be analyzed satisfactorily on the basis of rigid-perfectly plastic behaviour. The Tresca sandwich-shell yield condition is used and close agreement is obtained with the experimental results. The other collapse mode is a local bulging of the small end. It is shown in the analysis that perfectly plastic behaviour cannot account for this collapse mode. Consideration of kinematic-hardening leads to a pseudo-elastic analysis of a uniform shell. The observed deformation is found to be due to buckling of the Shanley type. Rayleigh’s method is employed to obtain an estimate of a length parameter which characterizes the critical condition for buckling. Agreement with the experimental results is not very satisfactory, probably because a constant value for the tangent modulus was assumed.