Rigid-plastic Method Research Articles

Effects of indenter geometry on pseudo-shakedown of steel plates under repeated mass impacts

Pseudo-shakedown is a typical phenomenon in the study of repeated impact loadings on ship and marine structures, and its occurrence is related to the elastic strain energy. Moreover, the permanent deflection and deformation mode of the structure under impacts with different indenter geometry exhibit significant differences, which affect the elastic strain energies of the structures. In this paper, horizontal repeated impact tests were conducted with spherical, ellipsoidal, wedged and rectangular indenters to analyze the effects of indenter geometry on pseudo-shakedown of steel plates. The deformation modes, deflection accumulations, rebound velocities and elastic strain energies were investigated in detail. The influence of indenter shape on elastic effect of a plate associated with the deformation mode and the energy dissipation form is revealed. Further dimensional analyses are applied to experimental data, and the empirical equations are obtained for the prediction of elastic strain energies corresponding to the permanent deflections of plates. Combined with the dimensionless empirical equation, the modified rigid-plastic method considering elastic strain energy achieves good consistency with experimental results, and it is employed to explore the occurrence mechanism of pseudo-shakedown. Results show that, to achieve pseudo-shakedown, two criteria are required, (i) U0≤Eem, (ii) sufficient large number n of impacts. The modified theoretical method can be employed to investigate the required number of repeated impacts for a plate to achieve pseudo-shakedown. For practical use, the impact number associated with Δwf=|Wnf−W(n−1)f| of 10−5m is recommended. This research can provide a deep insight in the mechanism of pseudo-shakedown phenomenon.

Application of rigid-plastic theory method in ship-ice collision

The rigid-plastic theory is widely used to estimate structural plastic damage in ship collision and some other structural impact cases under the assumption that the impactor is an idealized rigid body. This paper aims to extend the rigid-plastic method in ship collision to ship-ice collision, considering the energy dissipation caused by ice failure in the collision process. Based on three types of assumed collision scenarios between ship plates and ice floes, an approximate analytical plastic damage prediction method for ship plate impacted by ice floe is proposed, combining the rigid-plastic theory method with the energy approach of ice crushing. The analytical results have good correlations with experimental and numerical results in predicting maximal collision forces, plastic deformations of plate and so on. The proposed analytical formulations can provide a useful and convenient tool for the estimation of plastic damage of ship plates subjected to ice floe impact.

On the saturated impulse for a circular hollow beam under pressure pulse loading

The saturated impulse phenomenon, which may occur in a hollow beam with a circular cross-section, is examined when a rectangular pressure pulse loading is applied uniformly on the upper surface of the beam. A simplified 2DoF model of the dynamic response of a relatively long circular hollow section beam is developed to explore the role of the local and global deformations build up simultaneously during the beam response. In order to simplify the analytical formulation, the elastic deformations of the hollow beam are neglected, and a rigid-plastic method of analysis is applied. Finite element simulations using an elastic, perfectly plastic material model are carried out to verify the proposed analytical model and to reveal the influence of the elasticity on the beam response. The limit of the pressure pulse loading, beyond which saturated impulse is not defined for a hollow beam, is obtained numerically. The responses of hollow beams with lengths between 800 and 1200 mm, radius of 40 mm and several wall thicknesses are analysed. It is observed that the proposed 2DoF model can predict satisfactory the local and global saturated deflections while the saturated pressure pulse duration is underestimated due to the disregard of the stored elastic energy in the beam. It is suggested that the analytically predicted saturated impulse can be used as a lower bound estimate for the saturated impulse for a given beam geometry.

Response of a circular metallic hollow beam to an impulsive loading

A model of the dynamic response of a relatively long circular hollow section beam to a uniform blast modeled as an impulsive loading is developed in order to reveal the characteristic features of deformation and energy absorption of hollow section beams under such loading. A two-phase analytical model is proposed for a circular metallic hollow beam made of a strain-rate insensitive material. Both local and global deformations build up simultaneously during the first phase, and then only global bending occurs during the second phase. Because mainly large plastic deformations develop in the hollow section, the elastic deformations are neglected and a rigid-plastic method of analysis is applied. The responses of circular hollow beams with lengths between 600 and 1000mm are analyzed for beam radii varying between 50 and 70mm and wall thicknesses between 1.2 and 1.6mm. The model predictions are verified by numerical simulations and reasonable agreement is observed with respect to the characteristic displacements and deformed section shape. The energy partitioning during the deformation process is briefly discussed.

Pseudo-shakedown phenomenon for the mass impact loading of plating

The pseudo-shakedown phenomenon for the repeated and identical mass impact loadings on circular and rectangular plates, is studied using a rigid-plastic method of analysis. Comparisons are made with experimental data which has been published on the response of circular and square plates subjected to repeated mass impacts. Previous studies have explored the effect of only the current impact mass and ignored the accumulation of any masses from earlier impacts on a plate. This has led to a steady growth of the transverse displacements without the achievement of pseudo-shakedown. The effect of allowing the masses to accumulate on a plate surface, as, for example, in the loading of cargo in a hold, is shown to have an important influence on the behaviour. The asymptotic values of the associated expressions reveal that a pseudo-shakedown state is achieved for this case and has an associated modest value of the maximum permanent transverse displacement. The phenomenon of pseudo-shakedown is clarified and the equations are useful design tools for an estimate of the pseudo-shakedown behaviour of plating, which is loaded repeatedly with cargo and other masses in various practical situations.

Analysis of steel–concrete composite column subject to blast

The single-degree-of-freedom method is commonly used to approximate the dynamic response of structures subjected to blast loading. One of the limitations of this method is that it cannot capture the multi-failure modes of the structural members. The rigid–plastic method is thus, proposed in this paper as an alternative analytical approach to estimate the blast response of concrete-filled steel composite columns. The rigid–plastic results are compared with single-degree-of-freedom calculations as well as numerical simulations in order to assess the competency of the proposed method. Due to the assumption of rigid–plastic material behaviour in the rigid–plastic analysis, the accuracy of this method is influenced by the extent of plastic deformation of the structural member. For the case of impulsive blast loading, the rigid–plastic estimations are found to be closer to the numerical results than those obtained using the single-degree-of-freedom method. Numerical analysis was also conducted to compare the performance of concrete-filled steel composite column to a reinforced concrete column. A significant improvement in the blast resistance of the composite column was observed from the comparison.

Analysis of lateral extrusion of gear-like form parts

The analysis of lateral extrusion process was carried out. A three dimensional FE model was developed to analyze the effects of some important geometrical parameters such as initial billet dimensions, gap height and frictional condition on the required forging load, the material flow pattern and effective plastic strain distribution. The FE code of DEFORM-3D was employed. A series of experimental tests on commercial lead billets were carried out to verify the FE results. The simulation work has been performed by the rigid-plastic FE method. The results obtained using the numerical solutions have been compared with the experimental data for each case study in terms of required forming load and material flow pattern in different regions. Comparison between FE and experiment results showed good agreement. Both the simulation and experimental results highlight the major role of above mentioned parameters on the required forming load and material flow pattern. The results showed that the gap height has the greatest effect on the forming load and material flow. The results presented in this paper could be used as basic data in the design of the lateral extrusion process.

A better rigid-plastic estimate for earthquake-induced plastic displacements

The earthquake ductility demand on structures may be predicted by means of a rigid-plastic method, which derives the maximum plastic response of elastic-plastic oscillators from that of a simpler rigidplastic model. The maximum response of the latter is a purely plastic one and may be obtained from the earthquake rigid-plastic pseudo-spectrum, as a function of the oscillator yield acceleration. The results of a wide investigation presented in this paper show that such a method generally leads to a conservative and reliable enough estimate of the maximum plastic displacements. Small mean errors are in fact found for both comparatively short-period and long-period oscillators. In the medium period range, however, the rigid-plastic prediction is found to be less satisfactory. This is due to the appliance in that range of an empirical formula, which estimates the discrepancy between the elastic-plastic and the rigid-plastic peak response. To improve the rigid-plastic prediction in the medium period range, a new semi-empirical formula is derived in the paper which is shown to halve, on average, the error in estimating the earthquake ductility demand on medium period oscillators. Due to the new formula, the mean relative errors are always kept below 15%, whatever the earthquake and the oscillator. This makes the rigid-plastic method competitive with respect to other approximate methods, as discussed in the paper. Keywords Earthquake ductility demand, rigid-plastic method, seismic inelastic displacements prediction Language: en

A Single Stage Hot Forging Process of Alternator Poles

Based on precision forging method, a single stage hot forging process of alternator poles is put forword, which the heated blank can be forging by only one press in a special closed die. In the last this process is verified by the software of Deform-3D which is employed rigid-plastic FEM method.

Applying Element-Free Galerkin Method to Simulate Die Forging Problems

The analysis for die forging forming problems with finite element method can lose considerable accuracy due to severely distortional meshes. The element-free Galerkin method is suitable for large deformation analysis and provides a higher rate of convergence than that of the conventional finite element methods. A rigid-plastic meshless method based on the element-free Galerkin method has been applied to die forging problems. The arc-tangent friction model is used to handle frictional contact and the penalty method is applied to impose the volumetric incompressibility conditions. By dividing all integration points set into the point subset of the rigid zones and the point subset of the plastic zones, nonsmoothness of the rigid-plastic constitutive relation can be eliminated. A die forging example has been analyzed to demonstrate the performance of the method.

Releasing Algorithm for Volumetric Locking in Metal Forming Process Simulation Based on Element-Free Galerkin Method

The meshless methods effectively deal with large material distortion simulation. Based on the rigid (visco)plastic material model, the element-free Galerkin method (EFGM) is introduced to simulate the metal forming processes. Aiming at the volume locking and pressure oscillation during EFGM analysis, a volumetric strain rate mapping method is proposed based on pressure projection method. The releasing algorithm is established by modifying the volumetric strain rate in the functional equation. The volumetric strain rate calculated according to velocity field is mapped onto a lower-order space to reduce the number of independent discrete constrain equations. The numerical example shows that the releasing algorithm can effectively eliminate the volumetric locking and pressure oscillation without the expense of employing large support size in the rigid-plastic meshless method.

RELEASING ALGORITHM FOR VOLUME LOCKING IN RIGID-PLASTIC MESHLESS METHOD

The meshless Galerkin method is introduced to the analysis of the metal forming processes. The fundamental theories and basic equations for the rigid-plastic meshless method are developed. The releasing of the volume locking encountered in the analysis of the metal plastic forming problems is studied and a releasing algorithm is established by modifying the volumetric strain rate in the functional equation. The volumetric strain rate calculated according to velocity field is mapped onto a lower-order space to reduce the number of independent discrete constraint equations. The algorithm can release the volumetric locking without the expense of employing large support size in the rigid-plastic meshless method. A typical metal forming problem is analyzed. The results show that the algorithm can effectively release the volumetric locking problem.

The effects of partial shear connection in the hogging moment regions of composite beams Part II—Analytical study

In this paper, the development of an iterative-based analytical model to study the behaviour of composite beams subjected to hogging bending is described. Partial interaction concepts allowing for interface slip are considered, in conjunction with the inherent equilibrium and compatibility principles. The analysis results showed reasonable agreement with the results of the eight experimental beams reported in the earlier companion paper. The full flexural response of the beams including shear connector slip was predicted adequately until failure. The limited experimental data published in the literature was also compared. Favourable comparisons further verified the reliability and robustness of the model. An extensive parametric study was undertaken using the model that has been properly calibrated. In addition, a modified rigid-plastic method is proposed to improve on the approach currently used in practice, and to facilitate the inclusion of partial shear connection in the hogging moment regions of composite structures.

Inelastic deformation and failure of clamped aluminium plates under pulse pressure loading

An experimental and analytical study is presented of the inelastic deformation and failure (rupture) of clamped aluminium plates measuring 0.5 m×0.5 m at the clamped edge by 1 mm thick under pulse pressure loading. The pulse loading was applied by generating a dynamic pressure gradient across the plates using a fast differential pressure device. Both static and dynamic test results are reported together with the results of an investigation of the failure surface using scanning electron microscopy. An assumed-modes, elastic–plastic analysis of the plates using a finite strip model was used to predict the maximum displacement of the plates. A simple uniaxial strain-based failure criterion was used in the analysis to predict the failure pressure of the ruptured plates. The rigid-plastic method was used to estimate the permanent deformation of some of the plates. Reasonable agreement is obtained between the predictions of the simplified elastic–plastic analysis and the experimental results. The rigid-plastic results were less accurate at predicting the permanent deformation of the plates due to the long duration of the loading relative to the fundamental natural period of the plates.

Influence of end fixity on post-yield behaviors of a tubular member

For the evaluation of the capability of a tubular member of an offshore structure to absorb the collision energy, a simple method can be employed for the collision analysis without performing the detailed analysis. The most common simple method is the rigid-plastic method. However, in this method any characteristics for horizontal movement and rotation at the ends of the corresponding tubular member are not included. In a real structural system of an offshore structure, tubular members sustain a certain degree of elastic support from the adjacent structure. End fixity has influences in the behaviors of a tubular member. Three-dimensional FEM analysis can include the effect of end fixity fully, however in viewpoints of the inherent computational complexities of the 3-D approach, this is not the recommendable analysis at the initial design stage. In this paper, influence of end fixity on the behaviors of a tubular member is investigated, through a new approach and other approaches. A new analysis approach that includes the flexibility of the boundary points of the member is developed here. The flexibility at the ends of a tubular element is extracted using the rational reduction of the modeling characteristics. The property reduction is based on the static condensation of the related global stiffness matrix of a model to end nodal points of the tubular element. The load-displacement relation at the collision point of the tubular member with and without the end flexibility is obtained and compared. The new method lies between the rigid-plastic method and the 3-demensional analysis. It is self-evident that the rigid-plastic method gives high strengthening membrane effect of the member during global deformation, resulting in a steeper slope than the present method. On the while, full 3-D analysis gives less strengthening membrane effect on the member, resulting in a slow going load-displacement curve. Comparison of the load-displacement curves by the new approach with those by conventional methods gives the figures of the influence of end fixity on post-yielding behaviors of the relevant tubular member. One of the main contributions of this investigation is the development of an analytical rational procedure to figure out the post-yielding behaviors of a tubular member in offshore structures.

Strength of Concrete Filled Steel Box Columns Incorporating Local Buckling

Concrete filled steel box columns have recently experienced a renaissance in their use throughout the world. This has occurred due to the significant advantages that the construction method can provide. This paper deals with the strength behavior of short columns under the combined actions of axial compression and bending moment. The paper addresses the effect of steel plate slenderness limits on this behavior. An extensive set of experiments has been carried out and a numerical model developed elsewhere is augmented and calibrated with these results. A simple model for the determination of the strength-interaction diagram is also verified against both the test results and the numerical model developed in this paper. This model, based on the rigid plastic method of analysis, is existent in international codes of practice, but does not account for the effects of local buckling, which are found to be significant with large plate slenderness values, particularly for large values of axial force. Thus some suggested modifications are proposed to allow for the inclusion of slender plated columns in design.

ベルト型超高圧発生容器内部の応力解析

ベルト型超高圧発生容器内部の応力解析

Transient deformation modes of square plates subjected to explosive loadings

The phenomenon of transient deformation of square plates under intense dynamic loading has not been studied fully, either in experiment or theory. In this paper the experimental method for obtaining transient deformation profiles of square plate under explosive loading is demonstrated and evaluated. An optical technique proved to be reliable and accurate in obtaining the transient deformation mode of the square plate. Elastoplastic numerical analysis which includes finite deflection, material elasticity and strain hardening was carried out for one of the tests on an aluminium alloy plate to reproduce the transient response of the plate under measured pressure. The transient deformation profiles have also been obtained successfully by the numerical method and show good agreement with the experimental results. Numerical results are also presented for the impulsively loaded rectangular plates tested by Jones et al [Jones, N., Vran, T. and Tekin, S. A. (1970). Int. J. Solids Structures6, 1499–1512]. The combined experimental and numerical investigations provide valuable information for the understanding of transient behaviour of thin plates under explosive loading and for the development of an approximate procedure using the Rigid Plastic Method.

A rigid plastic method for the determination of collapse loads of infilled panels with openings

The work done in a yield zone which is able to both shear and rotate has been obtained for a material with a square yield criterion. Yield zones which either rotate or shear only are shown to be special cases. These yield zones are then used in analyses to obtain upper bounds on the collapse loads for masonary infills with openings in framed structures. Lower bounds on the collapse load are also obtained. In all cases analysed the discrepancies between the upper and lower bounds on the collapse load are small. Using the results obtained from the analyses, proposals are made for a design method for infilled panels with openings.

An Approximate Rigid-Plastic Analysis of Shell Intersections Loaded Dynamically

An approximate rigid-plastic method of analysis which may be used in order to estimate the behavior of various shell intersections subjected to large dynamic loads is presented herein. In particular, the two common cases of cylindrical nozzles intersecting either spherical or cylindrical shells are considered in some detail. The maximum permanent radial deflections of these two structures which arise from rectangular pressure pulses are presented for various geometrical parameters.