Grillages of maximum strength and maximum stiffness

Assuming a preassigned beam depth, minimum weight solutions are derived for both perfectly plastic and elastic grillages of given strength as well as elastic grillages of given stiffness. The solutions presented also give a minimum reinforcement volume for perfectly plastic fibre-reinforced plates. Common kinematic optimality conditions are stated for the foregoing classes of problems and a method is outlined for finding the optimal solution for any clamped boundary. Morley's claim regarding the non-existence of certain kinematically admissible optimal solutions is shown to be erroneous. The proposed technique is illustrated with a number of examples.     

Metallic friction under near-seizure conditions

In metal-working theory extreme frictional (perfectly rough) conditions are assumed to apply when the shear stress opposing motion at the tool-work interface is equal to the shear flow stress of the work material. This is normally likened to seizure (sticking) with zero velocity at the actual interface and with plastic flow occurring in the adjacent work material. If the flow stress is assumed constant as in ideal plasticity theory, then this condition can be readily defined. However, if the flow stress is allowed to vary with, for example, strain rate and temperature, it is no longer obvious at what value of flow stress the perfectly rough condition becomes applicable. With the assumption that the velocity changes from zero at the interface to the full rigid body velocity over a narrow plastic zone of intense shear, an analysis is presented in which it is proposed that the thickness of this zone (which must be finite in a strain-rate-sensitive material) and hence the associated strain rate, temperature and flow stress are determined by a minimum work criterion. Recent results in support of this are presented from machining experiments where the flow at the tool-chip interface approximates to perfectly rough conditions. It is suggested that for steady state conditions true seizure cannot occur and a possible mechanism is given for near-seizure conditions in which the velocity at the interface, although very low, is not zero.     

Elastic–plastic beam-on-foundation under quasi-static loading

An elastic–plastic discrete spring model is developed to represent the mechanical behavior of an elastic–plastic beam-on-foundation (BoF) system, and an analytical procedure of analyzing the BoF under general quasi-static loading is formulated. The paper describes a detailed numerical simulation and analysis for the case of a BoF subjected to a concentrated force at the mid-span, and various plastic collapse mechanisms of BoFs are identified. Two peculiar phenomena, i.e. the migration of plastic hinge in the beam and the successive propagation of plastic zone in the foundation, are demonstrated. It is found that any elastic, perfectly plastic BoF system can be characterized merely by three non-dimensional parameters, but the limit state of a rigid, perfectly plastic BoF is determined by a single non-dimensional parameter only. The non-dimensional relative rigidity of BoF and the ratio of the maximum elastic deformation energies dissipated in the beam and foundation both play important roles in governing the deformation scenario of an elastic–plastic BoF system.     

On the Effect of Isotropic Hardening on the Coefficient of Restitution for Single or Repeated Impacts Using a Semi-Analytical Method

A semi-analytical method is proposed for the simulation of moderately high-speed impacts of a relatively hard particle on an elastic–plastic substrate. Potential applications of the current modeling approach include shot-peening and ultrasonic peening as well as impacts on functional surfaces such as mechanical seals or bearings. The coefficients of restitution for single impacts on an elastic–perfectly plastic semi-infinite body or one with isotropic hardening have been computed for various impact velocities. The current approach is three dimensional and numerically efficient in terms of CPU time and memory space required. Numerical results are in good agreement with those obtained by other authors for elastic–perfectly plastic behavior. Coefficients of restitution resulting from repeated impacts at a constant initial velocity are also studied. Finally, equations fitting these numerical results are proposed.     

The influence of elastic shear deformation on the transverse shear failure of a fully clamped beam subjected to idealized blast loading

The influence of elastic shear deformation on the transverse shear response of a fully clamped beam is investigated in the present paper. The beam is made from a rigid, perfectly plastic material and subjected to a uniformly distributed pressure pulse loading. The elastic shear deformation is idealized by an elastic, perfectly plastic spring with a constant spring coefficient. Analytical solutions are obtained for the transverse shear response, which are then used to predict the occurrence of a transverse shear failure. The method presented in the paper may be extended to study the blast-induced shear failure of other structural elements when the elastic shear deformation needs to be considered.     

Plastic limit analysis with non linear kinematic strain hardening for metalworking processes applications

Limit analysis approaches are widely used to deal with metalworking processes analysis; however, they are applied only for perfectly plastic materials and recently for isotropic hardening ones excluding any kind of kinematic hardening. In the present work, using Implicit Standard Materials concept, sequential limit analysis approach and the finite element method, our objective consists in extending the limit analysis application for including linear and non linear kinematic strain hardenings. Because this plastic flow rule is non associative, the Implicit Standard Materials concept is adopted as a framework of non standard plasticity modeling. The sequential limit analysis procedure which considers the plastic behavior with non linear kinematic strain hardening as a succession of perfectly plastic behavior with yielding surfaces updated after each sequence of limit analysis and geometry updating is applied. Standard kinematic finite element method together with a regularization approach is used for performing two large compression cases (cold forging) in plane strain and axisymmetric conditions.     

On the dry elasto-plastic contact of nominally flat surfaces

A model to be used for numerical simulation of the contact of linear elastic perfectly plastic rough surfaces was developed. Energy dissipation due to plastic deformation is taken into account. Spectral theory and an FFT-techique are used to facilitate the numerical solution process.     

材料参数对点面正碰撞的柔度关系影响研究

采用2D轴对称有限元法(FEA)模拟计算了弹性、理想弹塑性和幂指数应变强化弹塑性钢球与刚性平面碰撞.分析了影响柔度关系的各种因素.弹塑性碰撞的FEA结果说明塑性变形是导致能量损失的主要原因.研究结果为多体系统动力学计算提供了有益的参考.     

The ploughing friction: analytical model with elastic recovery for a conical tip with a blunted spherical extremity

The current analytical models are insufficient to describe the ploughing part of the friction coefficient when there is elastic recovery at the rear part of the contact after passage of a moving tip. A solution for the case of a perfectly conical tip was proposed recently. This paper presents a model to describe the ploughing friction for a perfectly spherical tip and then develops this analysis for the case of a conical tip with a blunted spherical extremity. The major difficulty resides in taking into account the shape of the contact area in relation to the elastic, elastoplastic or plastic behaviour of the contact.     

An optimum reinforcement solution for a torsionless grillage with given minimum strength

The paper presents the minimum reinforcement solution for a simply-supported square torsionless grillage, with beams parallel to the sides of the square, for specified uniformly distributed transverse load at collapse, for the case where a minimum proportion of reinforcement (and therefore a minimum bending strength) must be provided at every point. The optimal design collapses in a mode satisfying certain conditions on curvature, and the corresponding moment field is developed using lines of load transfer (with finite jumps in moment) for concentrated forces, and the equation of bimoments for finite grillage segments. A solution is obtained only for a limited range of load magnitudes (up to about twice what may be carried with the specified minimum bending strength alone). However, the minimum volume of reinforcement is not much less than that for a simple practical design, with crossed uniform bands of extra reinforcement near midspan, which can cope with any magnitude of load.     

A simple algorithm for predominantly plastic flows with free surfaces

The upper bound method provides a convenient tool for evaluating the rates of work and sometimes the global forces in plastic deformation processes. Its application is restricted, however, in that plastic flows in domains with free surfaces, and also local stresses cannot be determined. We suggest a procedure which is free of these constraints. It is demonstrated on the example of a rigid tool penetrating a perfectly plastic body, including experimental comparisons.     

Plastic deformation of the surface layer’s microroughness by a sliding tool with strong contact friction

The plastic deformation of the discrete contacts of a tool with a circular-arc and an inclined profile with the periodical microroughnesses of the metallic part’s surface layer is modeled. The plane deformation theory of a perfectly plastic body is used. The plastic deformation process of the surface layer’s microroughnesses by a sliding tool with Prandtl’s high contact friction in which the plastic shear occurs in the direction of the slide of the tool, with the microroughnesses’ depressions being filled and a decrease of the surface roughness, is studied.     

Plastic limit loads of defective pipes under combined internal pressure and axial tension

In this paper, a finite element mathematical programming formulation is presented for the statical limit analysis of 3-D perfectly plastic structures. A direct iterative algorithm is employed in solving the above optimization formulation. The numerical procedure has been applied to carry out the plastic collapse analysis of defective pipes under combined internal pressure and axial tension. The engineering situation considered has a practical importance in the pipeline industry. The effects of four kinds of typical part-through slots on the collapse loads of pipes are investigated and evaluated.     

Rate-dependent transient extrusion

Plane strain slip line field solutions are developed for deformation at the edge of a cylindrical billet when this is backward extruded to form a thin-walled cup. The extrusion pressure for a perfectly plastic material is then derived assuming homogeneous compression in the centre of the billet. A geometric factor, derived from the slip line field, is identified which permits the extrusion pressure to be determined for a nonlinear viscous material.Theoretical results agree well with recent experimental data on back extrusion of highly rate-sensitive superplastic alloys. It is shown that an apparent steady state exists in the process and that extrusion pressure increases with ram speed with a rate index approximately equal to that of the material. The punch profile shape has a greater effect on extrusion pressure for viscous materials than for perfectly plastic ones. The method of analysis appears to have a generality beyond the particular process considered and may be used to optimize extrusion equipment designs.     

微结构几何形状对开孔泡沫金属屈服行为的影响

利用理想弹塑性梁在拉弯载荷作用下的屈服条件研究筋条截面形状为等边三角形和圆形的开孔泡沫金属在两轴载荷作用下的的屈服轨迹 ,并与现有数学模型的结果进行对比。理论分析结果表明筋条截面形状对泡沫金属的屈服行为有很大影响 ,特别是对筋条截面为非对称结构的泡沫金属 ;泡沫金属的屈服轨迹形状不但依赖于材料的相对密度 ,而且还与筋条截面形状密切相关。     

The influence of the relationship between yield strength and temperature on the stress state in a thin hollow disk

A thin hollow elastoplastic or perfectly plastic disk placed in a rigid cylindrical container and subjected to the action of a temperature field is considered. The conditions of plane stress state are assumed. The Mises yield condition is satisfied in the plastic zone. The main feature of the problem formulation is in the relationship between yield strength and temperature, taken in arbitrary form. A parametric analysis of the solution is carried out for the linear relationship. It was shown that the relationship between yield strength and temperature needs to be taken into account for some materials to define the stress-strain state in the disk and to estimate the conditions of the transition of the whole disk to the plastic state.     

A technique for calculating the continued deformation of a class of slipline field solutions

A numerical procedure is described for calculating the continued plane strain deformations of bodies made of rigid perfectly plastic materials. The technique is illustrated by calculating the continued deformation of a notched bar, with circular notch roots, pulled in tension.     

Influence of hardening rule on the elasto-plastic behaviour of a simple structure under cyclic loading

The modes of cyclic elasto-plastic deformation of a two-bar structure with unequal areas and lengths under the simultaneous action of sustained mechanical load and cyclic thermal history are investigated analytically using three types of elasto-plastic material models: perfectly plastic, linear kinematic hardening and linear isotropic hardening. This simple structure is shown to exhibit much of the behaviour of interest in design of structural components subjected to repeated thermal loads: viz, elastic shakedown, reversed plasticity and ratcheting. The cyclic plastic behaviour of the structure is developed in closed form and the effects of strain hardening, hardening rule and geometrical parameters of the two-bar assembly on the deformation modes are critically examined.     

An approximate method for a three-dimensional analysis of rolling

A theory, based on the extremum principle for rigid perfectly plastic materials, is given for the analysis of three-dimensional deformation in rolling. Theoretical solutions are obtained for single-pass rolling in terms of sideways spread, roll torque and the location of neutral points. The results on spread and roll torque showed excellent agreement with those found by experiments in the literature.     

Plastic collapse analysis of defective pipelines under multi-loading systems

In this paper, a finite element mathematical programming formulation is presented for the kinematic limit analysis of 3-D rigid–perfectly plastic bodies. A numerical path scheme for radial loading is adopted to deal with complex multi-loading systems. A direct iterative algorithm is employed in solving the above optimization formulation. The numerical procedure has been applied to carry out the plastic collapse analysis of defective pipelines under multi-loading systems. The engineering situation considered has a practical importance in the pipeline industry. The effects of four kinds of typical part-through slots on the collapse loads of pipelines are investigated and evaluated. Some typical failure modes corresponding to different configurations of slots and loading forms are studied.