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.     

Elastic behavior of ring-on-foundation

Motivated by a practical flexible crashworthy structure that protects the bridge pile against ship collision, elastic behavior of a closed circular beam (i.e., a circular ring) attached to an elastic foundation (R-o-F, in short) is analyzed. Based on the curved beam theory, the governing equation for the bending deformation of the ring is derived, in combination with adequate boundary conditions. The elastic deformation of the R-o-F under concentrated loading is analytically obtained by solving the boundary value problem (BVP). From this solution the equivalent stiffness of the R-o-F is given in analytical form. Based on the analytical model, a non-dimensional parameter, defined by the ratio of the stiffness of the elastic foundation to the bending stiffness of the beam, is identified and found to dominate the behavior of R-o-F. The adequacy of the analytical results is verified by finite element simulations on the R-o-F model with various prescribed structural parameters. The identified non-dimensional parameter provides a valuable guidance to the design of the crashworthy structure.     

Dynamic plastic behavior of a free–free beam striking the mid-span of a clamped beam with shear and membrane effects considered

Recently Yu et al. (Int. J. Solids Struct. 38 (2001) 261) made a study on the dynamic behavior of a flying free–free beam striking the tip of a cantilever beam using the rigid, perfectly plastic (r-p-p) material model. Later, also based on the r-p-p material model Yang and Yu (Mech. Struct. Mach. 29 (2001) 391) analyzed another impact problem of a free rotating hinge beam striking a cantilever beam. Both of these studies ignored the finite deflection effects on the plastic behavior of the colliding beams. However if the free–free beam strikes a clamped beam, the influence of finite-deflections, or, geometric changes, must be retained in the governing equation if the maximum permanent transverse displacement of the clamped beam exceeds the corresponding beam thickness. The problem becomes more interesting since the deformation mechanisms of the beam system and the partitioning of energy dissipation in the beams are significantly different from those predicted by ignoring the influence of membrane forces. Accordingly the failure modes of the structure are different.In the present paper, a theoretical model based on the r-p-p material idealization is proposed to simulate the dynamic behavior when the mid-point of a translating free–free beam impinging on the mid-span of a clamped beam with the beam axes perpendicular to each other. The plastic behavior of the beam system is explored with shear sliding and finite deflection effects taken into account. The final deflection, the dissipation of energy within the two beams after impact and the influence of the structural and material parameters are discussed. It is shown that membrane force plays an important role during the response process, especially when the deflection is of the same order as the thickness of the clamped beam.     

Local deformation models in analyzing beam-on-beam collisions

With the intention to reveal the local behavior of beam-on-beam collisions, several local deformation models in the collision between a free–free beam and a simply supported beam are proposed and examined. The conventional rigid, perfectly plastic material idealization is adopted in analyzing the global flexural deformation of the beams, while the coupling of the global flexural deformation with the local indentation is formulated. Numerical results demonstrate that various local models lead to similar estimate on the global energy partitioning, whatever they adopt the stick or non-stick assumption. It is also noted that the weaker local model results in higher local energy dissipation. In addition, the separation and multi-impact between the two beams are observed by using some local models with non-stick assumption.     

On the frictional behaviour of thermally loaded beams resting on a plane

The problem of an elastic beam resting on a frictional surface and loaded by a uniform temperature moment is treated analytically and numerically. The introduction of proper non-dimensional parameters identifies the deformation pattern which varies with monotonically increasing temperature load in a self-similar manner. This fact reduces the complexity of the mathematical system considerably and offers the derivation of the solution on an analytical basis. Several approaches are described, discussed and compared against each other. This problem is typical for a broader class of problems involving Coulomb friction in beam deformation. In addition to the fact that it is interesting from the structural as well as from the mathematical points of view, it is of practical importance, for example in the simulation of the cooling processes of hot rolled railway rails.     

Elastic–plastic response of unpressurised pipes subjected to axially-long radial indentation

Elastic–plastic force-deflection analysis of unpressurised pipes with long axial indentations are carried out. Solutions from an analytical method are compared to the corresponding finite element solutions and experimental test results. The analytical method is based on a simple energy-based approach developed to predict the initial gradients of the force-deflection curves and the limit loads of the indented rings using linear beam bending theory and upper bound theories. A comprehensive finite element study of indented unpressurised pipes is performed to study their sensitivities to the elastic–plastic responses. The finite element analysis covers six different materials, four different geometries and two different boundary conditions, and is compared with the corresponding analytical solutions. The results presented in this paper indicate that by using the analytical solutions for limit loads incorporating a representative flow stress as the average value of the yield stress and ultimate tensile stress, it is possible to obtain reasonably accurate predictions for the peak loads.     

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.     

Experimental study of a potential weakening effect in spheres with thin hard coatings

A potential weakening effect caused by very thin hard coatings on spherical substrates is investigated experimentally. This weakening effect reduces the resistance of the coated system to onset of plasticity. Half-coated spheres are prepared using an ion beam assisted deposition system. The coated and uncoated portions of these half-coated spheres are loaded by a rigid flat into their elastic–plastic regime of deformation and then unloaded. The resulting maximum interference after loading and residual interference at the completion of unloading are measured and used in an elastic–plastic loading index model to evaluate the plasticity levels of both the uncoated and coated portions on each sphere. The experimental results validate qualitatively the potential weakening effect, which was predicted theoretically in previous publications.     

Elastic–plastic adhesive contact of rough surfaces with asymmetric distribution of asperity heights

The elastic–plastic adhesive contact of rough surfaces is extended to include asymmetric distribution of asperity heights using the Weibull distribution with skewness as the key parameter to characterize asymmetry. The well-established elastic adhesion index and plasticity index are used to consider the different conditions that arise as a result of varying load and material parameters. The loading and unloading behaviour for different combinations of adhesion index, plasticity index and skewness values are obtained as functions of mean separation between the surfaces. It is seen that surfaces with negative skewness experience higher adhesion compared to surfaces with positive or zero skewness.     

Modelling of MHS cellular solid in large strains

The stress–strain characteristics of metal hollow sphere (MHS) material are obtained in relatively large strains under uniaxial compression in two characteristic loading directions. Based on the hypothesis of periodic repeatability of a representative block, large deformations of the material are modelled when assuming point connections between the spheres. The elastic deformations are neglected and a rigid perfectly plastic model is assumed for the base material. A structural approach using the limit analysis and the concept of an equivalent structure are then employed to describe the large plastic deformations during post-collapse process of metal hollow spheres, which undergo mainly a snap-through deformation. Stress vs. material density relationships are proposed for different strain levels in each direction of loading. The obtained results can be used to estimate the energy absorbing capacity of MHS materials under quasi-static loading. The theoretical predictions are compared with some test results and reasonable agreement is shown.     

Plastic deformation and contact area of an elastic–plastic contact of ellipsoid bodies after unloading

This paper presents theoretical and experimental results of the residual or plastic deformation and the plastic contact area of an elastic–plastic contact of ellipsoid bodies after unloading. There are three regime responses of the deformation and contact area: elastic, elastic–plastic and fully plastic. Experimental investigation is presented in order to validate the proposed model. A new technique is introduced to measure the plastic deformation and plastic contact area. Very good correlation is found between the theoretical prediction and the experimental results.     

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.     

Finite deformation of a fully fixed beam comprised of a non-linear material

The structural behaviour at finite deformation of a mild steel beam of rectangular cross-section, fully encastré at both ends and subjected to a concentrated load at mid-span, is examined in this paper. The axial tension, induced in the beam by virtue of its change in geometric configuration, gives rise to a load-carrying capacity of the beam in excess of that predicted by first-order flexural theory. Existing methods of analysis, assuming the beam to be composed solely of a linear elastic or a pure plastic material, are reviewed and an analysis is proposed for a beam composed of an elastic-plastic material. Experimental results are compared with theoretical predictions and the proposed elastic-plastic analysis is seen to give the most realistic prediction of the overall behaviour of the beam.     

Hot backward extrusion comparative analyses by a combined finite element method

Deformation and temperature of hot backward extrusion are complex owing to interaction between deformation and temperature. In this paper, two- and one-way axisymmetric hot backward extrusion problems are analyzed by a combined finite element method, which consists of the volumetrically elastic and deviatorically rigid–plastic finite element method and the heat transfer finite element method. The volumetrically elastic and deviatorically rigid–plastic finite element method is different from the conventional rigid–plastic finite element methods, and has some merits in comparison with the conventional methods. Because contact surfaces between workpiece and tools of the one-way extrusion are different from those of the two-way one, the deformation and temperature of the one-way extrusion are different from those of the two-way one. Contours of effective strain rate, effective strain, temperature, effective stress and hydrostatic stress, as well as plots at different reductions for the two extrusions are obtained successfully. Differences of calculated results for the two extrusions can be clearly seen through comparative analyses.Because the bulk modulus is introduced into the volumetrically elastic and deviatorically rigid–plastic finite element method, influence of temperature on hydrostatic stress can be considered in this paper.     

Consideration of geometric nonlinearity in rigid-plastic finite element formulation of continuum elements for large deformation

A rigid—plastic finite element formulation for the continuum elements employing the geometric nonlinearity during an incremental time step is presented. In sheet metal deformation, the displacement for each step is considerably large even though the effective strain increment is very small. For such large displacement problems, geometric nonlinearity must be considered. In the elastic—plastic finite element using continuum elements, general incremental formulations to include the geometric nonlinearity are available. However, in the conventional rigid—plastic finite element analysis using continuum, elements, the geometric nonlinearity has not been considered properly during an incremental time step. In this paper, in order to incorporate geometric nonlinearity to rigid—plastic continuum elements during a step, the convected coordinate system is introduced. To show the stability of strain distributions by the effect of geometric nonlinearity according to incremental step size, two sheet metal forming processes, stretching and deep drawing process, are analysed with various step sizes. Then the computed results using the derived equation are compared with those obtained without considering geometric nonlinearity.     

机械弹性车轮径向刚度和阻尼模型的分析

针对新型机械弹性车轮刚度特性,利用曲梁理论建立了弹性基础封闭圆环曲梁模型,对车轮刚度与輮轮抗弯刚度、铰链组弹性基础刚度及激振频率之间的关系进行了分析。结合车轮静态和动态试验分析结果,验证了根据曲梁理论所建模型的正确性,并分析了车轮刚度与车轮变形量、变形速率及激振频率之间的解析关系。根据分析结果建立了车轮刚度和阻尼的非线性解析模型,该模型反映了车轮变形量和激振频率对车轮刚度的影响,以及车轮变形速率和激振频率对车轮阻尼的影响,从而为车轮结构振动的进一步研究提供指导。     

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.     

Ductile damage micromodeling by particles’ debonding in metal matrix composites

The elastic–plastic behaviour of particle-reinforced metal matrix composites undergoing ductile damage is modelled using a two-level micro-structural approach. The considered heterogeneous material is a polycrystal containing intra-crystalline elastic particles. Ductile damage is initiated by the matrix/particle interface debonding and the subsequent voids growth with plastic straining of the crystalline matrix. Homogenization techniques are used twice: first at mesoscale to derive the equivalent grain behaviour and then to obtain the macroscopic behaviour of the material. Plastic deformation of the crystalline matrix is due to crystallographic gliding on geometrically well-defined slip systems. The associative plastic flow rule and the hardening law are described on the slip system level. The evolution of micro-voids volume fraction is related to the plastic strain. The elastic–plastic stress–strain response of particle composite is investigated. Predictions of the proposed model are compared to experimental data to illustrate the capability of the suggested method to represent material behaviour. Furthermore, specific aspects such as the stress triaxiality and yield surfaces are discussed.     

弹性地基上输送振荡流粘弹性管道的动力稳定性

基于线粘弹性理论,建立了弹性地基上输送振荡流粘弹性管道的运动微分方程,采用Galerkin法和解初值问题的Runge-Kutta法对含有周期系数的偏微分方程进行了求解。根据Floquet理论,研究了材料的量纲一延滞时间、量纲一流速以及量纲一刚度比对输送振荡流Kelvin-Voigt粘弹性管道动力不稳定区域的影响,给出了在这些参数变化时,频率比与激励参数平面上管道的动力稳定性区域和不稳定区域。