Shear and bending deformation of rigid-plastic circular plates by central pressure pulse

The dynamic plastic deformation of simply supported and clamped circular plates to a central pressure pulse is investigated theoretically. The plate material is assumed to be rigid-perfectly plastic and to obey a yield criterion which retains the transverse shear force as well as bending moments. Various patterns of deformation are obtained for a wide range of parameters which combine plastic bending and shear sliding. The dependence of the final central deflection and shear displacement on the relative shear strength, the load magnitude and the loaded area are discussed for a short duration pressure pulse. The influence of boundary conditions on shear and bending deformation is examined.     

Shear and bending response of a rigid-plastic beam subjected to impulsive loading

The dynamic response of a rigid-plastic beam is considered. The beam is subjected to the initial impulsive loading. Plastic yielding of the material in controlled by the square yield criterion which retains the transverse shear force as well as the bending moment. The beam under consideration is clamped at the left and simply supported at the right-hand end.     

The large rigid-plastic deformation of a circular cantilever beam subjected to impulsive loading

A quadrantal circular beam subjected to radial impact in its own plane at its tip by a rigid mass is studied on the basis of a large deformation formulation. The procedure for computing this dynamic response is given and numerical examples are shown in order to make a comparison with the results on the basis of small deformation formulation of the same problem.     

On the relation between rigid-plastic and elastic-plastic predictions of response to pulse loading

Using a simple model, comparisons are shown between the predictions of elastic-plastic and rigid-plastic analyses as to the permanent displacements due to pulse loading. Several pulse shapes are considered, and the comparisons are made over a large range of the ratio τ/T (pulse duration time/natural period of the structure). When the rise time of the pulse is not zero, these show a wavy character that was not seen in earlier comparisons of this type, where smaller ranges were used. Thus the two predictions are found to be very close at regular intervals, while the rigid-plastic prediction has negative (unconservative) errors in between, relative to the elastic-plastic one. These errors may be large even though the plastic deformation greatly exceeds the elastic displacement at yield. The ‘energy ratio’ criterion for validity of rigid-plastic analysis must be supplemented, for ‘long’ pulses, by consideration of the effect of pulse duration. The waviness of the elastic-plastic spectral plots is explained in terms of the similar shapes of the ‘dynamic amplification’ spectra of wholly elastic shock analysis.     

Bending of glass fibre-reinforced plastic (GFRP) plates on elastic supports

This study is concerned with the mechanical properties of a fibreglass reinforced polyester resin of laminar construction with consideration given to the application of the results to the analysis, in bending, of a plate of similar material. Tension and compression tests were performed to obtain the stress-strain relationship and ultimate stresses and strains. Because of the inherent scatter of results due to the nature of the material, average values, along with maximum and minimum limits, are determined. Flexural tests were conducted and moment-curvature relationships were obtained both theoretically and experimentally. Creep tests showed that, for loads well below the failure load, creep effects are almost negligible when the fibres are oriented to the longitudinal axis of the specimen. As the results in bending are not as scattered as those for tension and compression, this leads one to believe that they might be more appropriate for use in plate theory.

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Résumé On étudie les propriétés mécaniques d’une rśine polyester renforcée de fibres de verre et de structures laminaires, en ayant en vue l’application des résultats à l’étude en flexion d’une plaque d’un matériau similaire. Les essais de traction et de compression ont été réalisés afin d’obtenir la relation contrainte/déformation ainsi que les contrainteses et déformations ultimes. La nature du matériau déterminant une dispersion des résultats, on a fixé des valeurs moyennes comportant des limites maximales et minimales. On a réalisé des essais de flexion tant théoriques qu’expérimentaux, et obtenu des relations moment-courbure. Les essais de fluage montrent que pour des charges nettement au-dessous de la charge de rupture les effets du fluage sont presque négligeables si les fibres sont disposées longitudinalement dans l’éprouvette. Comme les résultats en flexion sont moins dispersés que ceux obtenus en traction et en compression, on peut supposer qu’ils se prêtent mieux à être utilisés dans la théorie des plaques.

     

Failure of ceramic/fibre-reinforced plastic composites under hypervelocity impact loading

The hypervelocity impact limit, V50, of alumina/fibre-reinforced plastic (FRP) target materials was studied with different adhesive layer thicknesses and two kinds of FRP. A high-speed camera was used to analyse the perforation phenomena of target materials. In addition, the dishing and bulging extent of FRP as a rear material were investigated using a digital planimeter from a series of high-speed photographs during the perforation of a projectile. In the case of the same adhesive layer thickness, the target material with more ductile FRP (A type) absorbed more impact energy than that with less ductile FRP (B type). In both target materials, the highest V50 was obtained at an adhesive layer thickness of 1.3 mm.     

Damage mechanisms under tensile and fatigue loading of continuous fibre-reinforced metal-matrix composites

Metal-matrix composites are gaining increasing attention for structural applications. However, the database relating to their mechanical properties and microstructural characterization remains limited. In the present study, aluminium-matrix composites reinforced with SiC fibres, α-Al₂O₃ fibres and carbon fibres have been investigated. Continuous fibre reinforcements, unidirectional in the 0° and 90° directions, were used. Tensile and compression tests were performed using specially designed test equipment for metal-matrix composites. The best results were achieved when cylindrical hour-glass shaped specimens were used. Fatigue testing of the composites showed that a pronounced improvement in the fatigue behaviour can be achieved upon the addition of fibre reinforcement.     

Strength and toughness of fibre-reinforced thermoplastics: effect of temperature and loading rate

Fracture mechanics tests of injection moulded short fibre polymer composites have been conducted to provide an experimental test of the toughness equation presented here. The toughness varies as a function of temperature and strain-rate. The temperature dependence was obtained from the ‘wet’ specimen which was preconditioned in water. A simplified expression has been obtained under a constant temperature and a constant strain-rate     

A physically based fatigue damage model for fibre-reinforced plastics under plane loading

The subject of the present article is a new layer-based fatigue damage model (FDM) for laminated multidirectional laminates exposed to general states of plane stress, which allows for simulating the stiffness and the strength degradation by means of a FEM analysis. The essential of the new model is its use of an energy approach which makes the fatigue life prediction of composites more physical and therewith its characterisation much less extensive. Since the failure analysis bases on an interacting failure criterion, the material degradation depends also on the failure mode and is layer-based. (Typical fatigue phenomena as stress redistributions and sequence effects can be analysed with the new model and due to its efficiency it is also applicable to larger structures.)The paper presents a partial validation of the model based on experimental results from the literature and different application examples. These are a shell with a hole and a rotor blade of a wind energy converter demonstrating the analysis of stress redistribution, sequence effects and the applicability of the model to large structures respectively.     

Impact loading of plates — An experimental investigation

The impact of projectiles at sub-ordnance velocities against mild steel, stainless steel and aluminium plates, has been studied in a series of experiments. The projectile mass, nose shape and hardness have been shown to have an important effect on penetration as does the target rigidity and support condition. All materials exhibit a clear ‘kink’ effect related to a change from energy absorption by plastic deformation to perforation with well-defined shear bands and no appreciable bulging.     

Response of pre-pressurized reinforced plates under blast loading

The effects of pre-pressurization on blast-loaded reinforced rectangular aluminum plates were studied experimentally. Rectangular clamped plates with rivet-attached stiffeners were used as a basic model of the fuselage skin of a commercial aircraft. Both non-pressurized and pre-pressurized plates (static pressure of 41.4 kPa) were considered to simulate the typical in-flight loads experienced by a commercial aircraft due to cabin pressurization. This work extends previous research on blast loading of pre-pressurized plates [Veldman RL, Ari-Gur J, Clum C, DeYoung A, Folkert J. Effects of pre-pressurization on blast response of clamped aluminum plates. Int J Impact Eng 2006;32(10):1678–95] to incorporate the effects of riveted stiffeners.     

Pulse pressure loading of clamped mild steel plates

Some results of a large series of pulse pressure loading tests on 1 m×1 m, clamped mild steel plates with different in-plane edge conditions are presented. A novel experimental device was used to produce uniform, repeatable pulse pressure loads of an approximate triangular form. The behaviour of the restrained plates was dominated by membrane effects leading to substantial spring-back. An assumed-modes, elastic–plastic analytical approach was used to predict the maximum and residual deflections of the test plates under dynamic loading with reasonably good success. Multi-element models of the test plates were developed in which the bi-axial behaviour of the plate was represented by one-dimensional finite strips. The in-plane restraint of the plate was approximated using non-linear translation springs and a slippage allowance. Satisfactory results were achieved owing to the careful determination and definition of the boundary conditions, which can significantly influence the results particularly if non-linear membrane forces and slippage occur. It has been shown that a simple methodology such as the one proposed in this paper can provide adequate predictions of the dynamic, large-deflection behaviour of pulse-loaded plates.     

Fracture process of thermally shocked discontinuous fibre-reinforced glass matrix composites under tensile loading

Fracture mechanisms of discontinuous carbon-fibre-reinforced glass matrix composites were experimentally studied for specimens with initial damage induced by thermal shock. First, matrix cracking due to thermal shock was observed using both optical microscopy and scanning acoustic microscopy (SAM) to reveal the damage state. Secondly, tensile stress-strain behaviour and acoustic emission during tensile tests were measured for specimens with and without thermal shock. The progress of microscopic damage during tensile loading was also investigated using both replica and in-situ SAM techniques. Finally, macroscopic transient thermal stresses during thermal shock were calculated using finite-element analysis. It is proved that the fracture process of the composite specimen with thermal-shock-induced cracks is different from that of the virgin specimen. This difference in fracture processes is attributed to the difference in the evolution of matrix cracking, which is affected by pre-existing microcracks in the matrix. This revised version was published online in November 2006 with corrections to the Cover Date.     

A non-discretized global method for free vibration of generally laminated fibre-reinforced pre-twisted cantilever plates

 The paper presents a computational method for characterizing the resonant frequency properties of cantilever pre-twisted plates composed of fibre-reinforced laminated composites. It aims to simulate a laminated turbomachinery blade or a fan blade with a relatively small aspect ratio for which the conventional beam model fails to provide accurate solutions. The strain and kinetic energy components are expressed in area integration equations with respect to the plate mid-surface. An energy functional is defined and a governing eigenvalue equation is derived. There is no domain mesh generation in the numerical analysis thus reducing accuracy loss due to discretization. New numerical solutions are presented and the effects of angle of pre-twist, aspect ratio, and symmetric and antisymmetric lamination for two different composite laminates are analyzed in detail. The limit of linear twisting curvature omitted in previous analysis is strictly adopted here and the consequences of exceeding the limit are discussed.     

The relative residual fibre displacement after indentation loading and unloading of fibre-reinforced ceramic composites

The interfacial properties of fibre-reinforced ceramic composites have been evaluated by using the indentation technique. The ratio of the residual fibre displacement after complete unloading to the fibre displacement at peak loading is examined. Assuming a constant interfacial shear stress at an unbonded interface, this ratio is 0.5. However, deviation of this ratio from 0.5 is always obtained from experimental results. Both Poisson's effect and the existence of the residual axial stress have been proposed to explain this deviation. A methodology is presented in this study to classify conditions for which either Poisson's effect or the residual axial stress dominates this deviation. The application of this methodology to Nicalon fibre-reinforced lithium aluminosilicate glass-ceramic is also illustrated.     

Dynamic enhancement of blast-resistant ultra high performance fibre-reinforced concrete under flexural and shear loading

Two independent projects are described in which drop-hammer techniques are used to investigate the dynamic increase factor (DIF) under both flexural and shear high-speed loading of a new ultra high performance fibre reinforced blast-resistant concrete. The results from both studies correlate well. The results show that a DIF of the flexural tensile strength rising from 1.0 at 1 s⁻¹ on a slope of 1/3 on a log (strain rate) versus log (DIF) plot can be used for design purposes. The results also show that no DIF should be used to increase the shear strength at high loading rates.     

爆炸荷载作用下复合材料加筋板的动力响应

为了减轻抗爆结构质量,采用玻璃纤维增强聚合物基复合材料（SMC）与碳纤维增强聚合物基复合材料（CFRP）预浸料,通过数值模拟和等效计算理论,对传统加筋抗爆板结构进行轻质高强设计。利用LS-DYNA有限元数值模拟软件进行分析,发现在爆炸荷载作用下加筋板的运动以弹性运动为主,该种复合材料具有较好的抗爆性能。对复合材料加筋板结构进行参数化分析,发现在爆炸荷载作用下横筋对加筋板结构最大位移值影响最大,纵筋和面板对加筋板的影响依次减小。结合刚度折算方法,建立了爆炸荷载作用下正交异性加筋板结构动力响应分析理论。利用该理论计算得到板结构在爆炸荷载作用下的最大位移,与数值模拟对比发现两者结果较为接近,为加筋抗爆板的设计提供了一种简化有效的计算方法。     

Performance of functionally graded plates under localised transverse loading

This paper presents a study of the bending of an isotropic functionally graded plate under localised transverse load through a combination of analytical and computational means. The analytical modelling is based on the recently developed three-dimensional elasticity solution, expanded to cover different loading types, whilst the Finite Element model uses graded isoparametric elements. The plate under consideration is assumed to be simply supported, with Young’s and shear moduli varying exponentially through the thickness and the Poisson’s ratio constant. Comparative analysis of stress and displacement fields in functionally graded and homogeneous plates subjected to uniformly distributed and patch loadings is carried out.