Generalization of Response Number for Dynamic Plastic Response of Shells Subjected to impulsive Loading

A dimensionless number, termed as response number in Zhao [Archive of Applied Mechanics 68 (1998) 524], has been suggested for the dynamic plastic response of beams and plates made up of rigidly perfect plastic materials subjected to dynamic loading. Many theoretical and experimental results can be reformulated into new concise forms with the response number. The concept of a new dimensionless number, response number, termed as Rn(n), is generalized in Zhao [Forschung im Ingenieurwesen 65 (1999) 107] to study the elastic, plastic, dynamic elastic as well as dynamic plastic buckling problems of columns, plates as well as shells. The response number Rn(n) is generalized to the dynamic behaviour of shells of various shapes in the present paper.

Application of response number for dynamic plastic response of plates subjected to impulsive loading

A dimensionless number, termed response number, is applied to the dynamic plastic response of plates subjected to dynamic loading. Many theoretical and experimental results presented by different researchers are reformulated into new concise forms with the response number. The advantage of the new forms is twofold: (1) they are more physically meaningful, and (2) they are independent of the choice of units, thus, they have wider range of applications.

Suggestion of a new dimensionless number for dynamic plastic response of beams and plates

A dimensionless number, termed response number in the present paper, is suggested for the dynamic plastic response of beams and plates made of rigid-perfectly plastic materials subjected to dynamic loading. It is obtained at dimensional reduction of the basic governing equations of beams and plates. The number is defined as the product of the Johnson's damage number and the square of the half of the slenderness ratio for a beam; the product of the damage number and the square of the half of the aspect ratio for a plate or membrane loaded dynamically. Response number can also be considered as the ratio of the inertia force at the impulsive loading to the plastic limit load of the structure. Three aspects are reflected in this dimensionless number: the inertia of the applied dynamic loading, the resistance ability of the material to the deformation caused by the loading and the geometrical influence of the structure on the dynamic response. For an impulsively loaded beam or plate, the final dimensionless deflection is solely dependent upon the response number. When the secondary effects of finite deflections, strain-rate sensitivity or transverse shear are taken into account, the response number is as useful as in the case of simple bending theory. Finally, the number is not only suitable to idealized dynamic loads but also applicable to dynamic loads of general shape.

Saturated duration for dynamic structural plastic response and fundamental periods of elastic vibration

The relationship is determined between saturated duration of rectangular pressure pulses applied to rigid, perfectly plastic structures and their fundamental periods of elastic vibration. It is shown that the ratio between the saturated duration and the fundamental period of elastic vibration of a structure is dependent upon two factors: the first one is the slenderness or thinness ratio of the structure; and the second one is the square root of ratio between the Young's elastic modulus and the yield stress of the structural material. Dimensional analysis shows that the aforementioned ratio is one of the basic similarity parameters for elastic-plastic modeling under dynamic loading.

Prediction of structural dynamic plastic shear failure by Johnson's damage number

It is proved that Johnson's damage number is the sole similarity parameter for dynamic plastic shear failure of structures loaded impulsively, therefore, dynamic plastic shear failure can be understood when damage number reaches a critical value. It is suggested that the damage number be generally used to predict the dynamic plastic shear failure of structures under various kinds of dynamic loads (impulsive loading, rectangular pressure pulse, exponential pressure pulse, etc.,). One of the advantages for using the damage number to predict such kind of failure is that it is conveniently used for dissimilar material modeling.

Parkes problems revisited - Application of response number

Response number R-n(n), proposed in [3, 4], is an important independent dimensionless number for the dynamic response of structures [2]. In this paper, the response number is applied to the dynamic plastic response of the well-known Parkes' problem, i.e., beams struck by concentrated mass.

Similarity consideration of structural bifurcation buckling

Many structural bifurcation buckling problems exhibit a scaling or power law property. Dimensional analysis is used to analyze the general scaling property. The concept of a new dimensionless number, the response number-Rn, suggested by the present author for the dynamic plastic response and failure of beams, plates and so on, subjected to large dynamic loading, is generalized in this paper to study the elastic, plastic, dynamic elastic as well as dynamic plastic buckling problems of columns, plates as well as shells. Structural bifurcation buckling can be considered when Rn(n) reaches a critical value.

骨动态压电响应的测试研究

测量应力波在骨内传播时骨的压电电位响应是困难的，困难之处在于电位参考点的选定，电位参考点必须是一个电位保持恒定的点，当应力波在骨内部传播时，应力波传及的部位都会产生压电电位变化，不存在电位保持恒定的部位，本文利用屏蔽内电位恒定的特点，将参考点移出骨试件选在屏蔽层上，解决了上述困难。测出了骨的压电电位响应，测试结果表明压电电位决定于应力梯度而不是应力，而且骨受拉伸时其压电电位（绝对值）大于受压缩时的压电电位。

Notch sensitivity of circular rings subjected to impact loading

'Notch-sensitive regions' have been observed during a series of experimental investigations into the dynamic plastic behaviour and failure of thin-walled metallic radially notched circular rings with are-shaped supports subjected to concentrated impact loads. The experimental results show that the exterior notches at some regions have no effect on the deformation of the rings, but do have effect at the remaining regions. The notch-sensitive region is theoretically determined by using the equivalent structures technique; fairly good agreement has been reached between the simple theory and the experimental results. Both dimensional and theoretical analyses prove that whether a plastic hinge formed or not at the notched section does not depend on the mean radius of the ring and the input kinetic energy. It depends on the weak coefficient of the notched section and the angle of the support. Generally speaking, there are mainly three failure modes for a notched circular ring with are-shaped support under impact loading: Mode I, large inelastic deformation when the notch is outside the sensitive region, in this case the ring deforms as a normal one; Mode II, large inelastic deformation only at some part of the ring and tearing occurred at the notched sections; Mode III, large inelastic deformation and total rupture occurred at the notched sections. It is believed that the present study could assist the understanding of the dynamic behaviour and failure of other kinds of nonstraight components with macroscopic imperfections under impulsive loading.

Influence of 2 secondary effects on shear failure of cantilever with attached mass block under impulsive loading

The influence of two secondary effects, rotatory inertia and presence of a crack, on the dynamic plastic shear failure of a cantilever with an attached mass block at its tip subjected to impulsive loading is investigated. It is illustrated that the consideration of the rotatory inertia of the cantilever and the presence of a crack at the upper root of the beam both increase the initial kinetic energy of the block required to cause shear failure at the interface between the beam tip and the tip mass, where the initial velocity has discontinuity Therefore, the influence of these two secondary effects on the dynamic shear failure is not negligible.

Extremum principle of crystal plasticity

An analytical method for determining slip shear rate under prescribed stress rate or prescribed strain rate has been presented on the basis of the incremental theory of crystal plasticity. The problem has been reduced to a quadric convex programming.In order to analyse the plastic response of crystals subjected to external load, two new extremum principles are proposed. They are equivalent to the boundary-value problem of crystal plasticity. By the new extremum principles, the slip shear rates are independent function which can be obtained from the variational equation.

ELECTROCATALYSIS AND DETERMINATION OF HYDRAZINE COMPOUNDS IN LIQUID-CHROMATOGRAPHY AT A MIXED-VALENT COBALT OXIDE CYANOCOBALTATE FILM ELECTRODE

A glassy carbon electrode coated with an electrodeposited film of mixed-valent cobalt oxide/cyanocobaltate (Co-O/CN-Co) enabled hydrazine compounds to be catalytically oxidized at the greatly reduced overpotential and in a wide operational pH range (pH 2.0-7.0). Electrocatalytic activity at the Co-O/CN-Co modified electrode was evaluated with respect to solution pH, film thickness, supporting electrolyte ions, potential scan rate, operating potential, concentration dependence and other variables. The Co-O/CN-Co film electrode was completely compatible with a conventional reversed-phase liquid chromatographic (RP-LC) system. Practical RP-LC amperometric detection (RP-LCEC) of hydrazines was performed. A dynamic linear response range over three orders of magnitude and a detection limit at the pmol level were readily obtained. The Co-O/CN-CO film electrode exhibited excellent electrocatalytic stability in the flowing streams.

Comparison of the Dynamic Response of a Saturated Soil Between Two Models

By comparing the dynamic responses of saturated soil to Biot's and Yamamoto's models, the properties of the two models have be pointed out. First of all, an analysis has been made for energy loss of each model from the basic equations. Then the damping of elastic waves in coarse sand and fine sand with loading frequency and soil's parameters have been calculated and the representation of viscous friction and Coulomb friction in the two models has been concluded. Finally, the variations of loading wave damping and stress phase angles with water depth and soil's parameters have been obtained as loading waves range in ocean waves.

The Response of Bucket Foundation under Horizontal Dynamic Loading

The experimental investigation of the response of suction bucket foundation in fine sand layer under horizontal dynamic loading has been carried out. The developments of settlement and excess pore pressure of sand foundation have been mainly studied. It is shown that the sand surrounding the bucket softens or even liquefies at the first stage if the loading amplitude is over a critical value, at later stage, the bucket settles and the sand layer consolidates gradually. With the solidification of the liquefied sand layer and the settlement of the bucket, the movement of the sand layer and the bucket reach a stable state.