Effects Of Changes In Geometry Research Articles

Collapse Behavior and Strength of Steel Silo Transition Junctions. Part II: Parametric Study

This paper presents the results of a major parametric study of the plastic collapse behavior and strength of the complex transition junctions in steel silos using an elastic-plastic large-deflection finite element analysis for axisymmetric shells. Both small-deflection and large-deflection theories are employed to obtain classical limit loads and to clarify the effect of changes in geometry. The collapse loads determined by the finite element analysis are compared with those predicted by a simple hand method derived by Rotter and an improved method developed in a comparison paper. These comparisons show that Rotter’s simple method is satisfactory only for junctions at which the shell segments are of similar thickness. The modified method gives a much closer overall approximation to the finite element results over the wide range of parameters studied. This paper also discusses the alternative possibilities of skirt or hopper collapse when a strong junction is used.

The problem of instability in liquid scintillation counting

In this paper, effects of geometry changes during 32P counting by a liquid scintillator are analyzed. The results obtained suggest that this effect is due to a precipitation of labelled compound from scintillation solution and settling on the bottom of the vial. Simultaneous sorption of labelled compound to the vial wall is also taken into consideration.

Post-yield behaviour of a rigid-plastic beam with partial axial and rotational end fixities

Complete load-deflection relationships of a rigid-plastic beam subjected to a non-symmetrically placed point load are derived. In addition to the inclusion of the effects of geometry change, the analysis considers the supports as being capable of variable combined axial and rotational restraints. As expected, the increase in load-carrying capacity with deflection can be quite large for certain support conditions.

The influence of geometrical fluctuations on electron tunneling barriers in proteins

We have recently developed a new classification of the amino acid side chains based on doublet acceptor energy levels (DALs). These energy levels, taken as the eigenvalue of the highest occupied molecular orbital in the radical anion, provide insight into the shape of the tunneling barrier in protein electron transfer. We have used this classification to characterize several transfer pathways in myoglobin. We present here a study of the effect of changes in geometry on the doublet acceptor levels. We find that, in general, this influence is rather small for reasonable changes in bond lengths and angles (e.g., those resulting from thermal fluctuations in the protein structure). However, we have found that for serine, threonine and water, changes in geometry that might take place as a result of fluctuations in hydrogen bond geometries lead to rather large changes in DAL. We investigate these correlations in some detail. The relation between protein fluctuations and changes in the shape of the electron tunneling barrier is discussed. Additionally, based on the energetics of changes in the OH bond distance, we discuss aspects of the relation between electron transfer and proton transfer.

The effect of blunting on the strain field at a crack tip under mixed modes 1 and 2

T he strain distribution near a crack tip deforming in plane strain under mixed Modes 1 and 2 loads is calculated using slip line field theory in the case of small-scale yielding. Large geometry change effects are taken into account. In particular it is found that: (i) true strains ahead of the blunting crack are lower in mixed Modes 1 and 2 than in Mode 1; (ii) when the Mode 2 component of load dominates, material points ahead of the blunting crack tip are swept below and past the tip as the magnitude of the load increases. For Mode 1-dominated loading, material points are swept in towards the tip; (iii) in fans not directly ahead of the notch tip, true strains can be both greater in mixed Modes 1 and 2 than in Mode 1 and greater than the strain directly ahead of the notch. The results are discussed in the context of strain-based fracture theories applicable to upper-shelf fracture.

A Study of Vortex Throttles Part 1: Experimental

Measurements have been made to determine the performance of various designs of vortex throttle using both air and water. Two basic types of throttles were used, square-edged and round-edged. Performance is expressed mainly in terms of Reynolds number and Euler number. The effect of changes in geometry on performance is studied and comparison made between performance for compressible subsonic flow and for incompressible non-cavitating flow. The maximum values of Euler number found for throttles with a unity tangential to axial port area ratio were about 66 for square-edged throttles and about 71 for round-edged throttles. The results agree with those of Zobel, although better performance than found by Zobel was obtained with a slightly modified axial port geometry. In one case severe cavitation was found to slightly improve throttle performance, with the indication that a throttle could be made with performance independent of cavitation. Some recommendations are given for optimum throttle design.

The stress field near a blunting crack tip under mixed modes 1 and 2

The distribution of stress near a crack tip deforming in plane strain under mixed Modes 1 and 2 loads is calculated using slip-line field theory. Large geometry change effects are taken into account. The results are compared and contrasted both with known Mode 1 large-deformation solutions and with previous mixed-mode solutions for a sharp crack. The results are then combined with stress-based fracture criteria to discuss mixed-mode fracture on the lower shelf.

Parkes revisited: On rigid-plastic and elastic-plastic dynamic structural analysis

In this paper we re-examine a classical problem of rigid-plastic structural dynamics solved by Parkes [1], namely that of finding the deformations of a beam carrying a mass at its tip which is subjected to a short pulse loading. A considerable body of “elementary rigid-plastic theory” has been developed based on the neglect of elastic strain components, the idealization of perfectly plastic behavior (absence of strain hardening or strain rate sensitivity), and the assumption of linear field equations ignoring effects of geometry changes. This theory provides a valuable conceptual framework for problems of dynamic plastic structural response, although corrections are required for many practical applications; for example, Parkes introduced a correction for effects of high strain rates shown to be needed by his experiments on steel beams. The neglect of elastic strains — elastic moduli taken infinite — is a crucial assumption, and its validity is the subject of the present paper. We study it by making comparison between “exact” numerical solutions furnished by an advanced finite element computer program for an elastic-plastic beam, and the rigid-plastic solution slightly modified to allow for large deflections. Further insight is gained by comparisons also with a simplified elastic-plastic approach based on treatment of elastic and plastic action in artificially separated stages. The main conclusions are that the initial travelling-hinge phase of the rigid-plastic solution is essentially a fiction, but that the subsequent mode form phase is a prominent and significant feature of the late-time part of the “actual” elastic-plastic response.

Modal stiffnesses of a pretensioned cable net

The paper is concerned with the structural mechanics of pretensioned saddle-shaped cable nets of the type shown in Fig. 1. Such nets are normally regarded as being non-linear systems; but it is shown that their behaviour may be described satisfactorily in terms of two distinct, and practically independent, sets of extensional and inextensional modes. Each set of modes may be studied by means of suitable linear analysis, and the eigenmodes may be found without difficulty. The stiffness of the extensional modes derives from the elasticity of the members, and is practically independent of the level of prestress in the net In contrast, the stiffness of the inextensional modes is independent of the elasticity of the members; it derives from geometry-change effects and is directly proportional to the level of prestress in the net. Usually, the most compliant inextensional mode of a net made from steel cables will be much less stiff than the extensional modes; but the circumstances of this are determined by the value of a single dimensionless group. An experiment performed in the laboratory on a small-scale model net confirms the theoretical results. The paper concludes with a short discussion on the applicability of the results of this paper to pretensioned cable nets in general.

Modelling of site induced structures in the electronic transitions of naphthalene in rare gas matrices

Various insertion modes of the naphthalene molecule in the rare gases were analysed by constructing the intermolecular potential energy functions for naphthalene in the substitutional sites. Spectral shifts. Stokes shifts and local librational frequencies for naphthalene-d 8 in the sites have been evaluated. The parametrization of the interaction potential for the excited naphthalene in rare gases and the effects of geometry changes and rigidity of matrix are discussed.

Analysis of stretching of sheet metals with hemispherical punch

The variational formulation applicable to sheet metal forming is derived by considering solution uniqueness and the effect of geometry change. From this variational formulation, a finite element model based on the membrane theory is developed, and the stretching of sheet metals with hemispherical punches is analyzed. Agreement of the computed solutions with experiments was generally good. The examination of the effects of interface friction and of modeling of constitutive relations by computation revealed importance of these parameters in deformation characteristics of punch stretching.

The visible excitation spectra of benzyl, benzyl- d7 and p-methylbenzyl in rigid solution at 77 K

The full low resolution fluorescence-excitation spectra of benzyl, benzyl- d 7 and p-methylbenzyl in rigid amorphous solution at 77 K are reported, together with the polarization spectrum of the visible excitation band of p-methylbenzyl. The three excitation spectra are roughly similar in their low energy region appearing like weakly allowed spectra having stronger “forbidden” components. The three spectra more or less agree with the mirror image of the benzyl and benzyl- d 7 fluorescences. The emission of p-methylbenzyl is strikingly different, showing a considerable relative strengthening of the allowed portion over the “forbidden” component and, with that, an apparent strong break with the absorption fluorescence mirror image rule. One interpretation anticipates an important effect of geometry change in pMB, due to electronic excitation, upon both the allowed and “forbidden” components of this well known weak transition. Alternatively, it may be that the elusive second excited state ( 2B 2) appears in the pMB excitation spectrum in such a coincident manner that the mirror image rule holds even while conferring upon the excitation spectrum a structure very much like the absorption and emissions of the two benzyl radicals. This second state, in any case, is supposed to lie very near tthe first excited ( 2A 2 −) state. The polarization results in pMB are consistent with either interpretation. Since theoretical predictions indicate that the ratio of 2B 2 − to 2A 2 − intensity should be much larger in p-methylbenzyl than in benzyl, it may well be that the 2B 2 − band is an important part of the excitation spectrum in the latter case. The necessary coincidence of energy and intensity required of the 2B 2 − transition with what should characterize the nontotally symmetric vibronic activity in the 2A 2 − transition is a complicating factor which these low resolution studies are not able to overcome in trying to resolve this question.

Plastic Analysis of Shallow Spherical Shells

Rigid-plastic yielding and postyielding of pressurized shallow spherical shells is considered. The analysis includes the contribution of the transverse shear to yielding. Two approximate numerical solutions are given for several shell configurations. The yield surface used is based on the von Mises criterion. The results show that the effects of geometry changes lead to “geometrical strengthening” and “geometrical weakening” of the shallow shells.

The Effect of Geometry Changes on the Load Carrying Capacity of Beams Under Transverse Load

This paper concerns the influence of geometry changes on the post-yield behavior of beams and other engineering structures. First, the extant literature on the subject is reviewed. Next, as a specific illustration, the particular problem of a simply supported axially restrained uniform beam, rectangular in cross section and made of rigid perfectly-plastic material, and subjected to vertical load uniformly distributed with respect to length measured along the current centerline of the beam is studied in detail. The beam’s response, following the initial yield associated with the formation of a central yield hinge, is in two consecutive phases. In the primary phase, plastic deformation is associated solely with the outwards movement of two boundaries such that the material behavior at beam cross sections stays rigid except precisely at these boundaries ; the phase terminates when each has moved out to a cross section originally at a distance of one-third of the semispan from the center. The secondary phase now begins with each of the two existing boundaries being joined by a new boundary that separates to travel inwards, and now plastic deformation completely extends over the two outer regions between the boundaries; the phase terminates when these boundaries reach the ends and the center of the beam, and then the beam’s response is simply that of a pure membrane, although this state is only asymptotically achieved. The analysis presented leads, for example, to a complete determination of the load deformation relationship, and the important influence of geometry changes on the response of the beam is thereby made clear. In particular, in practical circumstances of slender beams, it is found that even at central transverse deflections of the order of the beam thickness, the load carrying capacity is considerably enhanced and also the asymptotic membrane state is effectively realized. The results of the present exact analysis of the problem, which is based on the rate equations of equilibrium, extend those obtained earlier in approximate analyses given by other workers. Finally, mention is made of related beam problems, for which a similar analysis is possible and for which similar results obtain, and also of plate problems.

Effects of Geometry Change on Essential Features of Inelastic Behavior

Essential features include normality or lack of normality of the inelastic strain or displacement rates to a meaningful surface, convexity or concavity of this surface, stability, and uniqueness of the incremental response. The correlation between system features and those of its constituent elements is studied in the presence of significant geometric effects on equilibrium. The system is regarded as an assembly of a discrete number of constituents via finite element discretization; consequently, algebraic description is adopted. The carrying over of normality from the element to the system is proved by means of virtual work equations, and alternatively, by deriving a suitable matrix description of the system incremental laws. This description combined with some recent results in mathematical programming, leads to sufficient conditions for stability and for existence and uniqueness of the incremental response. These conditions are formulated for both individual elements and systems and can be used for actual calculations. Convexity does not in general carry over from element to system in the presence of significant geometry changes

Stretching vibrations of the methylene group and ring strain in the cycloalkanes

A normal coordinate treatment shows that the observed frequency differences for the stretching vibrations of the methylene group in the cycloalkanes are due to force constant changes. The effect of change in geometry on these vibrations is quite small.

Limit Analysis of Plates under Combined Loads

An approximate analysis is presented to estimate the carrying capacity of ductile symmetrically loaded circular plates under combined lateral load and edge compression. The effects of changes in geometry are taken into account in the derivation of load-displacement relationships for rigid-plastic plates beyond the yield point. Plastic interaction surfaces, which describe this load-displacement behavior, are obtained for simply supported and clamped plates subjected to the two independent loading parameters. The carrying capacity of a plate is then estimated as the intersection of an elastic load-response curve with a plastic interaction surface. The analysis indicates when a uniform edge compression is applied, the lateral load-carrying capacity of the plate is reduced.

Plastic Behaviour of Thin Cylindrical Pressure Vessels with Circular Cutouts and Radial Branches

Pressure tests were performed on four thin cylindrical aluminium vessels with circular cutouts and cover plates, and on two vessels with radial branches. In all cases a fairly well defined ‘limit pressure’ was observed—corresponding to plastic deformation in the vicinity of the cutout or branch—together with a moderate increase in pressure as deformation proceeded, which may be interpreted as a moderately strong ‘geometry-change effect’. The limit pressures observed for vessels with cutouts agree well with a lower-bound analysis which is described in outline. In general the observed limit pressures fit in well with those observed by other workers for vessels of different proportions. Correlation of geometry-change effects is not so simple, but a fairly clear picture of trends emerges from the study. The question of appropriate geometrical parameters for correlation of results is discussed, and a suggestion is made for taking into account any ‘extra’ cross-sectional area at the junction weld.

The safety of masonry arches

The paper describes the application of limit principles, derived from the plastic analysis of steel structures, to the masonry arch. Most voussoir arches have low stresses, and the lines of thrust lie well within the masonry, so that conventional factors of safety on stress have little relevance. However, a “geometrical” factor of safety may be defined by consideration of the arch of minimum thickness, of the same shape as the real arch, which would just contain a proper line of thrust. If the real profile of the arch is then discarded, and the calculations referred to an arch having the profile of the ideal line of thrust, it is shown that a simple analysis may be made of the effect of travelling point loads. The ideas are applied to the analysis of two actual bridges: (a) the stone arch between the western towers of Lincoln Cathedral, and (b) the Ponte Mosca in Turin. The paper is concerned only with the action of the masonry, and not with the design of the abutments to resist the thrust of the arch. However, the effect of geometry changes due to yielding of the abutments is discussed.

The effect of geometry change on the application of limit analysis to the design of pressure vessel nozzles

Previously published work on the elastic and limit analysis of flush nozzles in spherical pressure vessels and on the effect of change of geometry on the limit pressure is considered. It is proposed that a suitable design procedure for pressure vessel nozzles is to identify a calculated lower bound to the limit pressure with the test pressure.