Protection of large superconducting magnets: maximum permissible undetected quench voltage

For a quench detection scheme based on voltage measurement, a formula is derived for the maximum level of quench voltage that can be left undetected. This voltage sets a minimum voltage that must be detected by any voltage detection circuit. For ‘stable’ superconducting magnets wound with copper substrate composite conductor, this voltage is tens of millivolts, independent of current density. A formula is derived for the maximum permissible circuit delay time for the actuation of a dump circuit.     

The dynamics of double reversal of wave fronts in photorefractive crystals

Averaged equations are derived describing the process of relaxation of reversed waves in the case of complex light fields in a scheme of double reversing mirror. Qualitative agreement between the experimentally derived and calculated time dependences is obtained for an optical circuit employing a Bi₁₂TiO₂₀ crystal.     

On the tangent modulus tensor in hyperelasticity

Summary The tangent modulus tensor, denoted asD, plays a central role in nonlinear finite element simulation of elastomeric components such as seals. It is derived from the strain energy functionw for isotropic elastomers. Using Kronecker product notation, a compact expression forD has been derived in Nicholson [1] and Nicholson and Lin [2] for invariant-based strain energy functions such as the Mooney-Rivlin model. In the current investigation, a corresponding expression is derived for stretch ratio-based strain energy functions such as the Ogden model. Compressible, incompressible and near-incompressible elastomers are addressed. The derived expressions are considerably more elaborate than their counterparts for invariant based models. As illustration,D is evaluated and presented for the torsion of a natural rubber shaft described by a three term Ogden model, using coefficients reported by Treloar.     

Paper‐derived stoneware ceramics: Improvement of properties by calendering and evaluation of pyroplastic deformation behaviour

Paper‐derived ceramics are a new approach to produce thin, lightweight ceramic structures. These ceramics are derived from preceramic papers produced in a paper technological process. The amount of inorganic filler (e. g. stoneware) in the paper is increased up to 85 wt‐%. By firing at high temperatures the cellulose fibres are pyrolized and the inorganic content is sintered. One part of the technological process to produce papers is calendering. A calender consists of two rolls, between which the paper is rolled under pressure. By calendering the paper thickness is reduced and the surface of the paper is improved. Different calender parameters (pressure and temperature) are applied to the preceramic paper and ceramic properties like strength, density and surface roughness are investigated. The strength of paper‐derived stoneware ceramics can be improved by 125% to over 185 MPa by optimizing the calender process. Additionally paper‐derived stoneware ceramics were fired at 1180°C, 1200°C and 1220°C for 1 and for 2 hours at different support distances (10–150 mm) in order to determine the dependence of pyroplastic deformation on support distance. The results show a linear increase between maximum deformation and support distance by 1 hour dwell and a polynomic at 2 hours dwell. Furthermore the Pyroplastic Index (PI) was evaluated according to recent literature. The Pyroplastic Index was correlated to the amorphous content of the differently fired samples. With longer dwell and/or higher temperature the content of amorphous phase increases which lowers the bulk viscosity and supports the pyroplastic deformation. These investigations should give a direction for using paper‐derived stoneware ceramics for special design applications. Paper‐derived ceramics can be systematically deformed in many possible ways to achieve specific shapes.     

Exact stiffness matrix of mono-symmetric composite I-beams with arbitrary lamination

The exact stiffness matrix, based on the simultaneous solution of the ordinary differential equations, for the static analysis of mono-symmetric arbitrarily laminated composite I-beams is presented herein. For this, a general thin-walled composite beam theory with arbitrary lamination including torsional warping is developed by introducing Vlasov’s assumption. The equilibrium equations and force–deformation relations are derived from energy principles. The explicit expressions for displacement parameters are then derived using the displacement state vector consisting of 14 displacement parameters, and the exact stiffness matrix is determined using the force–deformation relations. In addition, the analytical solutions for symmetrically laminated composite beams with various boundary conditions are derived as a special case. Finally, a finite element procedure based on Hermitian interpolation polynomial is developed. To demonstrate the validity and the accuracy of this study, the numerical solutions are presented and compared with the analytical solutions and the finite element results using the Hermitian beam elements and ABAQUS’s shell element.     

Thermal-stress reduction for a Czochralski grown single crystal

In this paper an optimal-control approach for thermal-stress reduction inside a Czochralski-grown single crystal is presented. Using the lateral heat flux as a control variable, an optimal-control formulation for minimizing thermal stress with a given crystal shape is derived. Since the thermal stress is also affected by the lateral shape of crystals during growth, the level of the stress can be reduced by growing crystals into a suitable shape. Using the lateral shape as a control variable, a similar optimal-control formulation for stress reduction is derived. In both cases, the von Mises stress is used as an objective function for the constrained optimization problem. Euler–Lagrange equations are derived using the calculus of variations and Lagrange multipliers. Various stress-reduction strategies are explored by solving the Euler–Lagrange equations numerically.     

Mathematical Treatment of the Distribution of HN3 in the Liquid-Gas System during Exraction Separation of Uranium and Plutonium

The rates of HN₃ desorption from aqueous and organic solutions (20% TBP in a hydrocarbon diluent) as dependent on the phase stirring intensity and temperature were subjected to mathematical processing. The equation derived for the desorption constant is similar to the mathematical expression of the Arrhenius law. The activation energy of HN₃ desorption from solutions was estimated at 36±3 and 50±10 kJ mol^-1 for aqueous and organic solutions, respectively. The HN₃ desorption rate constant (under experimental conditions) for organic solvents is 6plusmn2 times lower than for aqueous solutions. The empirical values of the pre-exponential factors in the formulas for determining the HN₃ desorption constants were estimated. The empirical expressions derived for the desorption constants provide a possibility of estimating the HN₃ carry-over during reductive stripping of plutonium. The formulas derived are suitable for other extraction processes involving hydrazine decomposition into HN₃.     

Variational principles for linear coupled dynamic theory of thermoviscoelasticity

Variational principles for linear coupled dynamic theory of thermoviscoelasticity are constructed using variational theory of potential operators. The functional derived herein gives, when varied, all the governing equations, including the boundary and initial conditions, as the Euler equations. The procedure shown herein does not require, in contrast to Gurtin's method, the transformation of field equations into an equivalent set of integro-differential equations, and includes the initial conditions of the problem explicitly. Gurtin's variational principle for dynamic theory of thermoviscoelasticity is also derived and compared with the present one. Variational principles for elastodynamics, visco-elasticity, etc. are derived as special cases of the variational principle derived herein.     

Distributions of sources and normal dipoles over a quadrilateral panel

Summary The potential due to a distribution of sources or normal dipoles on a flat quadrilateral panel is evaluated for the cases where the density of the singularities is constant, linear, bilinear, or of arbitrary polynomial form. The results in the first two cases are consistent with those derived previously, but the present derivation is considered to be simplified. In particular, the constant dipole distribution is derived from a geometric argument which avoids direct integration; this derivation applies more generally on a curvilinear panel bounded by straight edges.Also presented are multipole expansions for the same potentials, suitable for use when the distance to the field point is substantially larger than the panel dimensions. Algorithms are derived to evaluate the coefficients in these expansions to an arbitrary order.     

A static fatigue model for the durability of glass fibre reinforced cement

This paper presents a model for predicting service lives for glass-fibre reinforced cement (grc) components using hot-water accelerated ageing. It improves on previous models, being derived from consideration of a specific proposed micro-mechanical strength loss mechanism based on static fatigue principles and can be applied from time = 0. The model fitted well to all available strength vs. time data pertaining to various grc formulations. The activation energies thus derived for the strength loss process (80–90 kJ mol^–1) were consistent with those derived previously and those proposed for general glass dissolution mechanisms. Updated acceleration factors for predicting service lives for grc are advanced. The model was also applied to grc made with modified cement matrices. For metakaolin modified matrices, the activation energy appeared similar to that for OPC-grc, thus the use of similar acceleration factors appears justified. There is some evidence that calcium sulphoaluminate modified grc degrades according to a different activation energy. More data are required for modified matrix grcs if the model is to be applied thereto with confidence.     

An equation for the density of a substance in the surface layer of liquid under its own saturated vapor

An equation is derived for the density of a substance in the surface layer of a liquid under its own saturated vapor, an equation from which expressions can be found for the surface tension and for the thickness of the surface layer. On the basis of irreversible thermodynamic processes, an expression is then also derived for the specific force, per unit mass, acting in the interphase region.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 25, No. 4, pp. 742–745, October, 1973.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 25, No. 4, pp. 736–741, October, 1973.     

Spark plasma sintering of sol-gel derived 45S5 Bioglass®-ceramics: Mechanical properties and biocompatibility evaluation

This work aims to find an efficient sintering technique and optimal sintering conditions of a novel sol-gel derived Bioglass®-ceramic powder so as to achieve much improved mechanical properties compared to conventional Bioglass®. To this end, the spark plasma sintering (SPS) technique was for the first time used to densify the sol-gel derived Bioglass®-ceramic powder. It was found that the sol-gel derived Bioglass®-ceramics sintered with the SPS technique at 950 °C for 15 min had a high Young's modulus value of ~ 110 GPa, which was comparable to that of compact bone and significantly higher than the maximal value achieved by the conventional heat treatment. Moreover, the Bioglass®-ceramic compacts sintered with SPS released alkaline ions slowly and as a result, these highly densified Bioglass®-ceramics exhibited better cytocompatibility at the early stage of cell culture testing, compared to the conventional Bioglass®. Hence, the SPS technique is recommended to be used in the process of sol-gel derived Bioglass®-ceramics and its tissue engineering scaffolds.     

A direct derivation of the equations of motion for 3D-flexible mechanical systems

Equations of motion for rigid bodies with the body-fixed co-ordinate system placed at or away from the centre of mass are derived in a clear and direct way by making use of the two basic equations of mechanics (Newton's second law and the corresponding law of angular momentum). The dynamic equations for flexible mechanical systems are derived using the principle of virtual work, which introduces inertia in a straightforward manner, because this principle treats inertia as a force. The flexible formulation is exemplified by the use of circular beam elements and some basic matrices are derived in a direct way using skew-symmetric matrices. The capabilities of the formulation are demonstrated through examples. Results are compared with and verified by examples from the literature. Derivations throughout the paper are simplified by means of skew-symmetric matrices. © 1998 John Wiley & Sons, Ltd.     

The Crack Extension Force of a Curved Crack Derived from the Principle of Virtual Work

A general method to determine the crack extension force F related to a finite segment of a curved crack is presented. A path independent integral expression that holds in curvilinear coordinates is derived from the principle of virtual work. An appropriate virtual displacement field allows variation of the position of a crack tip. F is related to the path independent integral expression through variation of a total energy expression. To illustrate the applicability of the method F is derived for the conical crack in axisymmetric loading. For a plane crack with a straight front F is identical to the J-integral, Rice (1968).     

Absolute thermoelectric power and temperature coefficient of resistance of thin continuous metal films

General expressions are derived in terms of a function F(K), which is equal to the ratio of film to bulk conductivity, for the following: the ratio of film to bulk resistivity, the absolute thermoelectric power of the film material and the ratio of film to bulk temperature coefficient of resistance. The exact and approximate forms of the function F(K) for various theories of the scattering mechanism at the film surfaces are reported. Also plots of the derived expressions using some of these forms are given.     

Operation parameters of standing-wave diffraction modulators based on the piezoelectrically induced strain-optic effect

Abstract

Optical response and electrical characteristics of standing-wave diffraction modulators working via diffraction of light on a piezoelectrically induced standing-wave strain-optic grating are calculated. The resonance distributions of the strain and frequency dependences of the elements of a lumped-element equivalent circuit are analytically derived for perpendicularly excited vibrations of plate piezoelectric resonators. The modulation index-driving power relation determined by material parameters, modulator dimensions and operation conditions is derived. Numerical evaluation of the operation characteristics and parameters is performed for a representative LiNbO₃ standing-wave diffraction modulator, which was applied successfully to mode-lock Nd-doped glass lasers.     

Application of the maximum rate of dissipation criterion to dilatant, pressure dependent plasticity models

The purpose of this paper is to demonstrate the efficacy of the maximum rate of dissipation criterion to derive constitutive relations for dilatant pressure dependent elastoplastic materials (including certain soil and rock mechanics models as well as models for crushable foams).Hitherto, it has been assumed in the literature that such materials do not satisfy the maximum rate of dissipation criterion without additional constraints. This paper elucidates how the approach using the maximum rate of dissipation can be applied to derive the constitutive equations for rate independent plasticity for both associative and non-associative materials in a consistent manner by using the tools of convex analysis (especially gauge functions) and rate of dissipation functions that are not “normlike” (a notion that will be discussed in the paper). The results obtained in the paper show that a wide class of models for which the “plastic potential” is not the same as the yield function (i.e., the flow rule is “non-associative”) can be derived from this assumption in a relatively straightforward manner and without the need for any additional constraints. Specifically, both the yield function and the flow potential can be derived from the rate of dissipation function through the maximization process.As examples of the application of the general approach, the evolution equations for the Drucker-Prager and crushable foam models (where plastic volume change occurs and the plastic strain rate is not directed along the normal to the yield surface) are derived.     

Modelling of elastic continua using a grillage of structural elements based on discrete element concepts

A framework is described for modelling an elastic continuum using a grillage of beam‐like structural elements derived from discrete element concepts. The beam element properties are derived in detail and implemented in a structural analysis code for validation against classical two‐dimensional plane elasticity solutions. The framework offers the possibility of modelling the onset and propagation of fracture in materials that are initially continuous, without the need for specialized elements or remeshing in the context of traditional finite elements. Copyright © 2001 John Wiley & Sons, Ltd.     

Calculation of natural and forced vibrations of a piping system. Part 2. Dynamic stiffness of a pipe bend

The notion of the dynamic flexibility factor of a pipe bend to be used in problems on the calculation of harmonic vibrations of pipelines is formulated. Based on the Vlasov semi-momentless theory, simplifying hypotheses are introduced that make it possible to reduce the problem statement to the solution of the quartic differential equation. Using the results of the dynamic analysis for toroidal shells, the procedure for taking into account the increased flexibility of pipe bends under dynamic loading has been developed. The expression for the flexibility factor is derived as a function of both the geometrical parameters of the bend and the vibration frequency. The efficiency of the derived expression for the flexibility factor is illustrated by a great number of examples. __________ Translated from Problemy Prochnosti, No. 2, pp. 52–71, March–April, 2007.     

A three-dimensional micromechanics model for the damage of brittle materials based on the growth and unilateral effect of elliptic microcracks

Based on the analysis of a representative elliptic microcrack embedded in a RVE, the additional compliance tensor induced by an embedded opening/closed microcrack is derived, and that corresponding to the kinked growth of a closed elliptic microcrack is also derived by making use of its approximately equivalent simplification. The effect of the microcracks is analyzed with the Taylor’s scheme by introducing an appropriate probability density function. A three-dimensional micromechanics damage model is obtained for brittle materials, assuming numerous randomly distributed elliptic microcracks and taking into account their deformation, frictional sliding, growth and kinked growth.