The effect of variations in the creep exponent on the buckling of circular cylindrical shells

The senior author solved the problem of axially symmetrical creep buckling of thin circular cylindrical shells subjected to uniform axial compression. In that analysis the constitutive equation was a power law, and the exponent was taken to be equal to three. The purpose of this work was to extend the solution to a range of values of the creep exponent, n. To cope with the increasing algebraic complexity, a digital computer was employed in two ways: to generate the set of equations symbolically, and then to solve these equations. The computer programs were used to generate numerical solutions for the cases in which n was equal to 3, 5, 7 and 9. Two simple extrapolation techniques were then employed to obtain approximate solutions to the critical time problem for values of n up to 29.     

An Integral Method to Calculate Water Saturation in a Centrifuge Experiment to Determine Capillary Pressure

The centrifuge method is commonly used to determine the capillary pressure of a porous medium, and the original approximating method for data analysis developed by Hassler and Brunner is still being used. Its limitations are, however, not well understood. Application to analyze experiments where one of the assumptions was obviously violated had been given in the literature. While the result appeared to be quite reasonable, it was not clear how close was it to reality. One of the objectives of this paper is to review the assumptions that is required to develop this method, so that the experimental condition in which it is applicable can be established. The other objective is to derive a completely different solution technique to this problem. There is no need to assume that the ratio of the inlet radius to the exit radius of the core to the center of the centrifuge be close to 1. With the freedom from this limitation it is, therefore, possible to construct machines at lower cost and to improve on the data quality by allowing longer cores.     

Numerical solutions of Navier-Stokes equations with an integrated compartment method (ICM)

The most common numerical methods that are used by physical scientists to approximate partial differential equations employ finite differences and/or finite elements. In addition, compartment analyses have been adopted by ecological system analysts to simulate the evolution of processes governed by differential equations without spatial derivatives. An integrated compartment method (ICM) is proposed to combine the merits of these three numerical techniques. The basic procedures of the ICM are first to discretize the region of interest into compartments, then to apply three integral theorems of vectors to transform the volume integral to the surface integral, and finally to use interpolation to relate the interfacial values in terms of compartment values to close the system. These procedures are applied to the Navier-Stokes equations to yield the computational algorithm from which computer programs can be coded. The computer code is designed to solve one-, two-, or three-dimensional problems as desired. The program is applied to two simple cases: wake formation behind an obstacle in a channel and circulatory motion of a body of fluid in the square cavity. These preliminary applications have shown promising results.     

Monte Carlo Simulation and Well Testing Applied in Evaluating Reservoir Properties in a Deforming Longwall Overburden

During longwall mining, the intact strata start to deform and fracture as the mining face progresses. Gob gas ventholes (GGVs) are drilled from the surface over a longwall panel before mining to capture methane from the fractured zone. Due to fracturing and bedding-plane separations, reservoir properties change extensively. This poses a major problem for venthole designers and methane control engineers and may become a safety and health concern for underground work force due to unexpected methane emissions: it is difficult to predict the location of major strata separations and their temporal magnitudes to best locate the ventholes. Measurements obtained at different times during longwall mining may not be helpful for this purpose as strata deformation is a dynamic process and the results from different tests may not be lumped together to analyze the data collectively. This article uses a combination of Monte Carlo (MC) simulation and well testing methods to analyze multiple data sets obtained from a GGV at different longwall face locations. The aim was to determine the magnitude of average strata separation before conducting well test analyses to determine the properties of a deformed reservoir. MC simulation was used to process cross-correlated and uncertain data distributions obtained from measurements to generate a set of normally distributed values for each data type. These values were further used to project the amount of strata separation to the timing of well test. Finally, well-test analyses were used to interpret test data and to evaluate reservoir properties.     

Systematic description of imperfect bifurcation behavior of symmetric systems

A systematic method is presented for describing experimental curves of force vs strain of a system with regular polygonal (dihedral group) symmetry subject to bifurcation behavior, with an aim toward overcoming the following problems : (1) it is difficult to judge whether the system is undergoing bifurcation or not ; (2) the perfect behavior of the system cannot be known due to the presence of initial imperfections ; (3) those curves are often qualitatively different from bifurcation diagrams predicted by mathematics. The tools employed are : the asymptotic theory for imperfect bifurcation, such as the Koiter law, and the stochastic theory of initial imperfections. The former theory is extended in this paper to the system with regular-polygonal symmetry to present asymptotic laws for recovering perfect curves with reference to the experimental ones. These laws are formulated for physically observable displacements, instead of the variables in the mathematical bifurcation diagrams, in order to make them readily applicable to the experimental curves. The stochastic theory is combined with an asymptotic law to develop a means to identify the multiplicity of the bifurcation point. The systematic method for describing the experimental curves developed in this manner is applied to the bifurcation analysis of regular-polygonal truss domes to testify its validity. Furthermore, this method is applied to the shear behavior of cylindrical sand specimens to show that they, in fact, are undergoing bifurcation, and, in turn, to demonstrate the importance of a viewpoint of bifurcation in the study of shear behavior of materials. The need of a dual viewpoint of bifurcation and plasticity in the study of constitutive relationship of materials is emphasized to conclude the paper.     

THE ANALYTIC RESOLUTIONS AND APPLICATIONS OF THE NON－LINEAR SEEPAGE FLOW EQUATIONS OF COAL INFUSION

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Minimum thickness control at various levels for topology optimization using the wavelet method

Especially in microsystem design, maintaining the minimum thickness of each structural member at a certain scale is often as important as achieving the maximum system performance. Several successful methods to suppress one-point hinges or checkerboards in topology optimization have been developed, but an efficient method to control the minimum thickness at a desire scale remains to be developed. The objective of this investigation is to develop a wavelet-based minimum thickness controlling method applicable to topology optimization and to show the effectiveness of the proposed method in MEMS design. The idea behind the thickness controlling method is to extend the wavelet shrinkage method developed for one-point hinge control to any scale-level minimum thickness control. The major difficulties in implementing this idea are the development of an efficient algorithm to detect all undesirable patterns of different scales and the hierarchical application of the wavelet shrinkage method over multiple scales. Some techniques to overcome these difficulties are developed and applied to some MEMS design problems.     

A Theoretical Model for the Simulation of Microdamage Accumulation and Repair in Compact Bone*

This paper describes a new theoretical approach to bone microdamage, in which a population of cracks is explicitly modelled. A given sample of bone is assumed to contain a certain number of cracks, whose growth characteristics are described with an equation containing stochastic variables to create statistical differences from one crack to another. This type of model allows us to predict a wide variety of data. The present paper illustrates the different types of prediction which can be made, including: (i) standard damage parameters such as the number and length of cracks and the reduction in stiffness; (ii) fatigue test data such as the number of cycles to failure as a function of stress level, including scatter; (iii) effects due to the living system, including repair, remodelling and adaptation. A useful feature of the model is our ability to examine the statistics of the crack population in detail to find, for example, the number of cracks which are potentially dangerous as opposed to those which are dormant, and to investigate the reasons for increased crack numbers in the bones of older people. The potential also exists to use the model to investigate different theories of bone remodelling and adaptation.     

感应同步器测角系统误差分析及补偿

本文讨论了提高感应同步器精度的硬件方法和软件方法。硬件方法即根据误差来源，针对不同谐波成分误差，用电路调节的方法消除误差。软件方法就是采用计算机通过误差曲线拟合来减小误差。     

METHOD OF THE LINEAR ELASTIC BAR CALCAULATION UNDER SMALL DEFORMATION CONDITIONS

先用几何图解法对一简单线弹性杆系变形作分析计算,发现功能原理更可行有效. 方法是假设用一个和载荷P 相垂直的力H（虚拟力）先作用于杆系,根据功能原理导出在载荷P 作用下的位移计算公式. 并把这一方法推广到多个杆件组成的弹性杆系（桁架）中,并建立相应计算公式. 可望实现计算机编程,大大简化这一类问题的工程计算.     

A Mathematical Analogy and a Unified Asymptotic Formulation for Singular Elastic and Electromagnetic Fields at Multimaterial Wedges

In the present contribution, the mathematical analogy existing between the singular stress field in elasticity due to antiplane loading and the singular electromagnetic fields in electromagnetism is derived with reference to the problem of isotropic multimaterial wedges. These configurations, where dissimilar sectors converge to the same vertex, are commonly observed in composite materials and may lead to singularities. The proposed analogy permits to extend several elastic solutions for the power of the stress-singularity already available in the elasticity literature to the analogous electromagnetic problems and viceversa. Finally, electromagnetic structures that cannot be treated according to the proposed analogy, such as those related to bi-isotropic multimaterial wedges, are discussed.     

Tyre load capacity and energy loss with respect to varying soil support stiffness

An analytical model is developed to predict the tyre deformation and the resultant energy loss due to tyre flexibility relative to various soil stiffnesses ranging from rigid unyielding support to soft soil. The analysis allows for examination of a pneumatic tyre with respect to the wheel load to be carried, the supporting ground rigidity and the rigidity of the tyre casing. The important tyre characteristics in providing for wheel load capability under motion are demonstrated to be the tyre carcass construction, dimension, inflation pressure and the ability of the tyre casing to recover some of the resultant energy losses incurred by the tyre under motion.     

Interaction of a diaphragm pressure gage with a viscoelastic halfspace

The results of an analysis to determine the interaction between a diaphragm pressure transducer and a solid propellant grain are presented. The solutions to a clamped circular plate and a halfspace are superposed to yield the desired solution. The boundary conditions on the halfspace are shown to be such that the solution to an internally pressurized Sneddon “penny-shaped” crack is applicable for an incompressible material. The problem is first solved elastically, in terms of a material-stiffness parameter which relates the diaphragm stiffness to the propellant stiffness. The solution is then extended to viscoelastic behavior through parameterization of the stiffness parameter. The electrical output of the diaphragm gage is determined and compared with the output from hydrostatic calibration, in order to determine the error or loss in gage sensitivity based on hydrostatic calibration, due to the interaction between the gage and the propellant.     

Tailoring of pinched hysteresis for nonlinear vibration absorption via asymptotic analysis

The method of multiple scales is adopted to investigate the dynamic response of a nonlinear Vibration Absorber (VA) whose constitutive behavior is governed by hysteresis with pinching. The asymptotic analysis is first devoted to study the response of the absorber to harmonic excitations and to evaluate its sensitivity to the main constitutive parameters. The frequency response obtained in closed form allows to carry out the stability analysis together with a parametric study leading to behavior charts characterizing multi-valued softening/hardening responses or single-valued, quasi-linear responses. A two-degree-of-freedom model of a primary nonlinear structure endowed with the hysteretic vibration absorber is investigated to explore transfers of energy from the structure to the absorber resulting into optimal vibration amplitude reduction. The asymptotic solution is proved to be in good agreement with the numerical solution obtained via continuation. The asymptotic approach is embedded into a differential evolutionary algorithm to obtain a multi-parameter optimization procedure by which the optimal hysteresis parameters are found.     

Linearized harmonic balance based derivation of slow flow for some class of autonomous single degree of freedom oscillators

In this paper we exploit the embedding of linearization in the harmonic balance method developed by Wu and its collaborators to propose an approach for deriving the slow flow for some class of damped autonomous single degree of freedom oscillators. The linearized harmonic balance method is used to compute the coefficients of the harmonics of an assumed form of the solution and to derive a system of two coupled ordinary differential equations related to the slow flow. A power series procedure is next used to decouple the coupled system and to obtain the slow flow. Two examples provided to illustrate the proposed procedure show excellent results.     

Aeroelastic response of an airfoil to gusts: Prediction and control strategies from computed energy maps

A method to predict the aeroelastic pitch response of an airfoil to gusts is presented. The prediction is based on energy maps generated by high-fidelity fluid dynamic simulations of the airfoil with prescribed pitch oscillations. The energy maps quantify the exchange of energy between the pitching airfoil and the flow, and serve as manifolds over which the dynamical states of aeroelastic airfoil system grow, decay and attain stationary states. This method allows us to study the full nonlinear response of the system to large gusts, and predict the growth and saturation of aeroelastic pitch instabilities. We also show that the manifold topology in these maps can be used to make informed modifications to the system parameters in order to control the response to gusts.     

Linking discrete particle simulation to continuum process modelling for granular matter: Theory and application

Two approaches are widely used to describe particle systems: the continuum approach at macroscopic scale and the discrete approach at particle scale. Each has its own advantages and disadvantages in the modelling of particle systems. It is of paramount significance to develop a theory to overcome the disadvantages of the two approaches. Averaging method to link the discrete to continuum approach is a potential technique to develop such a theory. This paper introduces an averaging method, including the theory and its application to the particle flow in a hopper and the particle-fluid flow in an ironmaking blast furnace.     

Hybrid method for determining the fraction of plastic work converted to heat

The fraction of plastic work converted to heat is typically measured either by nearly isothermal experiments, in which the thermal energy is measured during a deformation experiment with a calorimeter, or by adiabatic experiments, in which the thermal energy is determined from the temperature rise, measured either during the test or immediately after the test by dropping the sample into a calorimeter. In the present work, the temperature is measured with a single fine-wire thermocouple. The restriction to adiabatic loadings is relaxed by using a hybrid method that combines the measurements with finite difference simulations to calculate the heat losses that occur during the test. These heat losses are then accounted for in the final energy balance to determine the fraction of plastic work converted to heat. The method is applied to annealed 302 stainless steel. The results show that the fraction of plastic work converted to heat is a decreasing function ranging from 0.7 to 0.4 over a tensile strain range of 0 to 0.15. An analysis of the restrictions to this method and of the potential errors is given.     

Radiation Preheating can Trigger Transition from Deflagration to Detonation

In this article the possibility of radiation heat transfer to trigger transition to detonation is studied. It is assumed that the premixed deflagration front is able to emit and the unburnt mixture to absorb radiation heat effectively. Under this assumption the ability of the flame to significantly preheat the unburnt mixture and to form a promoting temperature gradient is investigated. First, we estimate the temperature rise due to the radiation preheating of the unburnt mixture, when it is traveling through deep flame wrinkles. Subsequently, we carry out numerical simulations of premixed gaseous combustion in a tube. The simulations confirm the possibility of formation of promoting temperature gradients within flame folds and initiation of the detonation waves. They demonstrate the plausibility of the proposed mechanism of the deflagration to detonation transition.