Finding minimum energy configurations for constrained beam buckling problems using the Viterbi algorithm

In this work, we present a novel technique to find approximate minimum energy configurations for thin elastic bodies using an instance of dynamic programming called the Viterbi algorithm. This method can be used to find approximate solutions for large deformation constrained buckling problems as well as problems where the strain energy function is non-convex. The approach does not require any gradient computations and could be considered a direct search method. The key idea is to consider a discretized version of the set of all possible configurations and use a computationally efficient search technique to find the minimum energy configuration. We illustrate the application of this method to a laterally constrained beam buckling problem where the presence of unilateral constraints together with the non-convexity of the energy function poses challenges for conventional schemes. The method can also be used as a means for generating “very good” starting points for other conventional gradient search algorithms. These uses, along with comparisons with a direct application of a gradient search and simulated annealing, are demonstrated in this work.     

Traction problem in electro-elasticity and bifurcation theory

This paper is the first of a series of two. It will deal with the problem of static traction problem with minor deformations for a material which is governed by the electrostriction phenomenon. Two approaches to this problem will be described. We can consider either the equilibrium equations which are naturally non-linear, or the equations after linearization. The linearization of equations must be done near a natural state. Locally, under some conditions, we can establish the existence and the uniqueness of the solutions. We use the local theorem of implicit functions. The problem can be approached more globally. If we consider the non-linear equations, we can use a natural principle of these equations: the independence of the choice of the observer, also known as objectivity property. This property makes it possible for us to take into account an action of the rotations group of the Euclidean space, and consequently to take into account all the trivial solutions. It is then possible to prove within the space of all configurations the existence of the non-linear equations solutions and to find their number.This work presents a thorough and detailed approach to a non-linear theory, the geometric arguments of which make it possible for us to prove the existence of all the solutions and to study their stability in the aggregate; this last aspect will be developed in the second paper. Not only can this theory anticipate the eventual existence of a stable solution, it can also anticipate that an unstable solution in terms of the elasticity can, thanks to the effect of an electric field, become stable in terms of the electro-elasticity.     

A New Technique to Determine Horizontal and Vertical Permeabilities from the Time-Delayed Response of a Vertical Interference Test

To determine the permeabilities from a vertical interference test, earlier investigators proposed correlations or type curves based on point source solutions or partially penetrated well solutions. However, it is impossible for these correlations or type curves to cover all possible scenarios in the real world. In more recent years, people use regression analysis to simultaneously match the pressure responses at the source interval and the observation point. With regression analysis, we face the problem of non-unique solutions. Sometimes, estimated permeability could be outside a reasonable range when analyzing noisy data from real tests. In this paper, a new technique is presented to estimate horizontal and vertical permeabilities from the time-delayed response in a wireline vertical interference test. In a vertical test, a pressure drawdown test period is followed by a pressure buildup test period. Because of the delay in response, the pressure at the observation probe continues to drop for some time while the pressure at the source interval is being built up. The maximum pressure drop at the observation probe with regard to the maximum pressure drop in the source interval is time-delayed. Using this time delay and the maximum pressure drop at the observation probe, vertical and horizontal permeabilities can be estimated. A novel numerical scheme is used. The new technique is compared with the previous methods, and it shows its superiority in accuracy. In addition, it can be used in different test configurations. Application issues in real testing conditions are discussed. Finally, two field tests are analyzed using this technique, while an earlier effort to analyze the tests using a conventional method was not successful due to poor data quality.     

Numerical solutions of time-fractional partial integrodifferential equations of Robin functions types in Hilbert space with error bounds and error estimates

This paper introduces an efficient numerical algorithm for solving a significant class of linear and nonlinear time-fractional partial differential equation governed by Fredholm–Volterra operator in the sense of Robin conditions. A direct approach based on the normalized orthonormal function systems that fitted from the Gram–Schmidt orthogonalization process is utilized to transcribe the problem under study into appropriate Hilbert space. Some functional analysis theories such as upper error bound and convergence behavior under some assumptions which give the hypothetical premise of the proposed calculation are likewise talked about. Mathematical properties of the numerical results obtained are analyzed as well as general features of many numerical solutions have been identified. At long last, the used outcomes demonstrate that the present calculation and mimicked toughening give a decent planning procedure to such models.     

高斯牛顿技术求解偶应力反问题

建立了便于敏度分析的偶应力反问题数值求解模型,给出了直接法和伴随法两种敏度计算格式.在反演计算中采用了高斯牛顿技术对未知本构参数进行识别,探讨了测点数目、初值选取和数据噪音对反演结果的影响,数值算例给出了令人满意的结果.     

On the coupled vibration of an ideal fluid with a linear elastic structure

The purpose of this paper is to analyse theoretically and numerieally the coupled vibration of an ideal fiuid with a linear elastie structure.It is proved in the paper that the natural frequencies of the coupled vibration do exist and are all real positive. The paper presents an efficient method to transform a coupled fluid-structure system to the structure with added mass and the ribrational analysis of the former is replaced by the latter in vacuum only. Numerical solution is outlined for the transformed problem and a compact frequecy equation is derived in which fluid variables do not appear. This simplifies the analysis significanily. A convergent proof has been given to guarantee the reliability of the solution. The paper also offers a general algorithm combined with Ritz method, boundary element method, and finite element method to analyse the transformed problem. Based on this algorithm, one can apply a known structural analysing program, with a little modification, to solve many different kinds     

Classification of the Spatial Equilibria of the Clamped Elastica: Symmetries and Zoology of Solutions

We investigate the configurations of twisted elastic rods under applied end loads and clamped boundary conditions. We classify all the possible equilibrium states of inextensible, unshearable, isotropic, uniform and naturally straight and prismatic rods. We show that all solutions of the clamped boundary value problem exhibit a π-flip symmetry. The Kirchhoff equations which describe the equilibria of these rods are integrated in a formal way which enable us to describe the boundary conditions in terms of 2 closed form equations involving 4 free parameters. We show that the flip symmetry property is equivalent to a reversibility property of the solutions of the Kirchhoff differential equations. We sort these solutions according to their period in the phase plane. We show how planar untwisted configurations as well as circularly closed configurations play an important role in the classification. This revised version was published online in June 2006 with corrections to the Cover Date.     

Viscoelastic flow between eccentric rotating cylinders: unstructured control volume method

This paper reports a convergent numerical algorithm for the Upper-Convected Maxwell (UCM) fluid between two eccentric cylinders at various eccentricity ratios (?); the outer cylinder is stationary, and the inner one rotating. The problem is solved by an unstructured control volume method (UCV), which is designed for a general viscoelastic flow problem with an arbitrary computational domain. A self-consistent false diffusion technique and an iteration scheme are used in combination to solve the problem. The computations of the UCM fluid using the numerical algorithm are carried out to a higher value of the Deborah number (De) at each eccentricity tested than hitherto possible with previous numerical simulations. The solutions are compared with previous numerical results, confirming the effectiveness of the UCV method as a general technique for solving viscoelastic flow problems.     

Large‐scale eigenvalue calculations for stability analysis of steady flows on massively parallel computers

This paper presents an approach for determining the linear stability of steady states of partial differential equations (PDEs) on massively parallel computers. Linearizing the transient behavior around a steady state solution leads to an eigenvalue problem. The eigenvalues with the largest real part are calculated using Arnoldi's iteration driven by a novel implementation of the Cayley transformation. The Cayley transformation requires the solution of a linear system at each Arnoldi iteration. This is done iteratively so that the algorithm scales with problem size. A representative model problem of three‐dimensional incompressible flow and heat transfer in a rotating disk reactor is used to analyze the effect of algorithmic parameters on the performance of the eigenvalue algorithm. Successful calculations of leading eigenvalues for matrix systems of order up to 4 million were performed, identifying the critical Grashof number for a Hopf bifurcation. Copyright © 2001 John Wiley & Sons, Ltd.     

跨声速弹性波场中的单侧界面问题

在具有单侧界面约束的双半平面中弹性波的传播与4个p参数有关,当它们不全为实数时,波场中同时存在体波与面波,这时的波场称为跨声速波场。Comninou和Dundurs曾用双侧解修正法把问题归结为奇异积分方程,本文则用函数方程法讨论了这个问题,给出了界面间隙分布与压力分布的显示解析解,并通过数值计算实例展示出波场的一些特征。     

The Sub-Harmonic Bifurcation of Stokes Waves

Steady periodic water waves on the free surface of an infinitely deep irrotational flow under gravity without surface tension (Stokes waves) can be described in terms of solutions of a quasi-linear equation which involves the Hilbert transform and which is the Euler-Lagrange equation of a simple functional. The unknowns are a 2π-periodic function w which gives the wave profile and the Froude number, a dimensionless parameter reflecting the wavelength when the wave speed is fixed (and vice versa). Although this equation is exact, it is quadratic (with no higher order terms) and the global structure of its solution set can be studied using elements of the theory of real analytic varieties and variational techniques. In this paper it is shown that there bifurcates from the first eigenvalue of the linearised problem a uniquely defined arc-wise connected set of solutions with prescribed minimal period which, although it is not necessarily maximal as a connected set of solutions and may possibly self-intersect, has a local real analytic parametrisation and contains a wave of greatest height in its closure (suitably defined). Moreover it contains infinitely many points which are either turning points or points where solutions with the prescribed minimal period bifurcate. (The numerical evidence is that only the former occurs, and this remains an open question.) It is also shown that there are infinitely many values of the Froude number at which Stokes waves, having a minimal wavelength that is an arbitrarily large integer multiple of the basic wavelength, bifurcate from the primary branch. These are the sub-harmonic bifurcations in the paper's title. (In 1925 Levi-Civita speculated that the minimal wavelength of a Stokes wave propagating with speed c did not exceed 2πc ²/g. This is disproved by our result on sub-harmonic bifurcation, since it shows that there are Stokes waves with bounded propagation speeds but arbitrarily large minimal wavelengths.) Although the work of Benjamin & Feir} and others [9, 10] has shown Stokes waves on deep water to be unstable, they retain a central place in theoretical hydrodynamics. The mathematical tools used to study them here are real analytic-function theory, spectral theory of periodic linear pseudo-differential operators and Morse theory, all combined with the deep influence of a paper by Plotnikov [36]. Accepted: December 6, 1999     

Projective synchronization of a class of chaotic systems by dynamic feedback control method

This paper investigates the projective synchronization problem of a class of chaotic systems in arbitrary dimensions. Firstly, a necessary and sufficient condition for the existence of the projective synchronization problem is presented. And this condition is equivalent to check whether a group of algebraic equations about \(\alpha \) have solutions or not. Secondly, an algorithm is proposed to obtain all the solutions of the projective synchronization problem. Thirdly, a simple and physically implementable controller is designed to ensure the realization of the projective synchronization. Finally, three numerical examples are provided to verify the effectiveness and the validity of the proposed results.     

Multiple three-dimensional equilibrium solutions for cantilever beams loaded by dead tip and uniform distributed loads

The development of multiple solutions for orthotropic cantilever beams in a fully three-dimensional setting is investigated. The governing equations are solved using an iterative shooting procedure that converts the original boundary value problem into a sequence of initial value problems that converge to the desired solution. This method is well suited to finding multiple equilibrium solutions. Several classes of equilibrium configurations are described and illustrated including planar shapes, buckled planar shapes and fully three-dimensional configurations which appear far removed from the initial plane of loading. The solutions for the planar shapes and the buckled configurations compare favourably to previously published results. The development of the far-removed shapes is shown to be qualitatively similar to that of the planar shapes. The behaviour is shown to be highly dependant upon the aspect ratio of the cross-section. For certain aspect ratios it is shown, somewhat surprisingly, that out-of-plane equilibrium solutions can exist at loads below those required for multiple planar solutions.     

A nonlinear programming approach to kinematic shakedown analysis of frictional materials

This paper develops a novel nonlinear numerical method to perform shakedown analysis of structures subjected to variable loads by means of nonlinear programming techniques and the displacement-based finite element method. The analysis is based on a general yield function which can take the form of most soil yield criteria (e.g. the Mohr–Coulomb or Drucker–Prager criterion). Using an associated flow rule, a general yield criterion can be directly introduced into the kinematic theorem of shakedown analysis without linearization. The plastic dissipation power can then be expressed in terms of the kinematically admissible velocity and a nonlinear formulation is obtained. By means of nonlinear mathematical programming techniques and the finite element method, a numerical model for kinematic shakedown analysis is developed as a nonlinear mathematical programming problem subject to only a small number of equality constraints. The objective function corresponds to the plastic dissipation power which is to be minimized and an upper bound to the shakedown load can be calculated. An effective, direct iterative algorithm is then proposed to solve the resulting nonlinear programming problem. The calculation is based on the kinematically admissible velocity with one-step calculation of the elastic stress field. Only a small number of equality constraints are introduced and the computational effort is very modest. The effectiveness and efficiency of the proposed numerical method have been validated by several numerical examples.     

Limitations of temperature measurements with holographic interferometry in the presence of pressure variations

In recent years oscillatory flows have shown to be a promising strategy to enhance heat transfer. However, the mechanisms underlying oscillatory heat transfer enhancement are not yet completely understood. One problem, when investigating heat transfer in oscillatory flows experimentally, is to resolve the temperature distribution as a function of time. This is one reason that most studies reported in the literature so far were restricted to frequencies of a few hertz. As shown in this paper, an appropriate tool to investigate oscillatory heat transfer phenomena at higher frequencies (1000 Hz) is real time holographic interferometry (HI) combined with high-speed cinematography. In the present paper HI was applied to study acoustically driven flow. To apply HI to such a physical situation it was necessary to expand its applicability to cases where changes in the refractive index are caused not only by temperature changes but also by pressure variations. For this purpose a new evaluation formula that accounts for pressure variations was derived. On the example of the acoustic field, we discuss the impact of the pressure variations on temperature measurements. Additionally, an image processing algorithm was developed that allows the measurement of time dependent temperature distributions. The uncertainties of the temperature measurements introduced by the image processing algorithm were found to be in the range of thermocouple measurements.     

On the existence of three solutions for a supercritical steady flow of a heavy fluid over obstructions

The paper is devoted to the solution of the steady problem of ideal incompressible fluid flow over a semi-circular cylinder located at the bottom. Calculations showed that the problem has at least three solutions for the Froude number. In the absence of an obstruction at the bottom, the proposed algorithm allows one to construct solitary waves up to limiting waves. The paper reports the most important wave characteristics: circulation, mass, and potential and kinetic energy. Analysis of the calculation results leads to the conclusion that all maximum values of the solitary-wave characteristics are attained before the maximum amplitude and the maximum of the mass does not coincide with the maxima of the total energy and the Froude number. Kemerovo State University, Kemerovo 650043. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 27–35, January–February, 1999.     

Combined Immersed Boundary/Large-Eddy-Simulations of Incompressible Three Dimensional Complex Flows

In this paper we show how the Immersed Boundary (IB) method can be used with the Large-Eddy-Simulation (LES) to compute moderately high Reynolds number flows in complex geometric configurations. The resulting combination gives an easy-to-use, inexpensive and accurate technique which can be an important step towards the application of computational fluid dynamics (CFD) to industrially relevant problems. This paper aims at describing the main features of the method, some of the important drawbacks and possible solutions. Several representative examples are discussed in order to show the flexibility and the range of the applicability of this technique.     

Low-thrust trajectory optimization for multiple target bodies tour mission

Spacecraft science missions to planets or asteroids have historically visited only one or several celestial bodies per mission. The research goal of this paper is to create a trajectory design algorithm that generates trajectory allowing a spacecraft to visit a significant number of asteroids during a single mission. For the problem of global trajectory optimization, even with recent advances in low-thrust trajectory optimization, a full enumeration of this problem is not possible. This work presents an algorithm to traverse the searching space in a practical fashion and generate solutions. The flight sequence is determined in ballistic scenario, and a differential evolution method is used with constructing a three-impulse transfer problem, then the local optimization is implemented with low-thrust propulsion on the basis of the solutions of impulsive trajectories. The proposed method enables trajectory design for multiple asteroids tour by using available low thrust propulsion technology within fuel and time duration constraints.     

A New Method for an Inhomogeneity with Stepwise Graded Interphase under Thermomechanical Loadings

The solution for a circular inhomogeneity embedded in an infinite elastic matrix with a multilayered interphase plays a fundamental role in many practical and theoretical problems. Therefore, improved analysis methods for this problem are of great interest. In this paper, a new procedure is presented to obtain the exact stress fields within the inhomogeneity and the matrix under thermomechanical loadings, without the need of solving the full multiphase composite problem. With this short-cut method, the problem is reduced to a single linear algebraic equation and two coupled linear algebraic equations which determine the only three real coefficients of the stress field within the inhomogeneity. In particular, the average stresses within the inhomogeneity can be calculated directly from the three real coefficients. Further, the other three unknown real coefficients associated with the stress field in the matrix can be determined subsequently. Hence, the influence of the stepwise graded interphase on the stress fields is manifested by its effect on the six real coefficients. All these results hold for stepwise graded interphase composed of any number of interphase layers. Several examples serve to illustrate the method and its advantages over other existing approaches. The explicit solutions are used to study the design of harmonic elastic inclusions, and the effect of a compliant interphase layer on thermal-mismatch induced residual stresses. This revised version was published online in August 2006 with corrections to the Cover Date.