Finite deflection analysis of elastic plate by the boundary element method

An integral equation formulation for finite deflection analysis of thin elastic plates is presented, based on general nonlinear differential equations which are equivalent to the von Kármán equations and by virtue of generalized Green identities. Boundary element discretization is applied and a relaxation iterative approach is employed to solve the nonlinear plate bending problems. A number of numerical examples are given; the results of computation are compared with the analytical solutions and good agreement is observed. It appears that the approach developed in this paper is effective.     

Using finite difference and differential transformation method to analyze of large deflections of orthotropic rectangular plate problem

This paper analyses the large deflections of an orthotropic rectangular clamped and simply supported thin plate. A hybrid method which combines the finite difference method and the differential transformation method is employed to reduce the partial differential equations describing the large deflections of the orthotropic plate to a set of algebraic equations. The simulation results indicate that significant errors are present in the numerical results obtained for the deflections of the orthotropic plate in the transient state when a step force is applied. The magnitude of the numerical error is found to reduce, and the deflection of the orthotropic plate to converge, as the number of sub-domains considered in the solution procedure increases. The deflection of the simply supported orthotropic plate is great than the clamped orthotropic plate. The current modeling results confirm the applicability of the proposed hybrid method to the solution of the large deflections of a rectangular orthotropic plate.     

Modelling and experimental validation of the deflection of a leveller for hot heavy plates

In order to successfully automate levelling processes, in particular for heavy plates, the deflection of the leveller has to be compensated based on a deflection model. In this work, a detailed mathematical deflection model of a hot leveller with bending mechanism and its experimental validation are presented. The roll intermesh profiles are calculated based on the deflection of the work rolls that are elastically supported by support rolls, frames, posts and adjustment screws. The deflection model is suited to compensate the effect of deflection on the roll intermesh and the plate flatness as well as to assess the loads of critical parts, for example the support rolls. A new experimental design to measure the deflection of a leveller is presented and successfully applied for model validation. The work roll deflection is measured directly by means of displacement sensors that are inserted in cut-outs of test plates. These test plates are modelled as linear elastic stripes. For normal load levels, the relative accuracy (repeatability) of the roll intermesh prediction of the model is better than 0.08 mm.     

On large Eddy simulation and variational multiscale methods in the numerical simulation of turbulent incompressible flows

Numerical simulation of turbulent flows is one of the great challenges in Computational Fluid Dynamics (CFD). In general, Direct Numerical Simulation (DNS) is not feasible due to limited computer resources (performance and memory), and the use of a turbulence model becomes necessary. The paper will discuss several aspects of two approaches of turbulent modeling—Large Eddy Simulation (LES) and Variational Multiscale (VMS) models. Topics which will be addressed are the detailed derivation of these models, the analysis of commutation errors in LES models as well as other results from mathematical analysis.     

Large amplitudes free vibrations and post-buckling analysis of unsymmetrically laminated composite beams on nonlinear elastic foundation

The purpose of this paper is to present efficient and accurate analytical expressions for large amplitude free vibration and post-buckling analysis of unsymmetrically laminated composite beams on elastic foundation. Geometric nonlinearity is considered using Von Karman’s strain–displacement relations. Besides, the elastic foundation has cubic nonlinearity with shearing layer. The nonlinear governing equation is solved by employing the variational iteration method (VIM). This study shows that the third-order approximation of the VIM leads to highly accurate solutions which are valid for a wide range of vibration amplitudes. The effects of different parameters on the ratio of nonlinear to linear natural frequency of beams and the post-buckling load–deflection relation are studied.     

On the topological pressure of random bundle transformations in sub-additive case

In this paper, we define the topological pressure for sub-additive potential via separated sets in random dynamical systems and give a proof of the relativized variational principle for the topological pressure.     

Computational implementation of stress integration in FE analysis of elasto-plastic large deformation problems

In this paper, we compare different numerical implementation algorithms for the rate type constitutive equation and present an integration scheme based on the physical meaning of the stress. Numerical implementation of various schemes is investigated in conjunction with the return mapping algorithm and the conditions to maintain plastic consistency. Jaumann and Truesdell rates are taken as the objective stress rates in the constitutive equation. An alternative numerical treatment for rate of deformation tensor D_ij is presented and is shown to maintain incremental objectivity. Numerical examples included a single element under rigid body rotation, a necking bifurcation of a bar in tension and a punch indentation process. It is shown that the use of Truesdell stress rate with specific numerical integration procedure gives more accurate results than other procedures presented.     

Application of homogenization and large deviations to a parabolic semilinear equation

We study the behavior of the solution of a partial differential equation with a linear parabolic operator with non-constant coefficients varying over length scale δ and nonlinear reaction term of scale 1/?. The behavior is required as ? tends to 0 with δ small compared to ?. We use the theory of backward stochastic differential equations corresponding to the parabolic equation. Since δ decreases faster than ?, we may apply the large deviations principle with homogenized coefficients.     

Modeling of an insurance system and its large deviations analysis

We model an insurance system consisting of one insurance company and one reinsurance company as a stochastic process in R². The claim sizes {X_i} are an iid sequence with light tails. The interarrival times {τ_i} between claims are also iid and exponentially distributed. There is a fixed premium rate c₁ that the customers pay; c<c₁ of this rate goes to the reinsurance company. If a claim size is greater than R the reinsurance company pays for the claim. We study the bankruptcy of this system before it is able to handle N number of claims. It is assumed that each company has initial reserves that grow linearly in N and that the reinsurance company has a larger reserve than the insurance company. If c and c₁ are chosen appropriately, the probability of bankruptcy decays exponentially in N. We use large deviations (LD) analysis to compute the exponential decay rate and approximate the bankruptcy probability. We find that the LD analysis of the system decouples: the LD decay rate γ of the system is the minimum of the LD decay rates of the companies when they are considered independently and separately. An analytical and numerical study of γ as a function of (c,R) is carried out.     

A lattice model for the fermionic projector in a static and isotropic spacetime

We introduce a lattice model for a static and isotropic system of relativistic fermions. An action principle is formulated, which describes a particle‐particle interaction of all fermions. The model is designed specifically for a numerical analysis of the nonlinear interaction, which is expected to lead to the formation of a Dirac sea structure. We discuss basic properties of the system. It is proved that the minimum of the variational principle is attained. First numerical results reveal an effect of spontaneous symmetry breaking. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Well posedness,large deviations and ergodicity of the stochastic 2D Oldroyd model of order one

In this work, we establish the unique global solvability of the stochastic two dimensional viscoelastic fluid flow equations, arising from the Oldroyd model for the non-Newtonian fluid flows perturbed by multiplicative Gaussian noise. A local monotonicity property of the linear and nonlinear operators and a stochastic generalization of the Minty–Browder technique are exploited in the proofs. The Laplace principle for the strong solution of the stochastic system is established in a suitable Polish space using a weak convergence approach. The Wentzell–Freidlin large deviation principle is proved using the well known results of Varadhan and Bryc. The large deviations for shot time are also considered. We also establish the existence of a unique ergodic and strongly mixing invariant measure for the stochastic system with additive Gaussian noise, using the exponential stability of strong solutions.     

Calculus of sequential normal compactness in variational analysis

In this paper we study some properties of sets, set-valued mappings, and extended-real-valued functions unified under the name of “sequential normal compactness.” These properties automatically hold in finite-dimensional spaces, while they play a major role in infinite-dimensional variational analysis. In particular, they are essential for calculus rules involving generalized differential constructions, for stability and metric regularity results and their broad applications, for necessary optimality conditions in constrained optimization and optimal control, etc. This paper contains principal results ensuring the preservation of sequential normal compactness properties under various operations over sets, set-valued mappings, and functions.     

Numerical analysis and modeling of large deformation and necking behavior of tensile specimens

The present paper is concerned with numerical simulations of large deformation and necking behavior of axisymmetric tensile specimens. In particular, an efficient framework for the numerical analysis of finite deformation behavior of elastic-rate-independent plastic problems is summarized which is based on a plastic predictor method. Furthermore, numerical modeling of conventional tensile tests as well as their finite deformation and localization phenomena are discussed in some detail, and the results will be compared to those obtained by simplified numerical simulations.     

Theorems of large deviations in the multivariate invariance principle

Let B be a real separable Banach space with norm |ß|_B, X, X₁, X₂, … be a sequence of centered independent identically distributed random variables taking values in B. Let s_n = s_n(t), 0 ≤ t ≤ 1 be the random broken line such that s_n(0) = 0, s_n(k/n) = n^−1/2 Σ_i=1^k X_i for n = 1, 2, … and k = 1, …, n. Denote |s_n|_B = sup_{0 ≤ t ≤ 1} |s_n(t)|_B and assume that w(t), 0 ≤ t ≤ 1 is the Wiener process such that covariances of w(1) and X are equal. We show that under appropriate conditions P(|s_n|_B > r) = P(|w|_B > r)(1 + o(1)) and give estimates of the remainder term. The results are new already in the case of B having finite dimension.     

基于简化的应变梯度理论下Kirchhoff板模型边值问题的提法及其应用北大核心CSCD

考虑应变梯度和速度梯度的影响,建立薄板控制微分方程及给出其边值问题的提法,修正了前人给出的薄板角点条件.采用Levy法,给出受分布力作用下简支板的挠度及自由振动频率的解析解.通过与文献中分子动力学数据对比,验证了该文模型的有效性并提出校核材料参数的一种方法.研究结果表明,增大弹性地基和应变梯度参数可以有效提高板的等效刚度,而速度梯度参数则相反.该文提出的板的边值问题为研究薄板在复杂支撑边界及外荷载等条件提供了理论依据.同时,有望为其有限元法、有限差分法和基于能量原理的Galerkin法等数值方法提供理论依据.     

On large deviation expansion of distribution of maximum likelihood estimator and its application in large sample estimation

For estimating an unknown parameter , the likelihood principle yields the maximum likelihood estimator. It is often favoured especially by the applied statistician, for its good properties in the large sample case. In this paper, a large deviation expansion for the distribution of the maximum likelihood estimator is obtained. The asymptotic expansion provides a useful tool to approximate the tail probability of the maximum likelihood estimator and to make statistical inference. Theoretical and numerical examples are given. Numerical results show that the large deviation approximation performs much better than the classical normal approximation.This work is supported in part by the Natural Science and Engineering Research Council of Canada under grant NSERC A-9216.This author is also partially supported by the National Science Foundation of China.     

Micropolar fluid system in a space of distributions and large time behavior

We analyze the well-posedness of the initial value problem for the generalized micropolar fluid system in a space of tempered distributions and also prove the existence of the stationary solutions. The asymptotic stability of solutions is showed in this space, and as a consequence, a criterium for vanishing small perturbations of initial data (stationary solution) at large time is obtained. A fast decay of the solutions is obtained when we assume more regularity on the initial data.     

Modeling and simulation of transient responses of a flexible beam floating in finite depth water under moving loads

The dynamic response of a free–free flexible beam floating in an unbounded water domain under the effect of moving loads is numerically analyzed. The water is assumed compressible and inviscid. The surface disturbance satisfies a linear free surface wave condition and an undisturbed condition at infinity. In the present work, a finite element procedure was developed directly in time domain and implemented to solve the two-dimensional problem of the transient behavior of an elastic beam floating on the surface of finite deep water under the passage of a moving force with uniform speed. The presented data demonstrates the applicability of the proposed mathematical model and numerical approach. The influences on the dynamic responses of floating beam of some factors were studied.