A new model for the analysis of reinforced concrete members with a coupled HdBNM/FEM

As a truly boundary-type meshless method, the hybrid boundary node method (HdBNM) does not require ‘boundary element mesh’, either for the purpose of interpolation of the solution variables or for the integration of ‘energy’. In this paper, the HdBNM is coupled with the finite element method (FEM) for predicting the mechanical behaviors of reinforced concrete. The steel bars are considered as body forces in the concrete. A bond model is presented to simulate the bond-slip between the concrete and steels using fictitious spring elements. The computational scale and cost for meshing can be further reduced. Numerical examples, in 2D and 3D cases, demonstrate the efficiency of the proposed approach.     

A MODIFIED UPWIND DIFFERENCE SCHEME FOR NONLINEAR PARABOLIC EQUATIONS IN A VARIABLE DOMAIN

The nonlinear parabolic equations in a variable domain are considered. A modified up-wind difference scheme is given in the variable domain. Stability in l norm and error estimate in norm are obtained.     

Positive solutions for a system of difference equations with coupled multi-point boundary conditions

We investigate the existence and nonexistence of positive solutions for a system of nonlinear second-order difference equations with parameters subject to coupled multi-point boundary conditions.     

Thermal analysis of moving induction heating of a hollow cylinder with subsequent spray cooling: Effect of velocity,initial position of coil,and geometry

In this paper, temperature analysis of the complete process of moving induction heat treatment is performed using numerical methods. A non-linear and transient magneto-thermal coupled problem with a moving coil which is considered as moving heat source, is investigated by an efficient finite-element procedure. A vertical hollow circular cylinder is heated by the moving coil at a given velocity along it, and the heated parts then quenched by a moving water–air spray. The effects of natural convection with air on the both inner and outer surfaces of cylinder, and also radiation of outer surface of cylinder with ambient are taken into account. For quenching of work-piece, a specific kind of atomized spray cooling which utilizes a mixture of water and air with different mass fractions is used. This procedure includes moving boundary conditions, temperature-dependent properties, and change in magnetic permeability of specified alloy at the Curie temperature. Obtained numerical results have been verified by comparison with analytical solutions using Green’s function methods. Also, the effect of velocity, initial position of inductor and inner to outer radius ratio on temperature distribution are investigated.     

A nonlinear iteration method for solving a two-dimensional nonlinear coupled system of parabolic and hyperbolic equations

A nonlinear iteration method for solving a class of two-dimensional nonlinear coupled systems of parabolic and hyperbolic equations is studied. A simple iterative finite difference scheme is designed; the calculation complexity is reduced by decoupling the nonlinear system, and the precision is assured by timely evaluation updating. A strict theoretical analysis is carried out as regards the convergence and approximation properties of the iterative scheme, and the related stability and approximation properties of the nonlinear fully implicit finite difference (FIFD) scheme. The iterative algorithm has a linear constringent ratio; its solution gives a second-order spatial approximation and first-order temporal approximation to the real solution. The corresponding nonlinear FIFD scheme is stable and gives the same order of approximation. Numerical tests verify the results of the theoretical analysis. The discrete functional analysis and inductive hypothesis reasoning techniques used in this paper are helpful for overcoming difficulties arising from the nonlinearity and coupling and lead to a related theoretical analysis for nonlinear FI schemes.     

Solitary wave solutions for a coupled pair of mKdV equations

Propagation of weakly nonlinear long waves is studied within the framework of a system of two coupled modified Korteweg-de Vries equations. We investigate analytically and numerically the various families of soliton states for the considered model. By scaling the functions and variables we find that the resulting coupled pair of equations has only one combined parameter. This parameter depends on the wave speed and the coupling coefficient. Explicit analytical expressions for both of the symmetric and antisymmetric states are determined. Numerical method is derived to solve the proposed system, many numerical tests have been conducted to study the behavior of the solution, and the existence of the asymmetric soliton states is displayed numerically.     

Positive solutions for a system of second-order multi-point discrete boundary value problems

We present some results for positive solutions of a system of nonlinear second-order difference equations, subject to multi-point boundary conditions.     

A beam segment element for dynamic analysis of large aqueducts

Large aqueduct structure is a complex structure that is commonly used in hydraulic engineering, especially in large-scale water conveying projects. The analysis of dynamic response for an aqueduct structure is necessary if the aqueduct is built in an earthquake area. Traditional 3D finite element analysis is time consuming and the existing simplified response method cannot take into account all the effects, such as the bending-torsion coupling effect and the constrained torsion, of the deformations of the thin wall structure of the aqueduct body. For this special structure, a simple and yet accurate model for dynamic analysis is needed. In this paper, a beam segment element is developed and used for the calculation of dynamic response for aqueduct structures. With the frame of the aqueduct being modeled using beam element, the proposed model can calculate the dynamic response of the whole aqueduct structures. Results are compared with that of a general purpose finite element analysis software using 3D finite element model. Good agreement is achieved between the two models. However, the proposed model needs less elements and much less computing time.     

Numerical Solution of Parabolic Problems with Nonlocal Boundary Conditions

In this article, the one-dimensional parabolic equation with three types of integral nonlocal boundary conditions is approximated by the implicit Euler finite difference scheme. Stability analysis is done in the maximum norm and it is proved that the radius of the stability region and the stiffness of the discrete scheme depends on the signs of coefficients in the nonlocal boundary condition. The known stability results are improved. In the case of a plain integral boundary condition, the conditional convergence rate is proved and the regularization relation between discrete time and space steps is proposed. The accuracy of the obtained estimates is illustrated by results of numerical experiments.     

Free vibration analysis of circular plates by differential transformation method

This study analyses the free vibrations of circular thin plates for simply supported, clamped and free boundary conditions. The solution method used is differential transform method (DTM), which is a semi-numerical-analytical solution technique that can be applied to various types of differential equations. By using DTM, the governing differential equations are reduced to recurrence relations and its related boundary/regularity conditions are transformed into a set of algebraic equations. The frequency equations are obtained for the possible combinations of the outer edge boundary conditions and the regularity conditions at the center of the circular plate. Numerical results for the dimensionless natural frequencies are presented and then compared to the Bessel function solution and the numerical solutions that appear in literature. It is observed that DTM is a robust and powerful tool for eigenvalue analysis of circular thin plates.     

An inverse coefficient problem for a quasilinear parabolic equation with periodic boundary and integral overdetermination condition

In this paper, the inverse problem of finding the time‐dependent coefficient of heat capacity together with the solution periodic boundary and integral overdetermination conditions is considered. Under some natural regularity and consistency conditions on the input data, the existence, uniqueness, and continuous dependence upon the data of the solution are shown. Some considerations on the numerical solution for this inverse problem are presented with an example. Copyright © 2014 John Wiley & Sons, Ltd.     

A construction of multiresolution analysis by integral equations

In this paper we present a versatile construction of multiresolution analysis of two variables by means of eigenvalue problems of the integral equation, for . As a consequence we show that if is the solution of the equation with , then constructs a two-variable multiresolution analysis.

     

Numerical results for positive solutions of a superlinear elliptic equation

In this work we present a numerical approach for finding positive solutions of the type −Δu = λf(u) for x  Ω, with Dirichlet boundary condition, where f is a superlinear function of u. We will show in which range of λ, this problem achieves multiple numerical solutions and what is the behavior of the branches of solutions.     

Blow‐up analysis for a system of heat equations coupled via nonlinear boundary conditions

In this paper, we study a system of heat equations coupled via nonlinear boundary conditions (1) Here p, q>0. We prove that the solutions always blow up in finite time for non‐trivial and non‐negative initial values. We also prove that the blow‐up occurs only on S_R = ?B_R for Ω = B_R = {x ? ?ⁿ:|x|<R}and under some assumptions on the initial values. Copyright © 2007 John Wiley & Sons, Ltd.     

On the coupled NBEM and FEM for a class of nonlinear exterior Dirichlet problem in R~(2*)

In this paper, based on the natural boundary reduction advanced by Feng and Yu, we couple the finite element approach with the natural boundary element method to study the weak solvability and Galerkin approximation of a class of nonlinear exterior boundary value problems. The analysis is mainly based on the variational formulation with constraints. We prove the error estimate of the finite element solution and obtain     

Dynamic analysis of a non-conservative band-wheel system with a moving boundary Part 1: Mathematical modelling

The dynamic band/wheel system with a moving boundary is very different from that with a fixed length, it is a non-conservative mass system and the boundary position is not fixed. In this paper, the moving boundary is one unknown to be determined associated with the string displacement, and the partial differential equation of the transverse vibrations of the band and the transversality condition of the moving boundary are derived by the calculus of variation and Hamilton’s principle. In order to verify the dynamic formulation is correct, we reduce the governing equation and separation point to coincide with the previous studies. It is found that the physical properties of the moving boundary could be obtained from the geometric constraint of the band/wheel system.     

A Parallel Preconditioned Iterative Realization of the Panel Method in 3D

The parallel version of precondition iterative techniques is developed for matrices arising from the panel boundary element method for three-dimensional simple connected domains with Dirichlet boundary conditions. Results were obtained on an nCube-2 parallel computer showing that preconditioned iterative methods are very well suited also in three-dimensional cases for implementation on an MIMD computer and that they are much more efficient than usual direct solution techniques.     

关于粗糙奇异积分算子的一点注记

研究R^n上一类沿多项式曲线的奇异积分算子,在一些相当弱的尺寸条件下建立了这些算子的L^p有界性．     

Existence of positive solutions for a system of semipositone coupled discrete boundary value problems

We study the existence of positive solutions for a system of nonlinear second-order difference equations with parameters and sign-changing nonlinearities, subject to multi-point coupled boundary conditions. In the proof of our main theorems we use the nonlinear alternative of Leray-Schauder type and the Guo-Krasnosel'skii fixed point theorem.     

Asymptotic analysis of a coupled nonlinear parabolic system

This paper deals with asymptotic analysis of a parabolic system with inner absorptions and coupled nonlinear boundary fluxes. Three simultaneous blow-up rates are established under different dominations of nonlinearities, and simply represented in a characteristic algebraic system introduced for the problem. In particular, it is observed that two of the multiple blow-up rates are absorption-related. This is substantially different from those for nonlinear parabolic problems with absorptions in all the previous literature, where the blow-up rates were known as absorptionindependent. The results of the paper rely on the scaling method with a complete classification for the nonlinear parameters of the model. The first example of absorption-related blow-up rates was recently proposed by the authors for a coupled parabolic system with mixed type nonlinearities. The present paper shows that the newly observed phenomena of absorptionrelated blow-up rates should be due to the coupling mechanism, rather than the mixed type nonlinearities.