Boundary element analysis for bending elastic plates with three generalized displacements

In this paper, the two fundamental differential equations for bending elastic plates with three generalized displacements are transformed into a set of boundary integral equations by Green formula. Three kinds of boundary conditions on edges have been strictly derived. So this paper gives a satisfactory method of boundary element analysis for solving the problem of bending elastic plates.     

Variable viscosity and slip velocity effects on the flow and heat transfer of a power-law fluid over a non-linearly stretching surface with heat flux and thermal radiation

The flow and heat transfer of a non-Newtonian power-law fluid over a non-linearly stretching surface has been studied numerically under conditions of constant heat flux and thermal radiation and evaluated for the effect of wall slip. The governing partial differential equations are transformed into a set of coupled non-linear ordinary differential equations which are using appropriate boundary conditions for various physical parameters. The remaining set of ordinary differential equations is solved numerically by fourth-order Runge–Kutta method using the shooting technique. The effects of the viscosity, the slip velocity, the radiation parameter, power-law index, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin friction and Nusselt numbers are presented. Comparison of numerical results is made with the earlier published results under limiting cases.     

Three-dimensional free vibration analysis of rotating laminated conical shells: layerwise differential quadrature (LW-DQ) method

This paper focuses on the free vibration analysis of thick, rotating laminated composite conical shells with different boundary conditions based on the three-dimensional theory, using the layerwise differential quadrature method (LW-DQM). The equations of motion are derived applying the Hamilton’s principle. In order to accurately account for the thickness effects, the layerwise theory is used to discretize the equations of motion and the related boundary conditions through the thickness of the shells. Then, the equations of motion as well as the boundary condition equations are transformed into a set of algebraic equation applying the DQM in the meridional direction. This study demonstrates the applicability, accuracy, stability and the fast rate of convergence of the present method, for free vibration analyses of rotating thick laminated conical shells. The presented results are compared with those of other shell theories obtained using conventional methods and a special case where the angle of the conical shell approaches zero, that is, a cylindrical shell and excellent agreements are achieved.     

INTERVAL ANALYSIS OF FUZZY-RANDOM HEAT CONDUCTION IN COMPOSITE TUBES

IntroductionThere are a lot of uncertainties such as fuzziness and random in the design andmanufacture in engineering.In generally speaking,methods to deal with the fuzzy-randomproblems are first to transfer the fuzzy set to real number set,and then the p…     

Bending problems of rectangular Reissner plate with free edges laid on tensionless Winkler foundations

In this paper,an analytical method for solving the bending problems of rectangularReissner plate with free edges under arbitrary loads laid on tensionless Winkler foundationsis proposed.By assuming proper form of Fourier series with supplementary terms,whichmeet derivable conditions,for deflection and shear force functions,the basic differentialequations with given boundary conditions can be transformed into a set of simple infinitealgebraic equations.For common Winkler foundations,this set of equations can be solveddirectly and for tensionless Winkler foundations,it is a set of weak nonlinear algebraicequations,the solution of which can be obtained easily by using iterative procedures.     

比例边界等几何分析方法Ⅰ:波导本征问题

提出比例边界等几何方法 (scaled boundary isogeometric analysis, SBIGA), 并用以求解波导本征值问题. 在比例边界等几何坐标变换的基础上, 利用加权余量法将控制偏微分方程进行离散处理, 半弱化为关于边界控制点变量的二阶常微分方程, 即 TE 波或 TM 波波导的比例边界等几何分析的频域方程以及波导动刚度方程, 同时利用连分式求解波导动刚度矩阵. 通过引入辅助变量进一步得出波导本征方程. 该方法只需在求解域的边界上进行等几何离散, 使问题降低一维, 计算工作量大为节约, 并且由于边界的等几何离散, 使得解的精度更高, 进一步节省求解自由度. 以矩形和 L 形波导的本征问题分析为例, 通过与解析解和其他数值方法比较, 结果表明该方法具有精度高、计算工作量小的优点.     

Comment on the paper “Transient MHD free convective flow past an infinite vertical plate embedded in a porous medium with viscous dissipation,Siva Reddy Sheri,R. Srinivasa Raju,Meccanica, DOI 10.1007/s11012-015-0285-y”

A numerical investigation of transient magnetohydrodynamic free convection flow past an infinite vertical plate embedded in a porous medium with viscous dissipation is presented in the above paper. The governing differential equations are transformed into a set of non-linear coupled partial differential equations and are solved numerically using the finite element method. Numerical results for the velocity, temperature and concentration profiles within the boundary layer are presented and discussed.     

Analytical solution for the problem of maximum exit velocity under Coulomb friction in gravity flow discharge chutes

In this paper, an analytical solution for the problem of finding profiles of gravity flow discharge chutes required to achieve maximum exit velocity under Coulomb friction is obtained by application of variational calculus. The model of a particle which moves down a rough curve in a uniform gravitational field is used to obtain a solution of the problem for various boundary conditions. The projection sign of the normal reaction force of the rough curve onto the normal to the curve and the restriction requiring that the tangential acceleration be non-negative are introduced as the additional constraints in the form of inequalities. These inequalities are transformed into equalities by introducing new state variables. Although this is fundamentally a constrained variational problem, by further introducing a new functional with an expanded set of unknown functions, it is transformed into an unconstrained problem where broken extremals appear. The obtained equations of the chute profiles contain a certain number of unknown constants which are determined from a corresponding system of nonlinear algebraic equations. The obtained results are compared with the known results from the literature.     

变系数曲线支承矩形厚板自由振动的傅里叶分析

本文给出了变系数曲线支承的Ａｍｂａｒｓｕｍｉａｎ矩形厚板自由振动问题的级数解，将位移和剪力在板域内展成重傅里叶级数，将其导数在边界上展成单傅里叶级数，通过傅里叶变换将控制微分方程和边界条件转化成关于位移级数的系数的一组无穷线性代数方程，最终将板的自由振动问题转化为矩阵特征值问题。     

Bending of rectangular thin plates with free edges laid on tensionless Winkler foundation

In this paper, the bending problem of rectangular thin plates with free edges laid on tensionless Winkler foundation has been solved by employing Fourier series with supplementary terms. By assuming proper form of series for deflection, the basic differential equation with given boundary conditions can be transformed into a set of infinite algebraic equations. Because the boundary of contact region cannot be determined in advance, these equations are weak nonlinear ones. They can be solved by using iterative procedures.Doctor candidate in Civil Engineering Department of Qinghua University at present.     

Transient responses of a magneto-electro-elastic hollow sphere for fully coupled spherically symmetric problem

By introducing a dependent variable and a special function satisfying the inhomogeneous mechanical boundary conditions, the governing equation for a new variable with homogeneous mechanical boundary conditions is derived. Then by means of the separation of variables technique and the electric and magnetic boundary conditions, the dynamic problem of a magneto-electro-elastic hollow sphere under spherically symmetric deformation is transformed to two Volterra integral equations of the second kind about two functions of time. Cubic Hermite polynomials are adopted to approximate the two undetermined functions at each time subinterval and the recursive formula is obtained to solve the integral equations successfully. The transient responses of displacements, stresses, electric and magnetic potentials are completely determined at the end. Numerical results are presented.     

Free vibration of composite plates with mixed boundary conditions based on higher-order shear deformation theory

A global higher-order shear deformation theory is devised to obtain the governing equations of composite plates under dynamic excitation. The time-harmonic solution leads to an eigenvalue problem for the natural frequencies of plates. The eigenvalue problem for rectangular plates is converted to a set of homogenous algebraic equations using differential quadrature method. The formulation of the problem allows direct application of various boundary conditions. Therefore, rectangular plates with mixed boundary conditions are also considered. To show the validity of results, the fundamental natural frequencies of composite plates with different boundary conditions and those of isotropic plates with mixed boundary conditions are compared against the results available in the literature.     

Precise integration method for solving singular perturbation problems

This paper presents a precise method for solving singularly perturbed boundary-value problems with the boundary layer at one end. The method divides the interval evenly and gives a set of algebraic equations in a matrix form by the precise integration relationship of each segment. Substituting the boundary conditions into the algebraic equations, the coefficient matrix can be transformed to the block tridiagonal matrix. Considering the nature of the problem, an efficient reduction method is given for solving singular perturbation problems. Since the precise integration relationship introduces no discrete error in the discrete process, the present method has high precision. Numerical examples show the validity of the present method.     

A unified approach to direct and inverse boundary layer solutions

A unified approach is presented for solving the two-dimensional incompressible boundary layer equations. Solutions are obtained for direct and inverse options using the same equation formulation by a simple interchange of boundary conditions. A modified form of the mechul function scheme obtains inverse solutions with specification of transformed wall shear, skin friction coefficient or displacement thickness distributions. Direct solutions may be obtained without altering the block tridiagonal structure of the system by simply requiring no corrections on the streamwise pressure gradient parameter. Fourth-order spline discretization approximates normal derivatives with two- and three-point backward differences approximating streamwise derivatives, yielding a fully implicit solution method. The resulting spline/finite difference equations are solved by Newton-Raphson iteration together with partial pivoting. The results of the study demonstrate the importance of proper linearization of all equations. The successful use of spline discretization is also tied to the use of strong two-point boundary conditions at the wall for cases involving reversed flow. Numerical solutions are presented for several non-similar flows and compared with published results.     

Stress concentration and stress intensity factors fop an infinite plane with several rows of elliptic holes and cracks

This paper deals with the stress concentration in plane with swveral arbitrarily distributed elliptic holes. By using the functions of complex variables, the stress functions in which the interactions of neighbouring holes are taken into consideration can be constructed. By applying the conformed mapping method to satisfy the boundary conditions of each hole, the governing equations can then be transformed into a set of simultaneous equations through boundary integrals. Moreover, the problems with crack can be derived by changing the elliptical rates of the ellipses, thereby an approximate solution of cracking problem may be obtained. Some computing examples are given in the paper.     

3-D CONSOLIDATION ANALYSIS OF LAYERED SOIL WITH ANISOTROPIC PERMEABILITY USING ANALYTICAL LAYER-ELEMENT METHOD

Starting with governing equations of a saturated soil with anisotropic permeability and based on multiple integral transforms,an analytical layer-element equation is established explicitly in the Laplace-Fourier transformed domain.A global matrix of layered soil can be obtained by assembling a set of analytical layer-elements,which is further solved in the transformed domain by considering boundary conditions.The numerical inversion of Laplace-Fourier transform is employed to acquire the actual solution.Numerical analysis for 3-D consolidation with anisotropic permeability of a layered soil system is presented,and the influence of anisotropy of permeability on the consolidation behavior is discussed.     

Free convection from an arbitrarily inclined plate in a porous medium

A mathematical model for the flow and heat transfer in the free convection from an arbitrary inclined isothermal flat plate embedded in a porous medium is presented, in which the Darcy–Boussinesq approximation is adopted to account for bouyancy force. A novel inclination parameter ξ is proposed such that all cases of the horizontal, inclined and vertical plates can be described by a single set of transformed boundary layer equations. Moreover, the similarity equations for the limiting cases of the horizontal and vertical plates are recovered from the transformed equations by setting ξ=0 and ξ=1, respectively. Detailed results for the skin friction coefficient and Nusselt number as well as for the dimensionless velocity and temperature profiles are presented for a wide range of the parameter ξ. A comparison with similarity solution shows excellent agreement.     

边界约束刚度不确定的结构振动特征值

利用摄动法 ,将随机的微分方程和边界条件化为一系列的确定性微分方程和边界条件。运用有限元离散方法 ,推导了统计特征值的二阶摄动近似表达 ,用算例对本文方法进行了说明并和 Monte-Carlo模拟法结果进行了比较     

Lie group analysis for thermophoretic and radiative augmentation of heat and mass transfer in a Brinkman-Darcy flow over a flat surface with heat generation

A boundary layer analysis is presented to investigate numerically the effects of radiation,thermophoresis and the dimensionless heat generation or absorption on hydromagnetic flow with heat and mass transfer over a flat surface in a porous medium.The boundary layer equations are transformed to non-linear ordinary differential equations using scaling group of transformations and they are solved numerically by using the fourth order Runge-Kutta method with shooting technique for some values of physical parameters.Comparisons with previously published work are performed and the results are found to be in very good agreement.Many results are obtained and a representative set is displayed graphically to illustrate the influence of the various parameters on the dimensionless velocity,temperature and concentration profiles as well as the local skin-friction coefficient,wall heat transfer,particle deposition rate and wall thermophoretic deposition velocity.The results show that the magnetic field induces acceleration of the flow,rather than deceleration(as in classical magnetohydrodynamics(MHD) boundary layer flow) but to reduce temperature and increase concentration of particles in boundary layer.Also,there is a strong dependency of the concentration in the boundary layer on both the Schmidt number and mass transfer parameter.     

An analytical symplectic approach to the vibration analysis of orthotropic graphene sheets

A nonlocal continuum orthotropic plate model is proposed to study the vibration behavior of single-layer graphene sheets (SLGSs) using an analytical symplectic approach.A Hamiltonian system is established by introduc-ing a total unknown vector consisting of the displacement amplitude,rotation angle,shear force,and bending moment. The high-order governing differential equation of the vibra-tion of SLGSs is transformed into a set of ordinary differential equations in symplectic space.Exact solutions for free vibra-tion are obtianed by the method of separation of variables without any trial shape functions and can be expanded in series of symplectic eigenfunctions. Analytical frequency equations are derived for all six possible boundary con-ditions. Vibration modes are expressed in terms of the symplectic eigenfunctions.In the numerical examples,com-parison is presented to verify the accuracy of the proposed method. Comprehensive numerical examples for graphene sheets with Levy-type boundary conditions are given.A para-metric study of the natural frequency is also included.