Element-Free Method Based on Lagrange Polynomial

In this paper, a simple element-free method using the Lagrange polynomial is proposed, in which finite-element subdivisions are not required. Most ordinary element-free approaches are based on the moving least squares (MLS). The present procedure, however, does not employ MLS interpolants. Instead of MLS, the Lagrange polynomial is employed here for the discretization. The Lagrange polynomial makes it possible to connect an approximate solution and its derivatives at any point directly with nodal values. Therefore, the essential boundary conditions can be easily satisfied, while it is quite difficult to do so in the ordinary element-free method. In addition, it is proved that the Lagrange basis is consistent. Consequently, the reproducing condition is satisfied by the Lagrange interpolation. Several numerical examples are presented in order to demonstrate the efficiency of the present procedure. It follows from numerical evaluations that relatively good approximation can be achieved in the nonlinear analyses of beams and plates.     

Application of the Analytical Strip Method to Antisymmetric Laminates

The analytical strip method is presented in this paper for the analysis of the bending-extension coupling problem of antisymmetric thin laminates. A system of three equations of equilibrium, governing the general response of antisymmetric laminates, is reduced to a single eighth-order partial differential equation (PDE) in terms of a displacement function. The PDE is then solved in a single series form to determine the displacement response of antisymmetric cross-ply and angle-ply laminates. The solution is applicable to rectangular laminates with two opposite edges simply supported and the other edges being simply supported, clamped, or free. The laminate can be subjected to any combination of concentrated, uniform, line, and patch loads. This method overcomes the limitations of other analytical methods (e.g., Navier’s and Levy’s) and provides an alternative to numerical, seminumerical, and approximate methods for rectangular plates with two parallel edges simply supported. The results obtained from this method compare very well with the ones derived using the finite-element program ANSYS and, where applicable, the existing classical laminated plate theory.     

Point-Estimate Method as Numerical Quadrature

Rosenblueth's point-estimate method for approximating the low-order moments of functions of random variables is widely used in geotechnical reliability analyses. It is a special case of numerical quadrature based on orthogonal polynomials. For normal variables, it corresponds to Gauss-Hermite quadrature, but Rosenblueth's procedure automatically generates the weights and abscissas of Gauss-Legendre and Gauss-Laguerre quadrature as well. Despite beliefs to the contrary, the method is not a form of Monte Carlo simulation or FOSM Taylor series expansion. The method is reasonably robust and can be satisfactorily accurate for a wide range of practical problems, although the computational requirements increase rapidly with the number of uncertain quantities. Caution should be exercised in applying the method when transformation of the uncertain quantities severely changes the form of the distributions or when moments of order greater than the two are involved. Examples with closed-form solutions serve to illustrate the use and accuracy of the method.     

Peridynamic Analysis of Impact Damage in Composite Laminates

The traditional methods for analyzing deformation in structures attempt to solve the partial differential equations of the classical theory of continuum mechanics. Yet these equations, because they require the partial derivatives of displacement to be known throughout the region modeled, are in some ways unsuitable for the modeling of discontinuities caused by damage, in which these derivatives fail to exist. As a means of avoiding this limitation, the peridynamic model of solid mechanics has been developed for applications involving discontinuities. The objective of this method is to treat crack and fracture as just another type of deformation, rather than as pathology that requires special mathematical treatment. The peridynamic theory is based on integral equations so there is no problem in applying the equations across discontinuities. The peridynamic method has been applied successfully to damage and failure analysis in composites. It predicts in detail the delamination and matrix damage process in composite laminates due to low velocity impact, and the simulation results of damage area correlates very well with the experimental data.     

Least-Squares Finite-Element Evaluation of Flow Nets

A novel least-squares implementation of the finite-element method is presented to evaluate stream functions in the solution of field problems. The method is programmatically similar to the solution of the Laplace equation, and is based on the development of a stream field that is orthogonal to an already calculated potential field. The main advantage of the method comes from the fact that it eliminates the need of identification of boundary conditions for the stream functions. Implementation of this method requires that the Laplace equation be solved first to calculate the nodal potentials. The Laplace equation, with an identity conductivity matrix is then solved again to calculate the nodal values of the stream functions. One arbitrary boundary condition is sufficient for the second solution. Examples of cofferdam and curtained dam flow with isotropic as well as orthotropic soil conductivity are presented to demonstrate the method.     

Spatial and temporal aspects of infant color vision

The present paper constitutes a review of the literature on young infants' chromatic discrimination capabilities. A series of early studies showed that infants as young as two months postnatal can make at least some chromatic discriminations between stationary, homogeneous fields of different wavelength compositions. Current studies of spatial and temporal contrast sensitivity functions (CSFs) for red/green isoluminant stimuli suggest that spatial chromatic CSFs show developmental changes in sensitivity and spatial scale, but not curve shape; while temporal chromatic CSFs (tCSFs) show developmental changes in sensitivity and curve shape, but not temporal scale. Infants can also code the direction of motion of moving isoluminant red/green gratings, for both continuous and quadrature motion. The possible mechanisms that underlie infants' chromatic discriminations are discussed.     

金属层合板板形翘曲变形行为

采用经典弹性力学方法建立了金属层合板翘曲解析计算力学模型,获得了厚度方向不均匀延伸与板形翘曲之间的定量关系;并分别建立了在线和离线两种状态下金属层合板翘曲变形的有限元数值模拟模型,对解析计算力学模型进行了验证;在此基础上,揭示了金属层合板产生板形翘曲缺陷的力学根源以及各因素对金属层合板板形翘曲缺陷演变的影响规律,同时对比分析了双层和三层结构层合板与均质板的翘曲变形差异以及铜/碳钢层合板与不锈钢/碳钢层合板二者之间的翘曲变形差异。研究表明,金属层合板翘曲高度与延伸差、厚度比呈正比关系,与厚度呈反比关系,且基层与覆层的切变模量相差越大,厚度比对金属层合板翘曲变形的影响越大。基于数值模型,模拟研究了层合板在理想均匀分布的初始温度下,历经去应力退火过程时,其板形翘曲的变形行为及规律,并与均质板进行比较。最后,在工业生产现场取样已翘曲层合板,通过测量其弯曲变形量进而反求其初始延伸差,验证了解析计算力学模型的准确性。      

连轧过程运动带钢稳定性研究

以某冷连轧机组轧制过程中两机架间运动带钢为研究对象,根据运动梁理论和运动薄板理论,分别建立了轧制过程运动带钢动力学模型。通过Galerkin截断,把描述系统运动的偏微分方程离散化。利用数值方法分析了轧制过程运动带钢的固有特性和稳定性。并对某连轧机组进行稳定性分析,分析结果表明：该机组第二和第三机架间运动板带的极限速度可以达到32m／s,并且基于运动梁模型和基于运动薄板模型所计算出的结果极为接近,验证了所建模型的正确性。     

Free Vibration of Open Circular Cylindrical Composite Shells with Point Supports

A variational full-field method is presented in this paper for the free vibration analysis of open circular cylindrical laminated shells supported at discrete points. A differential equation in matrix form is developed using the first-order shear deformable theory of shells, and rotary inertia is included. The displacement fields are defined by using very high-order interpolating polynomials and a large number of preselected nodal points on the reference surface of the shell. Each nodal point has 5 degrees of freedom, three displacement components, and two components of the rotation of the normal to the reference surface. The stiffness and mass matrices are obtained using the strain and kinetic energy functions. The numerical results are calculated for shallow and deep circular cylindrical panels with four-, six-, and eight-point supports along the two parallel straight edges. The values of the natural frequency obtained from the present method show good agreement with published data in the literature.     

Numerical Solution of Fractional Advection-Dispersion Equation

Numerical schemes and stability criteria are developed for solution of the one-dimensional fractional advection-dispersion equation (FRADE) derived by revising Fick’s first law. Employing 74 sets of dye test data measured on natural streams, it is found that the fractional order F of the partial differential operator acting on the dispersion term varies around the most frequently occurring value of F = 1.65 in the range of 1.4 to 2.0. Two series expansions are proposed for approximation of the limit definitions of fractional derivatives. On this ground, two three-term finite-difference schemes?“1.3 Backward Scheme” having the first-order accuracy and “F.3 Central Scheme” possessing the F-th order accuracy?are presented for fractional order derivatives. The F.3 scheme is found to perform better than does the 1.3 scheme in terms of error and stability analyses and is thus recommended for numerical solution of FRADE. The fractional dispersion model characterized by the FRADE and the F.3 scheme can accurately simulate the long-tailed dispersion processes in natural rivers.     

Efficient Meshfree Computation with Fast Treatment of Essential Boundary Conditions for Industrial Applications

This paper presents a fast treatment of essential boundary conditions in three-dimensional (3D) meshfree computation for computational efficiency. Due to the loss of Kronecker delta properties in the meshfree shape functions, the imposition of essential boundary conditions is tedious, especially in 3D applications. The proposed boundary singular kernel (BSK) method introduces singularities to the kernel functions associated with the essential and kinematically constrained boundary nodes so that the corresponding coefficients of the singular kernel shape functions recover nodal values, and consequently constraints can be imposed directly. In this work, the recovery of nodal value properties on essential boundary nodes is proved for general n-dimensional geometries. The extension of previously proposed two-dimensional BSK method to 3D formulation thus becomes straightforward, and essential boundary treatment consumes almost no additional cost to meshfree computation and makes the method affordable for industrial applications. The effectiveness of the proposed method is demonstrated in 3D metal forming examples.     

Two-Dimensional Simulation Model of Sediment Removal and Flow in Rectangular Sedimentation Basin

A steady, two-dimensional numerical model was created to study the hydrodynamics of a rectangular sedimentation basin under turbulent conditions. The strip integral method was used to formulate the flow equations, using a forward marching scheme for solving the governing partial differential equations of continuity, momentum, advection–diffusion, turbulent kinetic energy, and its dissipation. In this way the flow equations were converted to a set of ordinary differential equations (ODEs) in terms of the key physical parameters. These parameters, along with a set of shape functions, describe flow variables including the velocity, the concentration of suspended sediments, and both the kinetic energy and its dissipation rate. Four Gaussian distributions were investigated, one corresponding to each flow parameter. In order to calculate the turbulent shear stresses, a two-equation turbulence model (i.e., k-ε model) was used. A fourth order Runge–Kutta method numerically integrates the set of ODEs. Simulation results were compared with experimental data, and close agreement (generally within 5–10%) was observed.     

Discontinuous Galerkin Finite-Element Method for Transcritical Two-Dimensional Shallow Water Flows

A total variation diminishing Runge Kutta discontinuous Galerkin finite-element method for two-dimensional depth-averaged shallow water equations has been developed. The scheme is well suited to handle complicated geometries and requires a simple treatment of boundary conditions and source terms to obtain high-order accuracy. The explicit time integration, together with the use of orthogonal shape functions, makes the method for the investigated flows computationally as efficient as comparable finite-volume schemes. For smooth parts of the solution, the scheme is second order for linear elements and third order for quadratic shape functions both in time and space. Shocks are usually captured within only two elements. Several steady transcritical and transient flows are investigated to confirm the accuracy and convergence of the scheme. The results show excellent agreement with analytical solutions. For investigating a flume experiment of supercritical open-channel flow, the method allows very good decoupling of the numerical and mathematical model, resulting in a nearly grid-independent solution. The simulation of an actual dam break shows the applicability of the scheme to nontrivial bathymetry and wave propagation on a dry bed.     

Generalized Differential Quadrature for Frequency of Rotating Multilayered Conical Shell

This paper uses the generalized differential quadrature (GDQ) method to study the influence of boundary conditions on the natural frequency of a rotating thin truncated circular multilayered conical shell. The governing equations of motion include the effects of initial hoop tension and centrifugal and Coriolis accelerations due to rotation. The GDQ method is applied to the discrete grid points in the meridional direction. Results are obtained to study the influence of boundary conditions on the frequency at different circumferential wave numbers, rotating speeds, and geometric properties. The influences of the cone angle and layered configuration on the variation of frequency with rotating speed also are presented. To validate the accuracy and efficiency of the GDQ method, comparisons are made with those available in the open literature and very good agreements are achieved.     

Multiquadric Solution for Shallow Water Equations

A computational algorithm based on the multiquadric, which is a continuously differentiable radial basis function, is devised to solve the shallow water equations. The numerical solutions are evaluated at scattered collocation points and the spatial partial derivatives are formed directly from partial derivatives of the radial basis function, not by any difference scheme. The method does not require the generation of a grid as in the finite-element method and allows easy editing and refinement of the numerical model. To increase confidence in the multiquadric solution, a sensitivity and convergence analysis is performed using numerical models of a rectangular channel. Applications of the algorithm are made to compute the sea surface elevations and currents in Tolo Harbour, Hong Kong, during a typhoon attack. The numerical solution is shown to be robust and stable. The computed results are compared with measured data and good agreement is indicated.     

Toward an Improvement in the Identification of Bridge Deck Flutter Derivatives

This paper presents a short review of the state-of-the-art methods to identify bridge deck flutter derivatives and proposes a new algorithm to simultaneously extract the aeroelastic coefficients from free-vibration section-model tests, which is based on the improvement of the unifying least-squares (ULS) method and is therefore called modified unifying least-squares method. The advantages with respect to ULS are the faster and better convergence and the improvement in accuracy due to the introduction of weighting factors in the unifying error function. The method has been validated through numerically simulated noisy signals and experimental heaving and pitching time histories for two different bridge deck cross sections: a single-box and a multiple-box girder section model. The analysis of the artificial signals shows that a few system parameters are very difficult to be identified due to the fact that the problem is strongly ill-conditioned. Nevertheless, all the diagonal and off-diagonal components of the stiffness and damping matrices which significantly contribute to the output of the system are correctly estimated. The improvement with respect to other methods is extensively discussed. For the wind-tunnel test cases the accuracy of the identification procedure is evaluated through the comparison between measured signals and those simulated through the estimated mechanical and aerodynamic system parameters with very satisfactory results. With respect to many previous attempts of validation, this approach clearly shows the degree of accuracy that can be expected from the identification algorithm. Finally, for the considered test cases the linear model which stands behind the method seems to be an acceptable approximation of the physics of the phenomenon.     

Vehicle Condition Surveillance on Continuous Bridges Based on Response Sensitivity

This paper presents the parameter identification of a vehicle moving on a multispan continuous bridge deck modeled as a continuous beam based on dynamic response sensitivity analysis. This technique is for the monitoring of “road-friendliness” of vehicles using the highway pavement. The moving vehicle is modeled as a single degree-of-freedom system comprising three parameters, a two degrees-of-freedom system comprising five parameters, or a four degrees-of-freedom system comprising 12 parameters. The modified beam functions are used to calculate the response of the continuous bridge. Starting with an initial guess on the unknown parameters, the identification can be realized based on least-squares method and regularization technique from measured strain, velocity, or acceleration measurement from as few as a single sensor. Simulation studies and experimental results indicate that the identified results are acceptable, and the responses reconstructed from the identified parameters agree well with the measured responses.     

Unsaturated Soil Mechanics in Engineering Practice

Unsaturated soil mechanics has rapidly become a part of geotechnical engineering practice as a result of solutions that have emerged to a number of key problems (or challenges). The solutions have emerged from numerous research studies focusing on issues that have a hindrance to the usage of unsaturated soil mechanics. The primary challenges to the implementation of unsaturated soil mechanics can be stated as follows: (1) The need to understand the fundamental, theoretical behavior of an unsaturated soil; (2) the formulation of suitable constitutive equations and the testing for uniqueness of proposed constitutive relationships; (3) the ability to formulate and solve one or more nonlinear partial differential equations using numerical methods; (4) the determination of indirect techniques for the estimation of unsaturated soil property functions, and (5) in situ and laboratory devices for the measurement of a wide range of soil suctions. This paper explains the nature of each of the previous challenges and describes the solutions that have emerged from research studies. Computer technology has played a major role in achieving practical geotechnical engineering solutions. Computer technology has played an important role with regard to the estimation of unsaturated soil property functions and the solution of nonlinear partial differential equations. Breakthroughs in the in situ and laboratory measurement of soil suction are allowing unsaturated soil theories and formulations to be verified through use of the “observational method.”     

Spectral Method for Nonlinear Stochastic Partial Differential Equations of Elliptic Type

This paper is concerned with the numerical approximations of semi-linear stochastic partial differential equations of elliptic type in multi-dimensions. Convergence analysis and error estimates are presented for the numerical solutions based on the spectral method. Numerical results demonstrate the good performance of the spectral method.     

Roll Flattening Analytical Model in Flat Rolling by Boundary Integral Equation Method

In order to improve rolled strip quality, precise plate shape control theory should be established. Roll flattening theory is an important part of the plate shape theory. To improve the accuracy of roll flattening calculation based on semi-infinite body model, especially near the two roll barrel edges, a new and more accurate roll flattening model is proposed. Based on boundary integral equation method, an analytical model for solving a finite length semi-infinite body is established. The lateral surface displacement field of the finite length semi-infinite body is simulated by finite element method (FEM) and lateral surface displacement decay functions are established. Based on the boundary integral equation method, the numerical solution of the finite length semi-infinite body under the distributed force is obtained and an accurate roll flattening model is established. Different from the traditional semi-infinite body model, the matrix form of the new roll flattening model is established through the mathematical derivation. The result from the new model is more consistent with that by FEM especially near the edges.