A reconstructed edge-based smoothed DSG element based on global coordinates for analysis of Reissner–Mindlin plates

A reconstructed edge-based smoothed triangular element, which is incorporated with the discrete shear gap(DSG) method, is formulated based on the global coordinate for analysis of Reissner–Mindlin plates. A symbolic integration combined with the smoothing technique is implemented to calculate the smoothed finite element matrices,which is integrated along the boundaries of each smoothing cell. Numerical results show that the proposed element is free from shear locking, and its results are in good agreement with the exact solutions, even for very thin plates with extremely distorted elements. The proposed element gives more accurate results than the original DSG element without smoothing, and it can be taken as an alternative element for analysis of Reissner–Mindlin plates. The prominent feature of the present element is that the integration scheme is unified in the smoothed form for all of the finite element matrices.     

弱连续条件下的九参三角形板元

首先对薄板弯曲平衡方程的弱形式进行了推导,导出保证单元收敛的弱协调条件,即三角形顶点函数值连续和三边的法向导数积分连续这两个条件;对比拟协调元、广义协调元和双参数法中所使用的3个积分连续条件,本条件更弱;再对这3个积分协调条件的构成方法进行了总结和分析,现有采用积分连续条件构造的有限元大都采用了这些构成方法.采用弱协调条件构造有限元,比原来的构造范围更广,井以此构造出几种单元作为算例.采用这种构成法还可构造多种单元,它们都具有采用最小势能原理法构成有限元的简便的优点,并在任意网格下收敛到真解.     

基于平面偶应力-Reissner/Mindlin板比拟的偶应力有限元

偶应力理论的有限元列式面临本质性的C1连续性困难. 平面偶应力理论和Reissner/Mindlin板弯曲理论之间的比拟关系表明这两个理论系统的有 限元的同一性，而R/M板有限元并不存在C1连续性困难. 因此，研究将R/M板单元转化为具有一般位移自由度的平面偶应力单元的一般方法. 根据这一方法，将典型的8节点Serendipity型R/M板单元Q8S转化为一个4节点12 自由度的四边形平面偶应力单元，数值结果表明该单元具有良好的精度和收敛性     

基于边光滑有限元法的加筋板静力和自由振动分析

运用边光滑有限元法,研究分析了加筋板结构的静力和自由振动问题。在边光滑有限元法中,将基于边的应变光滑技术用于对原来的应变场进行光滑操作;由于应变光滑技术能够适当地软化原来过刚的有限元模型,从而能够得到更加接近于系统准确刚度的光滑有限元模型;鉴于三角形单元良好的适用性,选用三角形单元对模型进行网格划分;同时,为了解决低阶Reissner-Mindlin板单元弯曲过程中的横向剪切自锁问题,采用了一种新型的离散剪切间隙技术。算例的数值计算结果表明,与传统的有限元法相比,边光滑有限元法能够得到精度更高的计算结果,且收敛更快,计算效率更佳。     

饱和多孔介质大变形分析的一种有限元-有限体积混合方法

建立了饱和多孔介质大变形分析的一种有限元-有限体积混合计算方法.将饱和多孔介质视为由固体骨架和孔隙水组成的两相体,其基本方程包括动力平衡方程和渗流连续方程.基于u-p假定和更新的Lagrange方法,饱和多孔介质的动力平衡方程在空间域内采用有限元方法进行离散,而渗流连续方程在空阃域内则采用有限体积法进行离散.通过两个数值算例,一维有限弹性固结和动力荷载作用下堤坝动力响应的计算,验证了该方法的有效性.     

A DIRECTIONALLY ADAPTIVE METHODOLOGY USING AN EDGE-BASED ERROR ESTIMATE ON QUADRILATERAL GRIDS

The present paper describes a directionally adaptive finite element method for high-speed flows, using an edge-based error estimate on quadrilateral grids. The error of the numerical solution is estimated through its second derivatives and the resulting Hessian tensor is used to define a Riemannian metric. An improved mesh movement strategy, based on a spring analogy, but with no orthogonality constraints, is introduced to equidistribute the lengths of the edges of the elements in the defined metric. The grid adaptation procedure is validated on an analytical test case and the efficiency of the overall methodology is investigated on supersonic and hypersonic benchmarks.     

AN h-TYPE ADAPTIVE FINITE ELEMENT

ＡＮｈ－ＴＹＰＥＡＤＡＰＴＩＶＥＦＩＮＩＴＥＥＬＥＭＥＮＴ￥ＸｕＸｉｎｇ（徐兴）ＬｉｎｇＤａｏｓｈｅｎｇ（凌道盛）ＤｕＱｉｎｇｈｕａ（杜庆华）ＤｉｎｇＨａｏｊｉａｎｇ（丁皓江）（ＺｈｅｊｉａｎｇＵｎｉｖｅｒｓｉｔｙ．Ｈａｎｇｚｈｏｕ３１００２７．Ｐ．...     

Calculation of vertical velocity in three-dimensional,shallow water equation,finite element models

Computation of vertical velocity within the confines of a three-dimensional, finite element model is a difficult but important task. This paper examines four approaches to the solution of the overdetermined system of equations arising when the first-order continuity equation is solved in conjunction with two boundary conditions. The traditional (TRAD) method neglects one boundary condition, solving the continuity equation with the remaining boundary condition. The vertical derivative of continuity (VDC) method involves solution of the second-order equation obtained by differentiation of the continuity equation with respect to the vertical co-ordinate. The least squares (LS) method minimizes the residuals of the continuity equation (in discrete form) and the two boundary conditions. The adjoint (ADJ) method minimizes the residuals of the continuity equation (in continuous form) and the two boundary conditions. Two domains are considered: a quarter-annular harbour and the southwest coast of Vancouver Island. Results indicate that the highest-quality solution is obtained with both LS and ADJ. Furthermore, ADJ requires less CPU and memory than LS. Therefore the optimal method for computation of vertical velocity in a three-dimensional finite element model is the adjoint (ADJ) method. © 1997 John Wiley & Sons, Ltd.     

基于等几何分析的比例边界有限元方法

提出了一种具有比例边界有限元的半解析特性和等几何分析的几何特性的新方法。该新方法是在比例边界有限元框架中用NURBS曲线或曲面精确描述域边界几何形状,同时域边界位移场采用描述几何形状的NURBS形函数等参构造。这种新方法具有比例边界有限元固有的径向解析特性和NURBS的高阶连续性的优点。数值算例显示,与传统的比例边界有限元相比,基于等几何分析的比例边界有限元方法提高了域边界单元和域内应力场的连续性,减少了计算自由度。应用此方法可以用较少的计算自由度获得更高连续阶和更高精度的位移、应力和应变场。     

Formulation and implementation of a singular anisotropic finite element

The formulation and implementation of a singular finite element for analyzing homogeneous anistropic materials is presented in this paper. Lekhnitskii's stress function method is used to formulate the boundary value problem with the stress function expressed as a Laurent series. The development of the element stiffness matrix and the method of integrating the element to conventional displacement based finite element programs is shown. The stiffness matrix generation is based on a least squates collocation technique to satisfy displacement continuity boundary conditions at the element interface. Implementation of the element is demonstrated for cracked anisotropic materials subjected to inplane loading. Center cracked, on and off-axis coupons under tensile loading are analyzed using the element. It is shown that the stress distributions and intensity factors compare well with those obtained using other methods.     

Compatibility between finite volumes and finite elements using solutions of shallow water equations for substance transport

This paper formulates a finite volume analogue of a finite element schematization of three‐dimensional shallow water equations. The resulting finite volume schematization, when applied to the continuity equation, exactly reproduces the set of matrix equations that is obtained by the application of the corresponding finite element schematization to the continuity equation. The procedure allows the consistent and mass conserving coupling of the finite element Telemac model for three‐dimensional flow with the finite volume Delft3D‐WAQ model for water quality. The work has been carried out as part of a joint development by LNHE and WL∣Delft Hydraulics to explore the mutual interaction of their software. Copyright © 2006 John Wiley & Sons, Ltd.     

The improvement of numerical modeling in the solution of incompressible viscous flow problems using finite element method based on spherical Hankel shape functions

In this paper, the finite element method with new spherical Hankel shape functions is developed for simulating 2‐dimensional incompressible viscous fluid problems. In order to approximate the hydrodynamic variables, the finite element method based on new shape functions is reformulated. The governing equations are the Navier‐Stokes equations solved by the finite element method with the classic Lagrange and spherical Hankel shape functions. The new shape functions are derived using the first and second kinds of Bessel functions. In addition, these functions have properties such as piecewise continuity. For the enrichment of Hankel radial basis functions, polynomial terms are added to the functional expansion that only employs spherical Hankel radial basis functions in the approximation. In addition, the participation of spherical Bessel function fields has enhanced the robustness and efficiency of the interpolation. To demonstrate the efficiency and accuracy of these shape functions, 4 benchmark tests in fluid mechanics are considered. Then, the present model results are compared with the classic finite element results and available analytical and numerical solutions. The results show that the proposed method, even with less number of elements, is more accurate than the classic finite element method.     

Iterative solution techniques for the stokes and Navier-Stokes equations

The linear system arising from a Lagrange-Galerkin mixed finite element approximation of the Navier–Stokes and continuity equations is symmetric indefinite and has the same block structure as a system arising from a mixed finite element discretization of a Stokes problem. This paper considers the iterative solution of such a system, comparing the performance of the one-level preconditioned conjugate residual method for indefinite matrices with that of a more traditional two-level pressure correction approach. Asymptotic estimates for the amount of work involved in each method are given together with the results of related numerical experiments.     

Integration of B-spline geometry and ANCF finite element analysis

The goal of this investigation is to introduce a new computer procedure for the integration of B-spline geometry and the absolute nodal coordinate formulation (ANCF) finite element analysis. The procedure is based on developing a linear transformation that can be used to transform systematically the B-spline representation to an ANCF finite element mesh preserving the same geometry and the same degree of continuity. Such a linear transformation that relates the B-spline control points and the finite element position and gradient coordinates will facilitate the integration of computer aided design and analysis (ICADA). While ANCF finite elements automatically ensure the continuity of the position and gradient vectors at the nodal points, the B-spline representation allows for imposing a higher degree of continuity by decreasing the knot multiplicity. As shown in this investigation, a higher degree of continuity can be systematically achieved using ANCF finite elements by imposing linear algebraic constraint equations that can be used to eliminate nodal variables. The analysis presented in this study shows that continuity of the curvature vector and its derivative which corresponds in the cubic B-spline representation to zero knot multiplicity can be systematically achieved using ANCF finite elements. In this special case, as the knot multiplicity reduces to zero, the recurrence B-spline formula causes two segments to automatically blend together forming one cubic segment defined on a larger domain. Similarly in this special case, the algebraic constraint equations required for the C ³ continuity convert two ANCF cubic finite elements to one finite element, demonstrating the strong relationship between the B-spline representation and the ANCF finite element representation. For the same order of interpolation, higher degree of continuity at the finite element interface can lead to a coarser mesh and to a lower dimensional model. Using the B-spline/ANCF finite element transformation developed in this paper, the equations of motion of a finite element mesh that represents exactly the B-spline geometry can be developed. Because of the linearity of the transformation developed in this investigation, all the ANCF finite element desirable features are preserved; including the constant mass matrix that can be used to develop an optimum sparse matrix structure of the nonlinear multibody system dynamic equations.     

AN EULERIAN FINITE ELEMENT METHOD FOR TIME-DEPENDENT FREE SURFACE PROBLEMS IN HYDRODYNAMICS

A numerical method based on the finite element method is presented for simulating the two-dimensional transient motion of a viscous liquid with free surfaces. For ease of numerical treatment of the free surface expressed by a multiple-valued function, the marker particle method is employed. Numerous virtual particles are spread over all regions occupied by liquid. They move about on a fixed finite element mesh with the liquid velocity at their positions. These particles contribute nothing to the dynamics of the liquid and only serve as markers of liquid regions. The velocity field within liquid regions is calculated by solving the Navier– Stokes equations and the equation of continuity by the finite element method based on quadrilateral elements. A detailed discussion is given of the methodological problems arising in the implementation of the marker particle method on an unstructured finite element mesh and of the solutions to these problems. The proposed method is demonstrated on three sample problems: the broken dam problem, the impact of a falling liquid drop on a still liquid and the entry of a rigid block into water. Good agreement has been obtained in the comparison of the present numerical results with available experimental data.     

The Finite Element Analysis of Interaction Problem Through Water,Soil, Balloon and Pile

This paper presents the finite element analysis of an interaction problem involving water, soil, balloon and pile. A building with friction piles is considered, and balloons are introduced to the top of piles. To control the vertical displacement of the building, water is injected into or removed from the balloons. The two-dimensional incompressible Navier-Stokes equation is introduced, and the ALE (Arbitrary Lagrangian Eulerian) method is applied to the water flow analysis. The FS (Fractional Step) method is also applied in the finite element formulation. The soil, which is assumed as a linear elastic body, is subjected to the deformation analysis. The balloon and pile are assumed as a linear elastic truss and a rigid frame, and the deformation analysis is also performed. All the components are discretized by the finite element method in space and are interactively solved by taking into account continuity conditions of traction and displacement.     

A DOMAIN DECOMPOSITION ALGORITHM WITH FINITE ELEMENT-BOUNDARY ELEMENT COUPLING

A domain decomposition algorithm coupling the finite element and the boundary element was presented. It essentially involves subdivision of the analyzed domain into sub-regions being independently modeled by two methods, i.e., the finite element method (FEM) and the boundary element method (BEM). The original problem was restored with continuity and equilibrium conditions being satisfied on the interface of the two sub-regions using an iterative algorithm. To speed up the convergence rate of the iterative algorithm, a dynamically changing relaxation parameter during iteration was introduced. An advantage of the proposed algorithm is that the locations of the nodes on the interface of the two sub-domains can be inconsistent. The validity of the algorithm is demonstrated by the consistence of the results of a numerical example obtained by the proposed method and those by the FEM, the BEM and a present finite element-boundary element (FE-BE) coupling method.     

Dual variational formulation for Trefftz finite element method of elastic materials

A dual variational principle is presented for Trefftz finite element analysis. The proof of the stationary conditions of the variational functional and the theorem on the existence of extremum are provided in this paper. They are boundary displacement condition, surface traction condition and interelement continuity condition. Based on the assumed intraelement and frame fields, element stiffness matrix equation is obtained which can easily be implemented into computer programs for numerical analysis with Trefftz finite element method. Two numerical examples are considered to illustrate the effectiveness and applicability of the proposed element model.     

Quadrature element analysis of planar frameworks

The recently proposed weak form quadrature element method (QEM) is extended to the analysis of planar frameworks which are characterized by C1 continuity. Weak form quadrature elements for planar frameworks are developed. Examples are presented and comparison with the results of the finite element method is made to demonstrate the effectiveness and high computational efficiency of the QEM.