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1.
    
We present the development of a two‐dimensional Mixed‐Hybrid Finite Element (MHFE) model for the solution of the non‐linear equation of variably saturated flow in groundwater on unstructured triangular meshes. By this approach the Darcy velocity is approximated using lowest‐order Raviart–Thomas (RT0) elements and is ‘exactly’ mass conserving. Hybridization is used to overcome the ill‐conditioning of the mixed system. The scheme is globally first‐order in space. Nevertheless, numerical results employing non‐uniform meshes show second‐order accuracy of the pressure head and normal fluxes on specific grid points. The non‐linear systems of algebraic equations resulting from the MHFE discretization are solved using Picard or Newton iterations. Realistic sample tests show that the MHFE‐Newton approach achieves fast convergence in many situations, in particular, when a good initial guess is provided by either the Picard scheme or relaxation techniques. Copyright © 1999 John Wiley & Sons, Ltd.  相似文献   

2.
    
This article advocates a general procedure for the numerical investigation of pseudo‐rigid bodies. The equations of motion for pseudo‐rigid bodies are shown to be mathematically equivalent to those corresponding to certain constant‐strain finite element approximations for general deformable continua. A straightforward algorithmic implementation is achieved in a classical finite element framework. Also, a penalty formulation is suggested for modelling contact between pseudo‐rigid bodies. Representative planar simulations using a non‐linear elastic model demonstrate the predictive capacity of the pseudo‐rigid theory, as well as the robustness of the proposed computational procedure. Copyright © 1999 John Wiley & Sons, Ltd.  相似文献   

3.
    
This paper presents two algorithms for solving the discrete, quasi-static, small-displacement, linear elastic, contact problem with Coulomb friction. The algorithms are adoptions of a Newton method for solving B-differentiable equations and an interior point method for solving smooth, constrained equations. For the application of the former method, the contact problem is formulated as a system of B-differentiable equations involving the projection operator onto sets with simple structure; for the application of the latter method, the contact problem is formulated as a system of smooth equations involving complementarity conditions and with the non-negativity of variables treated as constraints. The two algorithms are numerically tested for two-dimensional problems containing up to 100 contact nodes and up to 100 time increments. Results show that at the present stage of development, the Newton method is superior both in robustness and speed. Additional comparison is made with a commercial finite element code. © 1998 John Wiley & Sons, Ltd.  相似文献   

4.
    
This paper presents a numerical method to solve the forward position problem in spatial mechanisms. The method may be incorporated in a software for the kinematic analysis of mechanisms, where the procedure is systematic and can be easily implemented, achieving a high degree of automation in simulation. The procedure presents high computational efficiency, enabling its incorporation in the control loop to solve the forward position problem in the case of a velocity control scheme. Also, in this paper preliminary results on the convergence of the proposed procedure are shown, and efficiency results of the method applied to representative spatial mechanisms are presented. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

5.
A three-dimensional finite-volume/Newton method is developed for solving thermal-capillary problems in materials processing. The conductive heat transfer, melt–solid interfaces, the melt–gas free surface, and the shape of grown material are calculated simultaneously. The implementation of interface and free surface boundary conditions, as well as co-ordinate transformation, is described in detail. During the Newton iterations, due to the complexity of the problem, the Jacobian matrix is estimated by finite differences, and the linear equations are solved by the ILU(0) preconditioned GMRES iterative method. Nearly quadratic convergence of the scheme is achieved. Sample calculations for floating-zone and Stepanov crystal growth are illustrated. © 1997 by John Wiley & Sons, Ltd.  相似文献   

6.
    
In this paper, we present a numerical algorithm based on group theory and numerical optimization to compute efficient quadrature rules for integration of bivariate polynomials over arbitrary polygons. These quadratures have desirable properties such as positivity of weights and interiority of nodes and can readily be used as software libraries where numerical integration within planar polygons is required. We have used this algorithm for the construction of symmetric and non‐symmetric quadrature rules over convex and concave polygons. While in the case of symmetric quadratures our results are comparable to available rules, the proposed algorithm has the advantage of being flexible enough so that it can be applied to arbitrary planar regions for the integration of generalized classes of functions. To demonstrate the efficiency of the new quadrature rules, we have tested them for the integration of rational polygonal shape functions over a regular hexagon. For a relative error of 10?8 in the computation of stiffness matrix entries, one needs at least 198 evaluation points when the region is partitioned, whereas 85 points suffice with our quadrature rule. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

7.
A generalized Newton method is proposed in conjunction with a higher-order Lagrangian finite element discretization of bodies undergoing finite elastic deformations. The method is based on a gradient-like modification of the Newton method, designed to suppress the sensitivity of higher-order elements during the early iterations, thus allowing for solutions to be obtained using moderately large step-sizes.  相似文献   

8.
在文献[1]中,本文作者研究了正交各向异性平面问题边界元素法的有关基本理论和计算公式,在上述工作的基础上,本文进一步研究各向异性平面问题边界邻域的应力分析。当采用边界元素法分析应力时,由于边界积分的奇异性,边界邻域应力的计算结果往往存在一定误差。为解决此问题,本文提出一个基于修正余能原理的所谓边境元素,包括四节点边境元素、八节点边境元素和三节点边境元素等。在边界元素法求解的基础上,进一步利用本文所述边境元素法,得到了非常满意的计算结果。   相似文献   

9.
    
We propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piecewise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear and nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

10.
    
Verification of the computation of local quantities of interest, e.g. the displacements at a point, the stresses in a local area and the stress intensity factors at crack tips, plays an important role in improving the structural design for safety. In this paper, the smoothed finite element method (SFEM) is used for finding upper and lower bounds on the local quantities of interest that are outputs of the displacement field for linear elasticity problems, based on bounds on strain energy in both the primal and dual problems. One important feature of SFEM is that it bounds the strain energy of the structure from above without needing the solutions of different subproblems that are based on elements or patches but only requires the direct finite element computation. Upper and lower bounds on two linear outputs and one quadratic output related with elasticity—the local reaction, the local displacement and the J‐integral—are computed by the proposed method in two different examples. Some issues with SFEM that remain to be resolved are also discussed. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

11.
    
This paper proposes a generalized finite element method based on the use of parametric solutions as enrichment functions. These parametric solutions are precomputed off‐line and stored in memory in the form of a computational vademecum so that they can be used on‐line with negligible cost. This renders a more efficient computational method than traditional finite element methods at performing simulations of processes. One key issue of the proposed method is the efficient computation of the parametric enrichments. These are computed and efficiently stored in memory by employing proper generalized decompositions. Although the presented method can be broadly applied, it is particularly well suited in manufacturing processes involving localized physics that depend on many parameters, such as welding. After introducing the vademecum‐generalized finite element method formulation, we present some numerical examples related to the simulation of thermal models encountered in welding processes. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

12.
    
A numerical method is presented for solving systems of non‐linear equations that contain some variables that are strictly positive and others that have no restriction on sign. Naturally positive variables arise frequently when modelling the behaviour of engineering systems, such as physical dimension, concentration of a chemical species, duration of an event, etc. When modelling systems of this type, it is also common to introduce additional variables that are not restricted in sign, such as stresses, displacements, velocities, accelerations, etc. Many numerical methods may experience performance difficulties due to the existence of spurious solutions which have negative components for one or more of the positive variables. Recently, the monomial method has been developed as an effective tool for systems with variables that are all strictly positive. This paper presents a hybrid method, combining the monomial method and Newton's method, for systems containing both types of variables. It is demonstrated that this hybrid method can be more effective in solving systems of equations with both positive and free variables than either method alone. Basins of attraction constructions are presented as a demonstration of the effectiveness of the hybrid method as applied to the design of a civil engineering frame structure. Copyright © 1999 John Wiley & Sons, Ltd.  相似文献   

13.
    
An advanced boundary element method (BEM) for solving two‐ (2D) and three‐dimensional (3D) problems in materials with microstructural effects is presented. The analysis is performed in the context of Mindlin's Form‐II gradient elastic theory. The fundamental solution of the equilibrium partial differential equation is explicitly derived. The integral representation of the problem, consisting of two boundary integral equations, one for displacements and the other for its normal derivative, is developed. The global boundary of the analyzed domain is discretized into quadratic line and quadrilateral elements for 2D and 3D problems, respectively. Representative 2D and 3D numerical examples are presented to illustrate the method, demonstrate its accuracy and efficiency and assess the gradient effect on the response. The importance of satisfying the correct boundary conditions in gradient elastic problems is illustrated with the solution of simple 2D problems. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

14.
    
This contribution presents a hierarchical variational multiscale framework to model propagating discontinuities at finite strains. Thereby the deformation map is decomposed into coarse‐scale and fine‐scale displacements, which results in a decoupled system of coarse‐scale and fine‐scale equations. Both are solved numerically by means of the finite element method whereby crack propagation is taken into account at the fine scale. Growing cracks are numerically handled by the introduction of discontinuous elements. A locality assumption on the fine‐scale solution and an adaptive scheme to resize the fine‐scale domain are introduced and demonstrated to increase the efficiency of the method. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

15.
    
Two real-domain numerical approximation methods for accurate computation of finite strain elasticity moduli are developed and their accuracy and computational efficiency are investigated, with reference to hyperelastic constitutive models with known analytical solutions. The methods are higher-order and higher floating-point precision numerical approximation, the latter being novel in this context. A general formula for higher-order approximation finite difference schemes is derived and a new procedure is proposed to implement increased floating-point precision. The accuracy of the approximated elasticity moduli is investigated numerically using higher-order approximations in standard double precision and increased quadruple precision. It is found that, as the order of the approximation increases, the elasticity moduli tend toward the analytical solution. Using higher floating-point precision, the approximated elasticity moduli for all orders of approximation are found to be more accurate than the standard double precision evaluation of the analytical moduli. Application of the techniques to a finite element problem shows that the numerically approximated methods obtain convergence equivalent to the analytical method but require greater computational effort. It is concluded that numerical approximation of elasticity moduli is a powerful and effective means of implementing advanced constitutive models in the finite element method without prior derivation of difficult analytical solutions.  相似文献   

16.
    
A method for structural dynamic contact problems with friction and wear is suggested. The method is obtained by including wear in the non‐smooth contact dynamics method of Moreau. A comparison of the method to the discrete energy‐momentum method of Simo and Tarnow is also outlined briefly. The fully discrete equations are treated using the augmented Lagrangian approach, where a non‐smooth Newton method is used as the equation solver. Two two‐dimensional examples are solved by the method. It is investigated how solutions of contact, friction and wear are influenced by inertia. It is shown that the quasi‐static assumption might be questionable for solving contact problems with friction and wear. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

17.
严旭  高琦  程茜  周红生  徐峥 《声学技术》2017,36(5):410-414
生物试样的弹性测量可为生物体疾病的早期诊断和治疗提供依据。利用压痕法对生物试样的弹性进行了测量,并用有限元软件对压痕过程进行了模拟。研究发现,试样厚度对弹性测量存在影响,试样厚度越大,测量结果越接近试样真实的杨氏模量。当试样厚度为压痕深度的75倍时,测量误差仅为0.74%。又研究了压头速度对弹性测量结果的影响。研究发现,当压头速度较大时,由于摩擦力的作用,测量结果与试样弹性的真实值之间存在一定的差异。在模拟过程中添加摩擦力可准确反演试样的弹性,误差在5%以下。  相似文献   

18.
The symmetric Galerkin boundary element method is used to solve boundary value problems by keeping the symmetric nature of the matrix obtained after discretization. The matrix elements are obtained from a double integral involving the double derivative of Green's operator, which is highly singular. The paper presents a regularization of the hypersingular integrals which depend only on the properties of Green's tensor. The method is presented in the case of Laplace's operator, with an example of application. The case of elasticity is finally addressed theoretically, showing an easy extension to any case of anisotropy. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

19.
A Finite Volume (FV) procedure is described for solving the elastic solid mechanics equations in three dimensions on an unstructured mesh, for bodies undergoing thermal or mechanical loads. The FV procedure is developed in parallel with the conventional FE Galerkin procedure so that the differences in each approach may be clearly distinguished. The matrix form of the FV procedure is described, and is implemented in parallel with the FE procedure, both for two-dimensional quadrilateral and three-dimensional brick meshes. The FV and FE procedures are then compared against a range of benchmark problems that test the basic capability of the FV technique. It is shown to be approximately as accurate as the FE procedure on similar meshes, though its system matrix set-up time is twice as long for a node by node set-up procedure.  相似文献   

20.
    
This work introduces a semi‐analytical formulation for the simulation and modeling of curved structures based on the scaled boundary finite element method (SBFEM). This approach adapts the fundamental idea of the SBFEM concept to scale a boundary to describe a geometry. Until now, scaling in SBFEM has exclusively been performed along a straight coordinate that enlarges, shrinks, or shifts a given boundary. In this novel approach, scaling is based on a polar or cylindrical coordinate system such that a boundary is shifted along a curved scaling direction. The derived formulations are used to compute the static and dynamic stiffness matrices of homogeneous curved structures. The resulting elements can be coupled to general SBFEM or FEM domains. For elastodynamic problems, computations are performed in the frequency domain. Results of this work are validated using the global matrix method and standard finite element analysis. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

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