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1.
In some previous geometric nonlinear finite element formulations, due to the use of axial displacement, the contribution of
all the elements lying between the reference node of zero axial displacement and the element to the foreshortening effect
should be taken into account. In this paper, a finite element formulation is proposed based on geometric nonlinear elastic
theory and finite element technique. The coupling deformation terms of an arbitrary point only relate to the nodal coordinates
of the element at which the point is located. Based on Hamilton principle, dynamic equations of elastic beams undergoing large
overall motions are derived. To investigate the effect of coupling deformation terms on system dynamic characters and reduce
the dynamic equations, a complete dynamic model and three reduced models of hub-beam are prospected. When the Cartesian deformation
coordinates are adopted, the results indicate that the terms related to the coupling deformation in the inertia forces of
dynamic equations have small effect on system dynamic behavior and may be neglected, whereas the terms related to coupling
deformation in the elastic forces are important for system dynamic behavior and should be considered in dynamic equation.
Numerical examples of the rotating beam and flexible beam system are carried out to demonstrate the accuracy and validity
of this dynamic model. Furthermore, it is shown that a small number of finite elements are needed to obtain a stable solution
using the present coupling finite element formulation. 相似文献
2.
《Computers & Structures》2003,81(8-11):655-671
A method is presented for the solution of the incompressible fluid flow equations using a Lagrangian formulation. The interpolation functions are those used in the meshless finite element method and the time integration is introduced in a semi-implicit way by a fractional step method. Classical stabilization terms used in the momentum equations are unnecessary due to the lack of convective terms in the Lagrangian formulation. Furthermore, the Lagrangian formulation simplifies the connections with fixed or moving solid structures, thus providing a very easy way to solve fluid–structure interaction problems. 相似文献
3.
A numerical model is presented for simulating single or two-phase flow and energy transport in hydrothermal reservoirs. The model is formulated via two non-linear equations for fluid pressure and enthalpy. Both equations are solved simultaneously using a new finite element technique which employs asymmetric weighting functions to overcome numerical oscillation. Non-linearity is treated by a modified Newton-Raphson scheme which takes into account derivative discontinuities in the non-linear coefficients. This scheme also treats unknown flux boundary conditions inplicitly, thus allowing larger time steps to be taken without inducing instability. The proposed model is applied to two test examples involving one-dimensional flow in both hot water and steam dominated reservoirs. Results indicate that the numerical technique presented is efficient and the model can be used to simulate both types of reservoirs. 相似文献
4.
The laminar boundary layer equations for the compressible flow due to the finite difference in rotation and temperature rates are solved for the case of uniform suction through the disk. The effects of viscous dissipation on the incompressible flow are taken into account for any rotation rate, whereas for a compressible fluid they are considered only for a disk rotating in a stationary fluid. For the general case, the governing equations are solved numerically using a standard finite element scheme. Series solutions are developed for those cases where the suction effect is dominant. Based on the above analytical and numerical solutions, a new asymptotic finite element scheme is presented. By using this scheme one can significantly improve the pointwise accuracy of the standard finite element scheme. 相似文献
5.
This paper assesses the use of a potential-based fluid finite element formulation to investigate earthquake excited dam–reservoir systems. The mathematical background of the analytical and numerical techniques is presented in a unified format. Frequency and time-domain analyses are conducted to validate the potential-based finite element formulation. A case study of a typical dam–reservoir system subjected to earthquake loading is presented. The dynamic response of the system is discussed to illustrate the effects of fluid–structure interaction and reservoir bottom absorption. The validated potential-based fluid elements and boundary conditions are shown to perform adequately for practical seismic analysis of dam–reservoir systems. 相似文献
6.
对热载荷作用下中心刚体与大变形薄板多体系统的动力学建模问题进行研究.基于Kirchhoff假设,从格林应变和曲率与绝对位移的非线性关系式出发,推导了非线性广义弹性力阵,用绝对节点坐标法建立了大变形矩形薄板的有限元离散的动力学变分方程.为了考虑刚体姿态运动、弹性变形和温度变化的相互耦合作用,推导了热流密度与绝对节点坐标之间的关系式.引入系统的运动学约束方程,建立了中心刚体-矩形板多体系统的考虑刚-柔-热耦合的热传导方程和带拉格朗日乘子的第一类拉格朗日动力学方程.为了有效地提高计算效率,将改进的中心差分法和广义-α法相结合,求解热传导方程和动力学方程,差分后的方程通过牛顿迭代法耦合求解.对刚-柔耦合和刚-柔-热三者耦合两种模型的仿真结果进行比较表明,刚体运动对温度梯度和热变形的影响显著.此外,本文建模方法考虑了几何非线性项,因此也考虑了热膨胀引起的轴向变形对横向变形的影响. 相似文献
7.
《Advances in Engineering Software》2005,36(10):664-680
The non-Newtonian effects in the flow of non-Newtonian fluids that can be modelled with generalised Newtonian constitutive equations are investigated using a numerical scheme based on the finite volume formulation. Collocated arrangement of variables is used and the pressure-correction method in conjunction with the SIMPLE scheme is applied. In order to avoid the diffusive effects of low order schemes, the approximation of the convection terms is carried out using the QUICK differencing scheme, which is of third order of accuracy. For modelling viscous non-Newtonian behaviour, the Power-Law, Quemada and the modified Bingham and Casson models are employed. Validation of the code is carried out upon comparison with numerical data available in the literature. Exploiting the lid-driven cavity flow a twofold investigation is carried out regarding the non-Newtonian effects first by using different models and secondly by using the shear-thinning and shear-thickening attributes of the fluid. 相似文献
8.
Conventional Lagrangian and Eulerian type formulation methods are applied to simulate some metal forming processes. These formulations possess certain difficulties when applied to finite strain deformation problems, especially when boundary conditions need to be updated during the course of deformation. An Arbitrary Lagrangian-Eulerian (ALE) formulation method is employed to overcome these difficulties. This paper presents an efficient mesh motion scheme for the ALE formulation method. A practical and more efficient scheme for handling supplementary constraint equations, arising from mesh motion algorithms, on the element level is presented. A procedure for handling boundary motion within the scheme and ensuring homogeneous mesh results is described. The presented scheme is employed to simulate punch forging and plane strain metal extrusion processes. 相似文献
9.
Harold S. Park Michel Devel Zhao Wang 《Computer Methods in Applied Mechanics and Engineering》2011,200(29-32):2447-2457
We present a new multiscale, finite deformation, electromechanical formulation to capture the response of surface-dominated nanomaterials to externally applied electric fields. To do so, we develop and discretize a total energy that combines both mechanical and electrostatic terms, where the mechanical potential energy is derived from any standard interatomic atomistic potential, and where the electrostatic potential energy is derived using a Gaussian-dipole approach. By utilizing Cauchy–Born kinematics, we derive both the bulk and surface electrostatic Piola–Kirchhoff stresses that are required to evaluate the resulting electromechanical finite element equilibrium equations, where the surface Piola–Kirchhoff stress enables us to capture the non-bulk electric field-driven polarization of atoms near the surfaces of nanomaterials. Because we minimize a total energy, the present formulation has distinct advantages as compared to previous approaches, where in particular, only one governing equation is required to be solved. This is in contrast to previous approaches which require either the staggered or monolithic solution of both the mechanical and electrostatic equations, along with coupling terms that link the two domains. The present approach thus leads to a significant reduction in computational expense both in terms of fewer equations to solve and also in eliminating the need to remesh either the mechanical or electrostatic domains due to being based on a total Lagrangian formulation. Though the approach can apply to three-dimensional cases, we concentrate in this paper on the one-dimensional case. We first derive the necessary formulas, then give numerical examples to validate the proposed approach in comparison to fully atomistic electromechanical calculations. 相似文献
10.
《Computer Methods in Applied Mechanics and Engineering》2002,191(13-14):1491-1503
This paper presents a higher order stabilized finite element formulation for hyperelastic large deformation problems involving incompressible or nearly incompressible materials. A Lagrangian finite element formulation is presented where mesh dependent terms are added element-wise to enhance the stability of the mixed finite element formulation. A reconstruction method based on local projections is used to compute the higher order derivatives that arise in the stabilization terms, specifically derivatives of the stress tensor. Linearization of the weak form is derived to enable a Newton–Raphson solution procedure of the resulting non-linear equations. Numerical experiments using the stabilization method with equal order shape functions for the displacement and pressure fields in hyperelastic problems show that the stabilized method is effective for some non-linear finite deformation problems. Finally, conclusions are inferred and extensions of this work are discussed. 相似文献
11.
A pseudospectral method for the calculation of 2-D flows of a viscous incompressible fluid in curvilinear domains is presented. The incompressible Navier-Stokes equations, expressed in terms of the primitive variables velocity and pressure, are solved in a non-orthogonal coordinate system. All the variables are expanded in double truncated series of Chebyshev polynomials. Time integration is performed by an implicit finite differences scheme for both the advective and diffusive terms. The pressure is calculated by the use of a truncated influence matrix involving all the collocation points in the field. A preconditioned iterative method is used to solve the system of linear equations resulting from the pseudospectral Chebyshev approximation. The algorithm is applied to the classical problem of the Green-Taylor vortices in order to check its accuracy; then 2 examples of viscous flow calculation are given in the case of a driven polar cavity and of a 2-D channel. 相似文献
12.
Zong-Kang Wang Georgi Djambazov Choi-Hong Lai Koulis Pericleous 《Computing and Visualization in Science》2007,10(3):123-134
The generation and near-field radiation of aerodynamic sound from a low-speed unsteady flow over a two-dimensional automobile
door cavity is simulated by using a source-extraction-based coupling method. In the coupling procedure, the unsteady cavity
flow field is first computed solving the Reynolds- averaged Navier–Stokes (RANS) equations. The radiated sound is then calculated
by using a set of acoustic perturbation equations with acoustic source terms which are extracted from the time-dependent solutions
of the unsteady flow. The aerodynamic and its resulting acoustic field are computed for the Reynolds number of 53,266 based
on the base length of the cavity. The free stream flow velocity is taken to be 50.9 m/s. As first stage of the numerical investigation
of flow-induced cavity noise, laminar flow is assumed. The CFD solver is based on a cell-centered finite volume method. A
dispersion-relation-preserving (DRP), optimized, fourth-order finite difference scheme with fully staggered-grid implementation
is used in the acoustic solver. 相似文献
13.
Leonardo E. Figueroa Gabriel N. Gatica Norbert Heuer 《Computer Methods in Applied Mechanics and Engineering》2008,198(2):280-291
In this paper we extend recent results on the a priori and a posteriori error analysis of an augmented mixed finite element method for the linear elasticity problem, to the case of incompressible fluid flows with symmetric stress tensor. Similarly as before, the present approach is based on the introduction of the Galerkin least-squares type terms arising from the constitutive and equilibrium equations, and from the relations defining the pressure in terms of the stress tensor and the rotation in terms of the displacement, all of them multiplied by stabilization parameters. We show that these parameters can be suitably chosen so that the resulting augmented variational formulation is defined by a strongly coercive bilinear form, whence the associated Galerkin scheme becomes well-posed for any choice of finite element subspaces. Next, we present a reliable and efficient residual-based a posteriori error estimator for the augmented mixed finite element scheme. Finally, several numerical results confirming the theoretical properties of this estimator, and illustrating the capability of the corresponding adaptive algorithm to localize the singularities and the large stress regions of the solution, are reported. 相似文献
14.
研究温度场中旋转刚体-梁系统的刚-柔耦合动力学特性.考虑几何非线性和热效应,从精确的应变-位移关系式出发,用虚功原理和有限单元法建立了旋转刚体-梁系统的刚-柔耦合动力学方程.由于非线性刚度阵与变形的高次项有关,将非线性刚度阵的各元素表示为广义坐标阵和常值阵的乘积.数值计算表明,该方法可避免重复积分,提高计算效率.在此基础上研究了在温度递增的情况下几何非线性对系统的刚-柔耦合动力学特性的影响,用频谱分析方法研究了系统的固有频率随中心刚体转动惯量和温度的变化. 相似文献
15.
P. Wapperom M. F. Webster 《Computer Methods in Applied Mechanics and Engineering》1999,180(3-4):281-304
Stability of a second-order finite element/finite volume (FE/FV) hybrid scheme is investigated on the basis of flows with increasing Weissenberg number. FEs are used to discretise the balances of mass and momentum. For the stress equation a FV method is used, based on the recent development with fluctuation distribution schemes for pure convection problems. Examples considered include a start-up channel flow, flow past a cylinder and the non-smooth 4:1 contraction flow for an Oldroyd-B fluid. A considerable gain in efficiency per time step can be obtained compared to an alternative pure FE implementation. A distribution based on the flux terms is unstable for higher Weissenberg numbers, and this is also true for a distribution based on source terms alone. The instability is identified as being caused by the interaction of the balance equations and stress equation. A combination of distribution schemes based on flux and source terms, however, gives a considerable improvement to the hybrid FE/FV implementation. With respect to limiting Weissenberg number attenuation, the hybrid scheme is more stable than the pure FE alternative for the smooth flow past a cylinder, but less so for the non-smooth contraction flow. The influence of additional strain-rate stabilisation techniques is also analysed and found to be beneficial. 相似文献
16.
Carlos V. Alonzo 《Computers & Fluids》1973,1(3):301-315
A method is presented for the finite difference solution of the equations of fluid motion. The complete Navier-Stokes equations are expressed in terms of tangential velocity, vorticity and stream function. The transformed equations are solved using an alternating direction implicit scheme. The classical problem of hydrodynamic stability of the rotational Couette flow is solved in two dimensions. Comparison with other numerical and experimental works shows that the method reported here is computationally stable, even when used with coarse grids and relatively large time increments. 相似文献
17.
This work presents a finite element formulation of equations proposed in a companion paper to describe the hyperelastic response of three-phase porous media. Attention is paid to the development of consistent tangents required by the Newton–Raphson procedure used to solve the highly non-linear finite element equations. Among several sources of non-linearity, we also model the permeability dependence on strain as typically observed in intensely jointed rock masses, thus introducing a further reason of hydro-mechanical coupling. Several numerical examples are presented to validate the considered poro-elastic laws and to assess the performance of the numerical formulation. These tests include comparisons with available experimental data relative to a sand column desaturation and with the Philip’s analytical solution for the propagation of a saturation front in an initially dry porous solid. Finally, the formulation is applied to problems of interest for dam engineering, namely the simulation of reservoir bank response to rapid drawdown and a three-dimensional study of concrete gravity dam interaction with foundation and abutment rock masses during reservoir operation. 相似文献
18.
P.R.F. Teixeira 《Computers & Fluids》2005,34(2):249-273
19.
In this paper the numerical approximation of a two-dimensional fluid–structure interaction problem is addressed. The fully coupled formulation of incompressible viscous fluid flow interacting with a flexibly supported airfoil is considered. The flow is described by the incompressible system of Navier–Stokes equations, where large values of the Reynolds number are considered. The Navier–Stokes equations are spatially discretized by the finite element method and stabilized with a modification of the Galerkin Least Squares (GLS) method; cf. [T. Gelhard, G. Lube, M.A. Olshanskii, J.-H. Starcke, Stabilized finite element schemes with LBB-stable elements for incompressible flows, Journal of Computational and Applied Mathematics 177 (2005) 243–267]. The motion of the computational domain is treated with the aid of Arbitrary Lagrangian Eulerian (ALE) method and the stabilizing terms are modified in a consistent way with the ALE formulation. 相似文献
20.
Christian Lundgaard Joe Alexandersen Mingdong Zhou Casper Schousboe Andreasen Ole Sigmund 《Structural and Multidisciplinary Optimization》2018,58(3):969-995
This study revisits the application of density-based topology optimization to fluid-structure-interaction problems. The Navier-Cauchy and Navier-Stokes equations are discretized using the finite element method and solved in a unified formulation. The physical modeling is limited to two dimensions, steady state, the influence of the structural deformations on the fluid flow is assumed negligible, and the structural and fluid properties are assumed constant. The optimization is based on adjoint sensitivity analysis and a robust formulation ensuring length-scale control and 0/1 designs. It is shown, that non-physical free-floating islands of solid elements can be removed by combining different objective functions in a weighted multi-objective formulation. The framework is tested for low and moderate Reynolds numbers on problems similar to previous works in the literature and two new flow mechanism problems. The optimized designs are consistent with respect to benchmark examples and the coupling between the fluid flow, the elastic structure and the optimization problem is clearly captured and illustrated in the optimized designs. The study reveals new features of topology optimization of FSI problems and may provide guidance for future research within the field. 相似文献