P-version hybrid analytical finite element method for plate bending problems

Two sets of trial functions with different variables are constructed for the admissible space of the finite element analysis. The trial functions satisfy the equilibrium differential equation inside elements, while the deflections and rotations on the edges of the elements are approximated by the Peano hierarchical interpolation functions. Then, a generalized variational principle is applied to set up the p-version hybrid analytical finite element method for plate bending problems. The accuracy of finite element computation can be improved by increasing the order of the interpolation polynomials with fixed mesh. In the finite element formulation, to obtain the stiffness matrices and the load vectors, it is only necessary to perform quadrature over the edges of the elements. These matrices and vectors possess an embedding structure. The conformability between the elements can be controlled automatically.This work is supported by the Natural Science Foundation of China and the Aeronautical Science Foundation of China.     

板弯曲与平面弹性有限元的同一性

本文建立平面弹性与板弯曲的相似理论，并用于将平面弹性的单元移植到板弯曲元，从而其分片试验，收敛性等性质也同时移植到板弯曲元，使两者处于同一水平上，同时又将此基于力法的板弯曲元入位移法的轨道，找出共相应的位移系统，并证明其适定性，从而为将此类单元装入位移法通用程序系统创造了条件。     

Two-way coupled analysis of lithium diffusion and diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries

A fully coupling model for the diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries is proposed. The effect of the mechanical stress on the lithium diffusion is accounted for by the mechanical part of the chemical potential derived from the Gibbs free energy along with the logarithmic stress and strain. Eight dimensionless parameters, governing the stress-assisted diffusion and the diffusion induced elastoplastic bending, are identified. It is found that the finite plasticity starting from the interface of the bilayer increases the chemical potential gradient and thereby facilitates the lithium diffusion. The full plastic flow makes the abnormal lithium concentration distribution possible, i.e., the concentration at the lithium inlet can be lower than the concentration at the interface (downstream). The increase in the thickness of the active layer during charging is much larger than the eigen-stretch due to lithiation, and this excess thickening is found to be caused by the lithiation induced plastic yield.     

金属板条在圆柱形模中弯曲成形的大变形有限元分析

本文采用大变形弹塑性有限元法对金属板条在柱形模中的压弯成形过程进行了数值模拟,并与实验进行了比较。首先给出了纠正的拉格朗日有限元公式和基于弹塑性乘法分解的超弹性塑性本构关系。对接触摩擦问题的处理采用了罚函数法。通过对数值结果的分析得出了一些对弯曲工艺的设计有指导价值的结论。     

A finite difference method at arbitrary meshes for the bending of plates with variable thickness

A finite difference method at arbitrary meshes for the bending of plates with variable thickness is presented in this paper.The method is completely general with respect to various boundary conditions,load cases and shapes of plates.This difference scheme is simple and the numerical results agree well with those obtained by other methods.     

有初应力钢筋混凝土压弯扭构件非线性有限元分析

钢管初应力是钢管混凝土在大跨度桥梁,高层超高层建筑应用中广大工程技术人员关心的问题,本文在钢材随动强化模型和混凝土边界模型的基础上编制了计算有初应力的钢管钢混凝压弯扭构件全过程曲线的非线性有元程序。     

Transient analysis of Cosserat rod with inextensibility and unshearability constraints using the least-squares finite element model

In this study, time-dependent fully discretized least-squares finite element model is developed for the transient response of Cosserat rod having inextensibility and unshearability constraints to simulate a surgical thread in space. Starting from the kinematics of the rod for large deformation, the linear and angular momentum equations along with constraint conditions for the sake of completeness are derived. Then, the α-family of time derivarive approximation is used to reduce the governing equations of motion to obtain a semi-discretized system of equations, which are then fully discretized using the least-squares approach to obtain the non-linear finite element equations. Newton׳s method is utilized to solve the non-linear finite element equations. Dynamic response due to impulse force and time-dependent follower force at the free end of the rod is presented as numerical examples.     

两性pH敏感凝胶瞬态溶胀问题的基本方程和数值解

聚电解质两性凝胶的侧链有可电离的酸性和碱性基团,因其能对所处溶液环境的pH值产生响应,又可称作两性pH敏感凝胶．两性pH敏感凝胶属于超弹性材料,其变形问题涉及力学-化学耦合．同时,由于凝胶的变形伴随着溶剂分子的迁移,导致变形不能瞬间完成,故应研究两性pH敏感凝胶变形发展的全过程．由于其实用价值高,研究难度大,两性pH敏感凝胶的瞬态溶胀问题近年来引起了国内外众多研究人员的关注．本文以非线性连续介质力学理论和孔隙弹性理论为基础,结合电离平衡、唐南平衡等条件,获得了能描述两性pH敏感凝胶材料在外界激励下形变发展全过程的基本方程,探究了外加载荷、溶液pH值、盐溶液浓度等因素对两性pH敏感凝胶瞬态溶胀的影响,所得结果对该材料的应用有一定参考价值．     

Differential quadrature method for bending of orthotropic plates with finite deformation and transverse shear effects

Based on the Reddy ‘s theory of plates with the effect of higher-order shear deformations, the governing equations for bending of orthotropic plates with finite deformations were established. The differential quadrature ( DQ ) method of nonlinear analysis to the problem was presented. New DQ approach, presented by Wang and Bert ( DQWB), is extended to handle the multiple boundary conditions of plates. The techniques were also further extended to simplify nonlinear computations. The numerical convergence and comparison of solutions were studied. The results show that the DQ method presented is very reliable and valid. Moreover, the influences of geometric and material parameters as well as the transverse shear deformations on nonlinear bending were investigated. Numerical results show the influence of the shear deformation on the static bending of orthotropic moderately thick plate is significant.     

Nonlinear vibration analysis of piezoelectric bending actuators: Theoretical and experimental studies

Piezoelectric bimorph actuators are used in a variety of applications, including micro positioning, vibration control, and micro robotics. The nature of the aforementioned applications calls for the dynamic characteristics identification of actuator at the embodiment design stage. For decades, many linear models have been presented to describe the dynamic behavior of this type of actuators; however, in many situations, such as resonant actuation, the piezoelectric actuators exhibit a softening nonlinear behavior; hence, an accurate dynamic model is demanded to properly predict the nonlinearity. In this study, first, the nonlinear stress–strain relationship of a piezoelectric material at high frequencies is modified. Then, based on the obtained constitutive equations and Euler–Bernoulli beam theory, a continuous nonlinear dynamic model for a piezoelectric bending actuator is presented. Next, the method of multiple scales is used to solve the discretized nonlinear differential equations. Finally, the results are compared with the ones obtained experimentally and nonlinear parameters are identified considering frequency response and phase response simultaneously. Also, in order to evaluate the accuracy of the proposed model, it is tested out of the identification range as well.     

Simulation of parametric ship rolling: Effects of hull bending and torsional elasticity

An enhanced mechanical model for simulating ship body oscillations and both the induced fluxural and twisting vibrations of the hull in the case of longitudinal seas is presented. The onset of parametric rolling, which may result from nonlinearly coupled heave-pitch-roll motions, and the effects of bending and torsional elasticity of the hull are considered in detail. It is shown that in the above sea conditions the flexural and/or twisting vibrations are likely to occur under a mechanism similar to that of parametric rolling.     

基于第二类四边形面积坐标的弹性力学纯弯解及MacNeal局限定理的破解

为了提高有限元的性能,弹性力学的解析解(齐次方程的通解)常常可用作有限元的试探函数。然而单元自由度数与完备的直角坐标解析解个数并不匹配,不完备的试函数会导致单元有方向依赖性。利用新型局部自然坐标——第二类四边形面积坐标QACM-II(S,T),给出了平面问题对应任意方向纯弯曲状态的应力函数解析解,即S3和T3的线性组合,并推导出了这两组应力函数对应的应力、应变和位移解析解。之后,利用QACM-II表示的解析解构造了非对称的平面4节点8自由度单元USQ4,该单元可以同时通过常应力/应变分片检验和纯弯测试,从而破解了MacNeal局限定理对平面低阶单元的限制。     

Three‐dimensional finite element analysis of transient fluid flow with free‐surface using marker surface method and adaptive grid refinement

For three‐dimensional finite element analysis of transient fluid flow with free‐surface, a new marker surface method is proposed, in which the fluid flow is represented by the marker surface composed of marker elements instead of marker particles used in the marker particle method. This also involves an adaptive grid that is created under a new criterion of element categorization of filling states and the locations in the total region at each time step. The marker surface is used in order to represent the free‐surface accurately, as well as to decrease the memory and computation time, and to effectively display the predicted three‐dimensional free‐surface. By using the adaptive grid in which the elements, finer than those in internal and external regions, are distributed in the surface region through refinement and coarsening procedures, the analysis of three‐dimensional transient fluid flow with free‐surface is achieved more efficiently. Through three‐dimensional analysis of two kinds of problems using several grids, the efficiency of the proposed marker surface method and the adaptive grid are verified. Copyright © 1999 John Wiley & Sons, Ltd.     

损伤因素对单层平面索网静力性能影响研究：有限元分析与试验验证

运用通用有限元软件ANSYS建立三维有限元模型,对横索与竖索连接节点失效、索预应力损失和锚固端失效这三种损伤因素的不同损伤工况下,单层平面索网结构的受力性能进行了非线性有限元分析,并与相应的试验结果进行了全面对比分析。结果表明：本文的有限元模型能够准确地分析计算上述三种损伤因素对单层平面索网结构受力性能的影响,包括结构...     

MPI+X: task-based parallelisation and dynamic load balance of finite element assembly

The main computing phases of numerical methods for solving partial differential equations are the algebraic system assembly and the iterative solver. This work focuses on the first task, in the context of a hybrid MPI+X paradigm. The matrix assembly consists of a loop over the elements, faces, edges or nodes of the MPI partitions to compute element matrices and vectors and then of their assemblies. In a MPI+X hybrid parallelism context, X has consisted traditionally of loop parallelism using OpenMP, with different techniques to avoid the race condition, but presenting efficiency or implementation drawbacks. We propose an alternative, based on task parallelism using some extensions to the OpenMP programming model. In addition, dynamic load balance will be applied, especially efficient in the presence of hybrid meshes. This paper presents the proposed methodology, its implementation and its validation through the solution of large computational mechanics problems up to 16k cores.     

Three‐dimensional finite element modelling of coupled free/porous flows: applications to industrial and environmental flows

Conjunctive modelling of free/porous flows provides a powerful and cost‐effective tool for designing industrial filters used in the process industry and also for quantifying surface–subsurface flow interactions, which play a significant role in urban flooding mechanisms resulting from sea‐level rise and climate changes. A number of well‐established schemes are available in the literature for simulation of such regimes; however, three‐dimensional (3D) modelling of such flow systems still presents numerical and practical challenges. This paper presents the development of a fully 3D, transient finite element model for the prediction and quantitative analyses of the hydrodynamic behaviour encountered in industrial filtrations and environmental flows represented by coupled flows. The weak‐variational formulation in this model is based on the use of C⁰ continuous equal‐order Lagrange polynomial functions for velocity and pressure fields represented by 3D hexahedral finite elements. A mixed UVWP finite element scheme based on the standard Galerkin technique satisfying the Ladyzhenskaya–Babuska–Brezzi stability criterion through incorporation of an artificial compressibility term in the continuity equation has been employed for the solution of coupled partial differential equations. We prove that the discretization generates unified stabilization for both the Navier–Stokes and Darcy equations and preserves the geometrical flexibility of the computational grids. A direct node‐linking procedure involving the rearrangement of the global stiffness matrix for the interface elements has been developed by the authors, which is utilized to couple the governing equations in a single model. A variety of numerical tests are conducted, indicating that the model is capable of yielding theoretically expected and accurate results for free, porous and coupled free/porous problems encountered in industrial and environmental engineering problems representing complex filtration (dead‐end and cross‐flow) and interacting surface–subsurface flows. The model is computationally cost‐effective, robust, reliable and easily implementable for practical design of filtration equipments, investigation of land use for water resource availability and assessment of the impacts of climatic variations on environmental catastrophes (i.e. coastal and urban floods). The model developed in this work results from the extension of a multi‐disciplinary project (AEROFIL) primarily sponsored by the European aerospace industries for development of a computer simulation package (Aircraft Cartridge Filter Analysis Modelling Program), which was successfully utilized and deployed for designing hydraulic dead‐end filters used in Airbus A380.Copyright © 2012 John Wiley & Sons, Ltd.     

Comparative study of lattice‐Boltzmann and finite volume methods for the simulation of laminar flow through a 4:1 planar contraction

In the present paper, a comparative study of numerical solutions for Newtonian fluids based on the lattice‐Boltzmann method (LBM) and the classical finite volume method (FVM) is presented for the laminar flow through a 4:1 planar contraction at a Reynolds number of value one, Re=1. In this study, the stress field for LBM is directly obtained from the distribution function. The calculations of the stress based on the FVM‐data use the evaluations of velocity gradients with finite differences. The stress field for both LBM and FVM is expressed in the present study in terms of the shear stress and the first normal stress difference. The lateral and axial profiles of the velocity, the shear stress and the first normal stress difference for both methods are investigated. It is shown that the LBM results for the velocity and the stresses are in excellent agreement with the FVM results. Copyright © 2004 John Wiley & Sons, Ltd.     

A combined vortex and panel method for numerical simulations of viscous flows: a comparative study of a vortex particle method and a finite volume method

This paper describes and compares two vorticity‐based integral approaches for the solution of the incompressible Navier–Stokes equations. Either a Lagrangian vortex particle method or an Eulerian finite volume scheme is implemented to solve the vorticity transport equation with a vorticity boundary condition. The Biot–Savart integral is used to compute the velocity field from a vorticity distribution over a fluid domain. The vorticity boundary condition is improved by the use of an iteration scheme connected with the well‐established panel method. In the early stages of development of flows around an impulsively started circular cylinder, and past an impulsively started foil with varying angles of attack, the computational results obtained by the Lagrangian vortex method are compared with those obtained by the Eulerian finite volume method. The comparison is performed separately for the pressure fields as well. The results obtained by the two methods are in good agreement, and give a better understanding of the vorticity‐based methods. Copyright © 2005 John Wiley & Sons, Ltd.     

Internal wave reflections and transmissions arising from a non-uniform mesh. Part III: The occurrence of evanescent waves in the Crank-Nicolson linear finite element scheme

The numerical scheme upon which this paper is based is the 1D Crank–Nicolson linear finite element scheme. In Part I of this series it was shown that for a certain range of incident wavelengths impinging on the interface of an expansion in nodal spacing, an evanescent (or spatially damped) wave results in the downstream region. Here in Part III an analysis is carried out to predict the wavelength and the spatial rate of damping for this wave. The results of the analysis are verified quantitatively with seven ‘hot-start’ numerical experiments and qualitatively with seven ‘cold-start’ experiments. Weare has shown that evanescent waves occur whenever the frequency of a disturbance at a boundary exceeds the maximum frequency given by the dispersion relation. In these circumstances the ‘extended dispersion’ relation can be used to determine the rate of spatial decay. In the context of a domain consisting of two regions with different nodal spacings, the use of the group velocity concept shows that evanescent waves have no energy flux associated with them when energy is conserved.