冲击动力问题的混合积分并行算法及应用

为了提高冲击动力问题的计算效率和速度,在分布式MIMD并行环境下,构造了冲击动力问题的混合时间步长显式积分并行算法。基于区域分裂法,该算法按照单元时间积分步长的大小来划分各个子区域,再把具有不同时间步长的子区域分配到网络机群中的各结点机上,并采用子循环的方法使各子区域的计算达到同步,然后通过消息传递软件―PVM来传递各子区域间的信息。最后通过工程算例可以看出:带有子循环的混合积分并行算法能够显著的提高运算效率和并行加速比,缩短计算时间。     

A spectral‐element method for modelling cavitation in transient fluid–structure interaction

In an underwater‐shock environment, cavitation (boiling) occurs as a result of reflection of the shock wave from the free surface and/or wetted structure causing the pressure in the water to fall below its vapour pressure. If the explosion is sufficiently distant from the structure, the motion of the fluid surrounding the structure may be assumed small, which allows linearization of the governing fluid equations. In 1984, Felippa and DeRuntz developed the cavitating acoustic finite‐element (CAFE) method for modelling this phenomenon. While their approach is robust, it is too expensive for realistic 3D simulations. In the work reported here, the efficiency and flexibility of the CAFE approach has been substantially improved by: (i) separating the total field into equilibrium, incident, and scattered components, (ii) replacing the bilinear CAFE basis functions with high‐order Legendre‐polynomial basis functions, which produces a cavitating acoustic spectral element (CASE) formulation, (iii) employing a simple, non‐conformal coupling method for the structure and fluid finite‐element models, and (iv) introducing structure–fluid time‐step subcycling. Field separation provides flexibility, as it admits non‐acoustic incident fields that propagate without numerical dispersion. The use of CASE affords a significant reduction in the number of fluid degrees of freedom required to reach a given level of accuracy. The combined use of subcycling and non‐conformal coupling affords order‐of‐magnitude savings in computational effort. These benefits are illustrated with 1D and 3D canonical underwatershock problems. Copyright © 2004 John Wiley & Sons, Ltd.     

Fast simulation of incremental sheet metal forming by adaptive remeshing and subcycling

In order to use incremental sheet forming (ISF) in an industrial context, it is necessary to provide fast and accurate simulation methods for virtual process design. Without reliable process simulations, first-time right production seams infeasible and the process loses its advantage of offering a short lead time. Previous work indicates that implicit finite element (FE) methods are at present not efficient enough to allow for the simulation of AISF for industrially relevant parts, mostly due to the fact that the moving contact requires a very small time step. Finite element methods based on explicit time integration can be sped up using mass or time scaling to enable the simulation of large-scale sheet metal forming problems. However, AISF still requires dedicated adaptive meshing methods to further reduce the calculation times. In this paper, an adaptive remeshing strategy based on a multi-mesh method is developed and applied to the simulation of AISF. It is combined with subcycling to further reduce the calculation times. For the forming of a cone shape, it is shown that savings in CPU time of up to 80 % are possible with acceptable loss of accuracy, and that the simulation time scales more moderately when the part size is increased, so that larger, industrially relevant parts become feasible.     

A solution to the parameter-identification conundrum: multi-scale interaction potentials

Softening is a structural property, not a material property. Any material will show softening, but in this paper the focus is primarily on cement and concrete, which show this property very clearly owing to their coarse heterogeneity (relative to common laboratory-scale specimen sizes). A new model approach is presented, based on pair-potentials describing the interaction between two neighbouring particles at any desired size/scale level. Because of the resemblance with a particle model an equivalent lattice can be constructed. The pair-potential is then the behavioral law of a single lattice element. This relation between force and displacement depends on the size of the considered lattice element as well as on the rotational stiffness at the nodes, which not only depends on the flexibility of the global lattice to which the element is connected but also on the flexural stiffness of the considered element itself. The potential $F-r$ relation is a structural property that can be directly measured in physical experiments, thereby solving size effects and boundary effects.     

Analysis and implementation of a new constant acceleration subcycling algorithm

An algorithm for explicit integration of structural dynamics problems with multiple time steps is proposed that averages accelerations to obtain subcycle states at a nodal interface between regions integrated with different time steps. With integer time step ratios, the resulting subcycle updates at the interface sum to give the same effect as a central difference update over a major cycle. The algorithm is shown to have good accuracy, and stability properties in linear elastic analysis similar to those of constant velocity subcycling algorithms. The implementation of a generalised form of the algorithm with non-integer time step ratios is presented. © 1997 John Wiley & Sons, Ltd.     

Monolithic and partitioned time integration methods for real-time heterogeneous simulations

Real-time (RT) heterogeneous simulations define a class of hybrid numerical–experimental techniques based on dynamic substructuring and capable of simulating the non-linear response of an emulated mechanical system. With this objective in mind, we present two direct coupling algorithms endowed with subcycling, capable of ensuring the continuity of acceleration between non-overlapping subdomains. In greater detail, firstly we introduce monolithic Rosenbrock L-stable algorithms and, in view of the analysis of complex emulated systems, we recall a recent direct parallel algorithm. Secondly, we propose an improved parallel version of the progenitor algorithm together with its solution procedure. Consequently, in order to reduce drift, we introduce a mass-orthogonal velocity projection characterized by a non-negative energy dissipation. Moreover, both a convergence analysis on a SDoF test problem and simulations on single- and four-DoF systems are presented. Lastly, a novel test rig devised to perform nonlinear substructured RT tests is introduced and a few test results are presented.     

Coupled lattice Boltzmann method and discrete element modelling of particle transport in turbulent fluid flows: Computational issues

This paper presents essential numerical procedures in the context of the coupled lattice Boltzmann (LB) and discrete element (DE) solution strategy for the simulation of particle transport in turbulent fluid flows. Key computational issues involved are (1) the standard LB formulation for the solution of incompressible fluid flows, (2) the incorporation of large eddy simulation (LES)‐based turbulence models in the LB equations for turbulent flows, (3) the computation of hydrodynamic interaction forces of the fluid and moving particles; and (4) the DE modelling of the interaction between solid particles. A complete list is provided for the conversion of relevant physical variables to lattice units to facilitate the understanding and implementation of the coupled methodology. Additional contributions made in this work include the application of the Smagorinsky turbulence model to moving particles and the proposal of a subcycling time integration scheme for the DE modelling to ensure an overall stable solution. A particle transport problem comprising 70 large particles and high Reynolds number (around 56 000) is provided to demonstrate the capability of the presented coupling strategy. Copyright © 2007 John Wiley & Sons, Ltd.     

Stress-intensity factor computation in three dimensions with quarter-point elements

A consistent method for computing stress-intensity factors from three-dimensional quarter-point element nodal displacements is presented. The method is generalized to permit functional evaluation of stress-intensity factors along the crack front. Embedded, surface, and corner crack problems are solved using the proposed technique. Results are compared to previous finite element and boundary element solutions. The comparison shows that use of the functional evaluation technique allows a dramatic decrease in problem size while still maintaining engineering accuracy. Next, a three-dimensional stress-intensity factor calibration of an unusual specimen configuration is presented. By taking advantage of the proposed technique, the calibration was performed with little difference in cost over the more usual two-dimensional approach. Moreover, the three-dimensional solution revealed intersting behaviour that would have been undetected by a two-dimensional solution. Finally, the results of a study on optimum size of the quarter-point element are presented. Surprisingly, Poisson ratio is shown to have marked effect on optimum element size.     

Delamination buckling of laminated plates

The subject of this paper is the buckling of laminated plates, with a pre-existing delamination, subjected to in-plane loading. Each laminate is modelled as an orthotropic Mindlin plate. The analysis is carried out by a combination of the finite element and asymptotic expansion methods. By applying the finite element method, plates with general delamination regions can be studied. The asymptotic expansion method reduces the number of unknown variables of the eigenvalue equation to that of the equation for a single Kirchhoff plate. Numerical results for the critical buckling load are presented for several examples. The effects of the shape, size and position of the delamination on the buckling load are studied through these examples.     

Hybrid stress finite element analysis of bending of a plate with a through flaw

A hybrid stress finite element procedure for the solution of bending stress intensity factors of a plate with a through-the-thickness crack is presented. Reissner's sixth-order plate theory including the effects of transverse shear deformation is used. The dominant singular crack tip stress field is embedded in the crack tip singular elements and only regular polynomial functions are assumed in the far field elements. The stress intensity factors can be calculated directly from the crack tip singular stress solution functions. The effects of the plate thickness, the ratio between the crack size and the inplane dimension of the plate, and the singular element size on the stress intensity factor solution are investigated. The effects of the explicit enforcement of traction-free conditions along crack surfaces, which are the natural boundary conditions in the present hybrid stress finite element model, are also investigated. The numerical results of bending of a plate with a straight central crack compare favourably with analytical solutions. It is also found that the explicit enforcement of traction-free conditions along crack surfaces is mandatory to obtain meaningful results for the Mode I type of bending stress intensity factor.     

A finite element model for single-sided crack patchings

A finite element model is established for analyzing the behavior of cracked plates which are repaired with a single-sided patch. The formulation is based on the Reissner-Mindlin plate theory with an assumed variation of the transverse shear and normal stresses through the thickness of the cracked -plate and patch. The generalized stress-strain relations relating the transverse shear stress resultants and the adhesive stresses to the displacements of the plate and patch are established by using a variational principle. By means of the finite element model presented herein, single-sided crack patching problems can be solved with a reasonable estimate of the adhesive stresses and the stress intensity factor. Numerical examples are provided to illustrate the effects of the patch size on the stress intensity factor in the cracked plate and the stress distribution in the adhesive layer, and compared with results from the previous analysis.     

Hypervelocity impact of mixtures

The study of the behavior of mixtures during shock loading entails several special problems which are both physical and computational in nature. On the physical level, many mixtures of interest such as engineering composites and water-saturated geological materials have consitituents which are both soft and porus. Thus hypervelocity impact produces enormous heating. The distribution of this heating between the constituents of the mixture must be understood before accurate predictions of Hugoniot states and release paths can be achieved. On the computational level, numerical solutions within a wavecode framework require simultaneous solutions of an equation of state and conservation of energy equation for each constituent of the mixture. At present, to achieve these solutions a numerical subcycling scheme is required.

In this paper these problems are discussed in detail. A formulation of the theory of mixtures will be presented which is both complex enough to encompass the essential physics of many problems and simple enough to be incorporated into many wave propagation codes. Results of calculations will be compared to impact and release experiments on a mixtures of water and powdered calcite.     

Efficient implicit finite element analysis of sheet forming processes

The computation time for implicit finite element analyses tends to increase disproportionally with increasing problem size. This is due to the repeated solution of linear sets of equations, if direct solvers are used. By using iterative linear equation solvers the total analysis time can be reduced for large systems. For plate or shell element models, however, the condition of the matrix is so ill that iterative solvers do not reach the huge time‐savings that are realized with solid elements. By introducing inertial effects into the implicit finite element code the condition number can be improved and iterative solvers perform much better. An additional advantage is that the inertial effects stabilize the Newton–Raphson iterations. This also applies to quasi‐static processes, for which the inertial effects finally do not affect the results. The presented method can readily be implemented in existing implicit finite element codes. Industrial size deep drawing simulations are executed to investigate the performance of the recommended strategy. It is concluded that the computation time is decreased by a factor of 5 to 10. Copyright © 2003 John Wiley & Sons, Ltd.     

Stiffness matrix for a beam element including transverse shear and axial force effects

A simple and direct procedure is presented for the formulation of an element stiffness matrix on element co-ordinates for a beam member and a beam-column member including shear deflections. The resulting stiffness matrices are compared with those obtained using the alternative formulation in terms of member flexibilities: The relative effects of axial force and shear force on the stiffness coefficients are presented. The critical buckling loads, considering the effects of shear force, are computed and compared with those available in the literature. Only prismatic members are considered.     

A nonlinear modified couple stress-based third-order theory of functionally graded plates

In this paper a general nonlinear third-order plate theory that accounts for (a) geometric nonlinearity, (b) microstructure-dependent size effects, and (c) two-constituent material variation through the plate thickness (i.e., functionally graded material plates) is presented using the principle of virtual displacements. A detailed derivation of the equations of motion, using Hamilton’s principle, is presented, and it is based on a modified couple stress theory, power-law variation of the material through the thickness, and the von Kármán nonlinear strains. The modified couple stress theory includes a material length scale parameter that can capture the size effect in a functionally graded material. The governing equations of motion derived herein for a general third-order theory with geometric nonlinearity, microstructure dependent size effect, and material gradation through the thickness are specialized to classical and shear deformation plate theories available in the literature. The theory presented herein also can be used to develop finite element models and determine the effect of the geometric nonlinearity, microstructure-dependent size effects, and material grading through the thickness on bending and postbuckling response of elastic plates.     

复合材料加筋板的大变形有限元分析

本文将考虑横向剪切变形的Mindlin's理论应用于复合材料加筋板的大变形分析,在Total-Lagrange坐标系下推导了八结点等参弯曲板单元和三结点等参梁单元的增量平衡方程和切线刚度矩阵,非线性问题采用增量法和Newton-Raphson迭代法相结合的方法求解.本文通过一些算例,证明了所采用单元具有良好的收敛性和足够的精度,并讨论了边界条件、纤维铺设角和加筋疏密等因素对复合材加料筋板非线性解的影响.     

A time-based arc-length like method to remove step size effects during fracture propagation

An arc-length like method is presented which alters the size of the time increment when simulating crack propagation problems. By allowing the time increment to change during the time step a constraint can be imposed, which is used to enforce the fracture to propagate a single element length per time step. This removes the effect of the (interface) element size on propagating fractures, and therefore allows smooth fracture propagation during the simulation. The benefits of the scheme are demonstrated for three cases: mode-I crack propagation in a double cantilever beam, a shear fracture including inertial and viscoplastic effects in the surrounding material, and a pressurized fracture inside a poroelastic material. These cases highlight the ability of this scheme to obtain more accurate and nonoscillatory results for the force–displacement relation, to remove numerically induced stepwise fracture propagation, and to allow for arbitrary propagation velocities. An added benefit is that plastic strains surrounding a fracture are no longer affected by the (interface) element size.     

Elastic property prediction by finite element analysis with random distribution of materials for heterogeneous solids

In the present paper, finite element method is employed to predict the effective material properties of heterogeneous materials via random distributions of the constituent materials. With the random distributing strategy, massive parametric analysis via finite element becomes feasible for multi-phase heterogeneous solids. Using a two-phase bi-continuous material as an example, the effects of the specimen size with respect to the characteristic size of the micro-structural size and the element density on the predicted effective properties are considered. The numerical predictions of the effective properties are checked by two analytical bounds which were proposed by Hashin and Shtrikemn (1963) through the principle of variation and the matrix-fiber model. Some discussions on the finite element prediction are also made to clarify the status of the present work in the composite mechanics research.     

声场-结构耦合系统灵敏度分析及优化设计研究

给出了低频声－结构耦合系统的有限元方程，并在此基础上提出声一结构耦合系统的包含尺寸和形状设计变量的优化设计模型，建立基于灵敏度分析求解的优化设计方法，重点推导了耦合系统的特征频率和声压级响应关于设计变量的灵敏度方程。在JIFEX软件中实现上述理论和算法，并通过灵敏度比较和优化设计的数值算例，进一步说明该研究方法对声结构耦合系统的工程设计具有实用意义。     

Monte Carlo simulation of polycrystalline microstructures and finite element stress analysis

A two-dimensional numerical model of microstructural effects is presented, with an aim to understand the mechanical performance in polycrystalline materials. The microstructural calculations are firstly carried out on a square lattice by means of a 2-D Monte Carlo (MC) simulation for grain growth, then the conventional finite element method is applied to perform stress analysis of a plane strain problem. The mean grain size and the average stress are calculated during the MC evolution. The simulation result shows that the mean grain size increases with the simulation time, which is about 3.2 at 100 Monte Carlo step (MCS), and about 13.5 at 5000 MCS. The stress distributions are heterogeneous in materials because of the existence of grains. The mechanical property of grain boundary significantly affects the average stress. As the grains grow, the average stress without grain boundary effect slightly decreases as the simulation time, while the one with strengthening effect significantly decreases, and the one with weakening effect increases. The average stress and the grain size agree well with the Hall–Petch relationship.