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.     

基于h型自适应有限元法在薄板冲压成型中的应用

在对薄板冲压成型这一过程进行有限元仿真分析时,难以精确分析场变量发生剧烈变化的应力集中及应变梯度大的区域,如何平衡精度和效率间的关系是冲压成型仿真的关键.因此,基于非线性有限元大变形的相关理论,针对动态仿真的网格自适应关键技术,建立了自适应分析模式下的薄板冲压成型算法.为了提高计算精度,提出基于单元应变能增量的能量误差...     

Multi‐time‐step and two‐scale domain decomposition method for non‐linear structural dynamics

In this paper we propose a method to improve the means of taking into account the specific time‐scale and space‐scale characteristics in time‐dependent non‐linear problems. This method enables the use of arbitrary time steps in each subdomain: these can be coupled by prescribing continuous velocities at the interfaces, which are modelled using a dual Schur formulation. For certain subdomains, in space, we adopt a two‐scale resolution technique inspired by the multigrid methods in order to obtain the part of the solution related to small variation lengths on a refined scale and the part corresponding to large variation lengths on a coarse scale. For non‐linear problems, we propose an algorithm with a single iteration level to deal with both the non‐linear equilibrium and the two space scales thanks to a two‐grid method in which the relaxation steps are performed using a non‐linear, preconditioned conjugate gradient algorithm. Finally, we present an example which demonstrates the feasibility of the method. Copyright © 2003 John Wiley & Sons, Ltd.     

Fluid-structure interaction of panel in supersonic fluid passage

Fluid-structure interaction of panel in supersonic fluid passage is studied with subcycling and spline interpolation based predict-correct scheme. The passage is formed with two parallel panels, one is rigid and the other is flexible. The interaction between fluid flows and flexible panel is numerically studied, mainly focused on the effect of dynamic pressure and distance between two parallel panels. Subcycling and spline interpolation based predict-correct scheme is utilized to combine the vibration and fluid analysis and to stabilize long-term calculations to get accurate results. It ＇ s demonstrated that the flutter characteristic of flexible panel is more complex with the increase of dynamic pressure and the decrease of distance between two parallel panels. Via analyzing the propagation and reflection of disturbance in passage, it＇ s determined as a main cause of the variations.     

Asynchronous multi‐domain variational integrators for non‐linear problems

We develop an asynchronous time integration and coupling method with domain decomposition for linear and non‐linear problems in mechanics. To ensure stability in the time integration and in coupling between domains, we use variational integrators with local Lagrange multipliers to enforce continuity at the domain interfaces. The asynchronous integrator lets each domain step with its own time step, using a smaller time step where required by stability and accuracy constraints and a larger time step where allowed. We show that in practice the time step is limited by accuracy requirements rather than by stability requirements. Copyright © 2008 John Wiley & Sons, Ltd.     

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。     

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.     

Subcycling first- and second-order generalizations of the trapezoidal rule

Subcycling algorithms which employ multiple timesteps have been previously proposed for explicit direct integration of first- and second-order systems of equations arising in finite element analysis, as well as for integration using explicit/implicit partitions of a model. The author has recently extended this work to implicit/implicit multi-timestep partitions of both first- and second-order systems. In this paper, improved algorithms for multi-timestep implicit integration are introduced, that overcome some weaknesses of those proposed previously. In particular, in the second-order case, improved stability is obtained. Some of the energy conservation properties of the Newmark family of algorithms are shown to be preserved in the new multi-timestep extensions of the Newmark method. In the first-order case, the generalized trapezoidal rule is extended to multiple timesteps, in a simple way that permits an implicit/implicit partition. Explicit special cases of the present algorithms exist. These are compared to algorithms proposed previously. © 1998 John Wiley & Sons, Ltd.     

A time‐staggered partitioned coupling algorithm for transient heat conduction

We present a time‐staggered partitioned coupling algorithm for transient heat conduction finite element simulations. This algorithm divides a large structural mesh into a number of smaller subdomains, solves the individual subdomains separately and couples the solutions to obtain the response to the original problem. The proposed algorithm is a mixed multi‐timestep algorithm and enables arbitrary time integration schemes and meshes to be coupled with different timesteps in the various subdomains. In this procedure, the solution of each partition is separately evaluated over a system timestep after which the interfacial conditions are enforced making this a staggered algorithm that facilitates parallel computation. We present examples showing the feasibility of the coupling algorithm and discuss the merits in terms of convergence and stability. Copyright © 2009 John Wiley & Sons, Ltd.     

Multi‐time‐step explicit–implicit method for non‐linear structural dynamics

We present a method with domain decomposition to solve time‐dependent non‐linear problems. This method enables arbitrary numeric schemes of the Newmark family to be coupled with different time steps in each subdomain: this coupling is achieved by prescribing continuity of velocities at the interface. We are more specifically interested in the coupling of implicit/explicit numeric schemes taking into account material and geometric non‐linearities. The interfaces are modelled using a dual Schur formulation where the Lagrange multipliers represent the interfacial forces. Unlike the continuous formulation, the discretized formulation of the dynamic problem is unable to verify simultaneously the continuity of displacements, velocities and accelerations at the interfaces. We show that, within the framework of the Newmark family of numeric schemes, continuity of velocities at the interfaces enables the definition of an algorithm which is stable for all cases envisaged. To prove this stability, we use an energy method, i.e. a global method over the whole time interval, in order to verify the algorithms properties. Then, we propose to extend this to non‐linear situations in the following cases: implicit linear/explicit non‐linear, explicit non‐linear/explicit non‐linear and implicit non‐linear/explicit non‐linear. Finally, we present some examples showing the feasibility of the method. Copyright © 2001 John Wiley & Sons, Ltd.