考虑嵌入移动孔洞的多相材料布局优化

工程结构设计问题中经常需要预先嵌入一个或多个固定形状的孔洞以满足某些功能性或者制造性设计要求.为了有效求解这种带有嵌入可移动孔洞的多相材料连续体结构布局优化问题,通常需要同时优化这些嵌入孔洞的位置和方向及多相材料结构的拓扑构型,以改善结构的整体性能.为此,本文采用参数化的水平集函数描述嵌入孔洞的几何形状,并将定义多相材料结构拓扑的材料密度以及描述嵌入孔洞的位置和方向的几何参数视为所考虑优化问题的设计变量.为了避免由于孔洞移动造成的重新划分网格的繁琐及改善计算效率,使用平滑化的Heaviside函数将所有嵌入孔洞映射为固定网格上的密度场.同时,提出了一种在有限元水平上调用的类SIMP材料插值格式,用于优化问题的材料参数化,进而实现多相材料结构拓扑构型和嵌入孔洞位置和方向的同步优化.这种材料插值格式便于几何变量的解析灵敏度分析,使得当前的优化问题可以用基于梯度的优化算法求解.优化算例证明所提方法可以有效地处理带有多个嵌入孔洞的多相材料结构布局优化问题.      

爆炸冲击波对玻璃幕墙破坏作用的多物质ALE有限元模拟

应用LS-DYNA显式程序,基于多物质的ALE有限元法,利用罚函数实现了爆炸冲击波与玻璃幕墙结构间的耦合作用,重现了玻璃幕墙防爆炸实验中爆炸荷载的产生及其与玻璃幕墙相互作用的三维动态过程。研究了爆炸冲击波作用下幕墙结构的动态响应行为,分析了幕墙内外层玻璃的破坏情况。研究表明,数值模拟结果与实验结果一致,这为玻璃幕墙的抗爆设计及改进提供了重要的参考依据。     

An arbitrary Lagrangian–Eulerian formulation for the numerical simulation of flow patterns generated by the hydromedusa Aequorea victoria

A new geometrically conservative arbitrary Lagrangian–Eulerian (ALE) formulation is presented for the moving boundary problems in the swirl-free cylindrical coordinates. The governing equations are multiplied with the radial distance and integrated over arbitrary moving Lagrangian–Eulerian quadrilateral elements. Therefore, the continuity and the geometric conservation equations take very simple form similar to those of the Cartesian coordinates. The continuity equation is satisfied exactly within each element and a special attention is given to satisfy the geometric conservation law (GCL) at the discrete level. The equation of motion of a deforming body is solved in addition to the Navier–Stokes equations in a fully-coupled form. The mesh deformation is achieved by solving the linear elasticity equation at each time level while avoiding remeshing in order to enhance numerical robustness. The resulting algebraic linear systems are solved using an ILU(k) preconditioned GMRES method provided by the PETSc library. The present ALE method is validated for the steady and oscillatory flow around a sphere in a cylindrical tube and applied to the investigation of the flow patterns around a free-swimming hydromedusa Aequorea victoria (crystal jellyfish). The calculations for the hydromedusa indicate the shed of the opposite signed vortex rings very close to each other and the formation of large induced velocities along the line of interaction while the ring vortices moving away from the hydromedusa. In addition, the propulsion efficiency of the free-swimming hydromedusa is computed and its value is compared with values from the literature for several other species.     

High order conservative Lagrangian schemes with Lax–Wendroff type time discretization for the compressible Euler equations

In this paper, we explore the Lax–Wendroff (LW) type time discretization as an alternative procedure to the high order Runge–Kutta time discretization adopted for the high order essentially non-oscillatory (ENO) Lagrangian schemes developed in 3 and 5. The LW time discretization is based on a Taylor expansion in time, coupled with a local Cauchy–Kowalewski procedure to utilize the partial differential equation (PDE) repeatedly to convert all time derivatives to spatial derivatives, and then to discretize these spatial derivatives based on high order ENO reconstruction. Extensive numerical examples are presented, for both the second-order spatial discretization using quadrilateral meshes [3] and third-order spatial discretization using curvilinear meshes [5]. Comparing with the Runge–Kutta time discretization procedure, an advantage of the LW time discretization is the apparent saving in computational cost and memory requirement, at least for the two-dimensional Euler equations that we have used in the numerical tests.     

A fully discrete ALE method over untwisted time–space control volumes

In this paper, a fully discrete high‐resolution arbitrary Lagrangian–Eulerian (ALE) method is developed over untwisted time–space control volumes. In the framework of the finite volume method, 2D Euler equations are discretized over untwisted moving control volumes, and the resulting numerical flux is computed using the generalized Riemann problem solver. Then, the fluid flows between meshes at two successive time steps can be updated without a remapping process in the classic ALE method. This remapping‐free ALE method directly couples the mesh motion into a physical variable update to reflect the temporal evolution in the whole process. An untwisted moving mesh is generated in terms of the vorticity‐free part of the fluid velocity according to the Helmholtz theorem. Some typical numerical tests show the competitive performance of the current method. Copyright © 2016 John Wiley & Sons, Ltd.     

Vectorization,threading, and cache‐blocking considerations for hydrocodes on emerging architectures

The computational efficiency of existing hydrocodes is expected to suffer as computer architectures advance beyond the traditional parallel central processing unit (CPU) model 1 . Concerning new computer architectures, sources of relative performance degradation might include reduced memory bandwidth per core, increased resource contention due to concurrency, increased single instruction, multiple data (SIMD) length, and increasingly complex memory hierarchies. Concerning existing codes, any performance degradation will be influenced by a lack of attention to performance in their design and implementation. This work reports on considerations for improving computational performance in preparation for current and expected changes to computer architecture. The algorithms studied will include increasingly complex prototypes for radiation hydrodynamics codes, such as gradient routines and diffusion matrix assembly (e.g., in 1 - 6 ). The meshes considered for the algorithms are structured or unstructured meshes. The considerations applied for performance improvements are meant to be general in terms of architecture (not specifically graphical processing unit (GPUs) or multi‐core machines, for example) and include techniques for vectorization, threading, tiling, and cache blocking. Out of a survey of optimization techniques on applications such as diffusion and hydrodynamics, we make general recommendations with a view toward making these techniques conceptually accessible to the applications code developer. Published 2015. This article is a U.S. Government work and is in the public domain in the USA.     

Delayed mesh relaxation for multi-material ALE formulation

Multi-Material Arbitrary Lagrangian–Eulerian (ALE) finite element methods can solve large deformations in fast dynamic problems like explosions because the mesh motion can be independent of the material motion. However materials must flow between elements and this advection involves numerical dissipations. The rezoning mesh method presented in this paper was designed to reduce these numerical errors for shock wave propagation. The mesh moves to refine the elements near the shock front. This refinement limits the advection fluxes and so the numerical diffusion. This technique is applied to the numerical simulations of airblast problems for which a parameter controlling the mesh refinement is studied.     

地下坑道对其临界震塌爆距处钻地武器爆炸载荷的动力响应

利用非线性显式动力有限元程序,采用多物质流固耦合计算方法,就GBU-28钻地弹在地下坑道临界震塌爆距处爆炸时,对地下直墙拱坑道的动力响应进行数值模拟。根据围岩动力稳定性和混凝土动态强度判据,结合模拟结果,分析衬砌结构与围岩的相互作用。钻地弹在直墙圆拱断面的坑道临界震塌爆距处爆炸时:围岩处于临界破坏状态,但混凝土衬砌结构处于稳定状态;拱顶的应力峰值明显,且柱状装药情况下,爆炸近区的应力较集团装药情况下的大;拱肩位置出现应力集中;围岩与衬砌结构特征位置处的相互作用载荷与对应质点的振动速度相互耦合,基本成对应的关系。     

ALE有限元方法研究及应用

将ALE（Arbitrary Lagrangian-Eulerian)描述引入到有限元方法中， 从而使有限元方法在解决大范围自由移动边界问题，特别是液体大幅晃动、流－固耦合、加工成型、接触、大变形等问题时获得极大成功。本文综述了ALE有限元方法的研究现状以及在不同领域的应用，并对 今后的研究及应用做了展望。