NURBS-Enhanced Finite Element Method (NEFEM)

The development of NURBS-Enhanced Finite Element Method (NEFEM) is revisited. This technique allows a seamless integration of the CAD boundary representation of the domain and the finite element method (FEM). The importance of the geometrical model in finite element simulations is addressed and the benefits and potential of NEFEM are discussed and compared with respect to other curved finite element techniques.     

A direct hybrid finite element – Wave based modelling technique for efficient coupled vibro-acoustic analysis

This paper presents a newly developed hybrid simulation technique for coupled structural–acoustic analysis, which applies a wave based model for the acoustic cavity and a direct or modally reduced Finite Element model for the structural part. The resulting hybrid model benefits from the computational efficiency of the wave based method, while retaining the Finite Element Method’s ability to model the structural part of the problem in great detail. Application of this approach to the analysis of three fully coupled vibro-acoustic problems with an increasing modelling complexity shows the improved computational efficiency as compared to classical Finite Element procedures and illustrates the potential of the hybrid method as a powerful tool for the analysis of coupled structural–acoustic systems in the low- and mid-frequency range.     

基于边界面法的完整实体应力分析理论与应用

提出基于边界面法（Boundary Face Method,BFM）的完整实体应力分析方法.在该分析中,避免对结构作几何上的简化,结构的所有局部细节都按实际形状尺寸作为三维实体处理.以边界积分方程为理论基础的BFM是完整实体应力分析的自然选择.在该方法中,边界积分和场变量插值都在实体边界曲面的参数空间里实现.高斯积分点的几何数据,如坐标、雅可比和外法向量都直接由曲面算得,而不是通过单元插值近似获得,从而避免几何误差.该方法的实现直接基于边界表征的CAD模型,可做到与CAD软件的无缝连接.线弹性问题的应用实例表明,该方法可以简单有效地模拟具有细小特征的复杂结构,并且计算结果的应力精度比边界元法（Boundary Element Method,BEM）和有限元法（Finite Element Method,FEM）高.     

Increasing solution stability for finite-element modeling of elasto-plastic shell response

The present article introduces a highly efficient numerical simulation strategy for the analysis of elasto-plastic shell structures. An isoparametric Finite Element, based on a Finite Rotation Reissner–Mindlin shell theory in isoparametric formulation, is enhanced by a Layered Approach for a realistic simulation of nonlinear material behaviour. A general material model including isotropic hardening effects is embedded into each material point. A new, highly accurate integration scheme is combined with consistently linearized constitutive relations in order to achieve quadratic rate of convergence. A global Riks–Wempner–Wessels iteration scheme enhanced by a linear Line-Search procedure was used to trace arbitrary deformation paths. Numerical examples show the efficiency of the present concept.     

Effective time step restrictions for explicit MPM simulation

Time steps for explicit MPM simulation in computer graphics are often selected by trial and error due to the challenges in automatically selecting stable time step sizes. Our time integration scheme uses time step restrictions that take into account forces, collisions, and even grid-to-particle transfers calculated near the end of the time step. We propose a novel set of time step restrictions that allow a time step to be selected that is stable, efficient to compute, and not too far from optimal. We derive the general solution for the sound speed in nonlinear isotropic hyperelastic materials, which we use to enforce the classical CFL time step restriction. We identify a single-particle instability in explicit MPM integration and propose a corresponding time step restriction in the fluid case. We also propose a reflection-based boundary condition for domain walls that supports separation and accurate Coulomb friction while preventing particles from penetrating the domain walls.     

Asynchronous Eulerian Liquid Simulation

We present a novel method for simulating liquid with asynchronous time steps on Eulerian grids. Previous approaches focus on Smoothed Particle Hydrodynamics (SPH), Material Point Method (MPM) or tetrahedral Finite Element Method (FEM) but the method for simulating liquid purely on Eulerian grids have not yet been investigated. We address several challenges specifically arising from the Eulerian asynchronous time integrator such as regional pressure solve, asynchronous advection, interpolation, regional volume preservation, and dedicated segregation of the simulation domain according to the liquid velocity. We demonstrate our method on top of staggered grids combined with the level set method and the semi-Lagrangian scheme. We run several examples and show that our method considerably outperforms the global adaptive time step method with respect to the computational runtime on scenes where a large variance of velocity is present.     

Adjustable Constrained Soft-Tissue Dynamics

Physically based simulation is often combined with geometric mesh animation to add realistic soft-body dynamics to virtual characters. This is commonly done using constraint-based simulation whereby a soft-tissue simulation is constrained to geometric animation of a subpart (or otherwise proxy representation) of the character. We observe that standard constraint-based simulation suffers from an important flaw that limits the expressiveness of soft-body dynamics. Namely, under correct physics, the frequency and amplitude of soft-tissue dynamics arising from constraints (“inertial amplitude”) are coupled, and cannot be adjusted independently merely by adjusting the material properties of the model. This means that the space of physically based simulations is inherently limited and cannot capture all effects typically expected by computer animators. For example, animators need the ability to adjust the frequency, inertial amplitude, gravity sag and damping properties of the virtual character, independently from each other, as these are the primary visual characteristics of the soft-tissue dynamics. We demonstrate that independence can be achieved by transforming the equations of motion into a non-inertial reference coordinate frame, then scaling the resulting inertial forces, and then converting the equations of motion back to the inertial frame. Such scaling of inertia makes it possible for the animator to set the character's inertial amplitude independently from frequency. We also provide exact controls for the amount of character's gravity sag, and the damping properties. In our examples, we use linear blend skinning and pose-space deformation for geometric mesh animation, and the Finite Element Method for soft-body constrained simulation; but our idea of scaling inertial forces is general and applicable to other animation and simulation methods. We demonstrate our technique on several character examples.     

Simulation of the behavior of the calfskin used as shoe upper material in footwear CAD

The aim of this work is to propound a mechanical behavior model for simulating the deformation of the shoe upper material in gait for footwear CAD applications. The chosen material is calfskin. The proposed material behavior for the working range is a linear elastic orthotropic model which considers large deformation and membrane and bending loading. The model was obtained from tensile tests and validated with two experiments: a test to measure the leather resistance to damage on lasting and a test that models the shoe forming process using lasts. The framework of this work is the simulation of the footwear deformation while walking for footwear computer-aided design, and these tests have been chosen because, in them, the shoe upper material is deformed in a similar way to those deformations that occur during a complete step. The tests have been simulated using the Finite Element Method. The results of this simulation show that, in most of the cases, the orthotropic model closely represents the real behavior of the leathers analyzed in this work.     

Finite Element/Fictitious Domain programming for flows with particles made simple

Flows with suspended particles is a challenging task and important in many applications such as sedimentation, rheology and fluidized suspensions. The coupling between the suspending liquid flow and the particles’ motion is the central point in the complete understanding of the phenomena that occur in these applications. Finite Element/Fictitious Domain is an important class of method used to solve this problem. In this work we propose a simple object oriented implementation for simulations of flows with suspended particles in the plane using the Fictitious Domain method together with Lagrange multipliers to solve the Navier–Stokes and rigid body equations with a fully implicitly and fully coupled Finite Element approach. To have an efficient implementation for Fictitious Domain/Finite Element method, we introduce a new topological data structure that is concise in terms of storage and very suitable for searching the elements of the mesh intersected by the particles.     

Splitting meshless deforming objects with explicit surface tracking

We present a novel algorithm for efficiently splitting deformable solids along arbitrary piecewise linear crack surfaces in cutting and fracture simulations. The algorithm combines a meshless discretization of the deformation field with explicit surface tracking using a triangle mesh. We decompose the splitting operation into a first step where we synthesize crack surfaces, and a second step where we use the newly synthesized surfaces to update the meshless discretization of the deformation field. We present a novel visibility graph for facilitating fast update of shape functions in the meshless discretization. The separation of the splitting operation into two steps, along with our novel visibility graph, enables high flexibility and control over the splitting trajectories, provides fast dynamic update of the meshless discretization, and allows for an easy implementation. As a result, our algorithm is scalable, versatile, and suitable for a large range of applications, from computer animation to interactive medical simulation.     

An easy and efficient combination of the Mixed Finite Element Method and the Method of Lines for the resolution of Richards’ Equation

In this work, the Mixed Hybrid Finite Element (MHFE) method is combined with the Method Of Lines (MOL) for an accurate resolution of the Richard's Equation (RE). The combination of these methods is often complicated since hybridization requires a discrete approximation of the time derivative whereas with the MOL, it should remain continuous. In this paper, we use the new mass lumping technique developed in Younes et al. [Younes, A., Ackerer, P., Lehmann, F., 2006. A new mass lumping scheme for the mixed hybrid finite element method. International Journal for Numerical Methods in Engineering 67, pp. 89–107.] for the MHFE method. With this formulation, the MOL is easily implemented and sophisticated time integration packages can be used without significant amount of work.Numerical simulations are performed on both homogeneous and heterogeneous porous media to show the efficiency and robustness of the developed scheme.     

Level set topology optimization of cooling and heating devices using a simplified convection model

This paper studies topology optimization of convective heat transfer problems in two and three dimensions. The convective fluxes are approximated by Newton’s Law of Cooling (NLC). The geometry is described by a Level Set Method (LSM) and the temperature field is predicted by the eXtended Finite Element Method (XFEM). A constraint on the spatial gradient of the level set field is introduced to penalize small, sub-element-size geometric features. Numerical studies show that the LSM-XFEM provides improved accuracy over previously studied density methods and LSMs using Ersatz material models. It is shown that the NLC model with an iso-thermal fluid phase may over predict the convective heat flux and thus promote the formation of very thin fluid channels, depending on the Biot number characterizing the heat transfer problem. Approximating the temperature field in the fluid phase by a diffusive model mitigates this issue but an explicit feature size control is still necessary to prevent the formation of small solid members, in particular at low Biot numbers. The proposed constraint on the gradient of the level set field is shown to suppress sub-element-size features but necessitates a continuation strategy to prevent the optimization process from stagnating as geometric features merge.     

Asynchronous Evolution for Fully‐Implicit and Semi‐Implicit Time Integration

We propose a series of techniques for hybridizing implicit and semi‐implicit time integration methods in a manner that retains much of the speed of the implicit method without sacrificing all of the higher quality vibrations one obtains with methods that handle elastic forces explicitly. We propose our scheme in the context of asynchronous methods, where different parts of the mesh are evolved at different time steps. Whereas traditional asynchronous methods evolve each element independently, we partition all of our elements into two groups: one group evolved at the frame rate using a fully implicit scheme, and another group which takes a number of substeps per frame using a scheme that is implicit on damping forces and explicit on the elastic forces. This allows for a straightforward coupling between the implicit and semi‐implicit methods at frame boundaries for added stability. As has been stressed by various authors, asynchronous schemes take some of the pressure off of mesh generation, allowing time evolution to remain efficient even in the face of sliver elements. Finally, we propose a force distributing projection method which allows one to redistribute the forces felt on boundaries between implicit and semi‐implicit regions of the mesh in a manner that yields improved visual quality.     

基于有限元法的滚珠丝杠传动过程中的温度场和热变形仿真

为减小精密机床进给传动过程中传动发热对机床进给精度的影响,考虑丝杠导程引起表面积变化及螺母移动对温度场的影响,建立滚珠丝杠传动过程中温度场和热变形的数学模型. 应用有限元法(Finite Element Method, FEM)对该模型进行数值模拟,得到滚珠丝杠传动过程中温度场的分布规律以及温度对丝杠变形的影响关系. 结果可为机床进给传动系统散热结构的设计和丝杠热变形误差补偿设计提供依据.     

Improving the computational efficiency in finite element analysis of shells with uncertain properties

This work is concerned with improving the computational efficiency of the most time consuming tasks performed in Monte Carlo simulation-based Finite Element Analysis (FEA) of shell structures with uncertain properties. For this purpose, stochastic field values are generated on a coarse mesh and then interpolated onto the fine mesh used for the standard FEA computations; the cost-effective TRIC shell element is used to ensure the formation of stiffness matrices in reasonable processing times; the solution of finite element equations is efficiently handled with hybrid schemes combining both iterative and direct solution concepts; additional computational gains are achieved with the use of parallel computing through the straightforward partitioning of the overall Monte Carlo simulation process. The adoption of such advanced computational approaches allows simulation-based probabilistic or stochastic FEA of shells to be performed in affordable computing times and therefore become more tractable in structural engineering practice. The computational procedures described in this work are evaluated on a cluster of 16 networked PCs using three linear elastic test problems with uncertain material and/or geometric parameters: (a) the Scordelis-Lo shell, (b) a pinched cylinder and (c) a 3D steel frame discretized with shell elements.     

Deformable part inspection using a spring–mass system

In order to inspect deformable parts, recent works use virtual deformation on a digitized version of a real-part to bring the part model back to its nominal shape. This simulation mimics the real process called fixturing, which is normally used by the manufacturer to bring back the part into its nominal shape once installed. To perform such virtual deformation Finite Element Methods (FEMs) are used in order to meet the precision requirements of the inspection process. This paper presents a method based on a spring–mass system, whose formulation is much simpler than the FEM, which allows the calculation of deformations of shell type parts with accuracy comparable to FEM. Furthermore, due to the simplicity in its formulation the algorithm can be implemented more easily than the FEM. The system is composed of two types of springs: one type models membrane behavior of the part’s mesh model and the second type models the flexion behavior between each mesh elements. We show that by applying the proposed mass-spring model, it is possible to reduce the calculation time by 80% over standard FEM calculation opening the door to real-time inspection.     

An object-oriented approach to the Generalized Finite Element Method

The Generalized Finite Element Method (GFEM) is a meshbased approach that can be considered as one instance of the Partition of Unity Method (PUM). The partition of unity is provided by conventional interpolations used in the Finite Element Method (FEM) which are extrinsically enriched by other functions specially chosen for the analyzed problem. The similarities and differences between GFEM and FEM are pointed out here to expand a FEM computational environment. Such environment is an object-oriented system that allows linear and non-linear, static and dynamic structural analysis and has an extense finite element library. The aiming is to enclose the GFEM formulation with a minimum impact in the code structure and meet requirements for extensibility and robustness. The implementation proposed here make it possible to combine different kinds of elements and analysis models with the GFEM enrichment strategies. Numerical examples, for linear analysis, are presented in order to demonstrate the code expansion and to illustrate some of the above mentioned combinations.     

Adaptation of CAD model topology for finite element analysis

The preparation of a Finite Element Analysis (FEA) model from a Computer Aided Design (CAD) model is still a difficult task since its Boundary Representation (B-Rep) is often composed of a large number of faces, some of which may be narrow or feature short edges that are smaller than the desired FE size (for mesh generation). Consequently, these faces and edges are considered as geometric artefacts that are irrelevant for the automatic mesh generation process. Such inconsistencies often cause either poorly-shaped elements or meshes that are locally over-densified. These inconsistencies not only slow down the solver (using too many elements) but also produce poor or inappropriate simulation results. In this context, we propose a “Mesh Constraint Topology” (MCT) model with automatic adaptation operators aimed at transforming a CAD model boundary decomposition into a FE model, featuring only mesh-relevant faces, edges and vertices, i.e., an explicit data model that is intrinsically adapted to the meshing process. We provide a set of criteria that can be used to transform CAD model boundary topology using MCT transformations, i.e., edge deletion, vertex deletion, edge collapsing, and merging of vertices. The proposed simplification criteria take into account a size map, a discretization error threshold and boundary conditions. Applications and results are presented through the adaptation of CAD models using the proposed simplification criteria.     

基于边界元素法的柔软物体变形模拟

在计算机动画和虚拟现实技术中，基于物理的建模方法是高真实感地模拟物体受力变形和运动的有效途径．近年来基于边界元的物理模型方法因其简捷的计算模式而受到关注，该文针对当前边界元模型在视觉效果和计算量上的一些缺陷，分别提出了两方面的改进方法，基于LOD的动态自适应多分辨率网格边界元模型和近似的非线性边界元的物理模型，分别用于在不损失视觉效果的前提下减少计算量以及模拟物体大变形，并提出了相应的加速算法，取得了较好的效果．