Virtual Element Formulation for Finite Strain Elastodynamics Dedicated to Professor Karl Stark Pister for his 95th birthday

The virtual element method(VEM)can be seen as an extension of the classical finite element method(FEM)based on Galerkin projection.It allows meshes with highly irregular shaped elements,including concave shapes.So far the virtual element method has been applied to various engineering problems such as elasto-plasticity,multiphysics,damage and fracture mechanics.This work focuses on the extension of the virtual element method to efficient modeling of nonlinear elasto-dynamics undergoing large deformations.Within this framework,we employ low-order ansatz functions in two and three dimensions for elements that can have arbitrary polygonal shape.The formulations considered in this contribution are based on minimization of potential function for both the static and the dynamic behavior.Generally the construction of a virtual element is based on a projection part and a stabilization part.While the stiffness matrix needs a suitable stabilization,the mass matrix can be calculated using only the projection part.For the implicit time integration scheme,Newmark-Method is used.To show the performance of the method,various two-and three-dimensional numerical examples in are presented.

Virtual Element Discretization of Optimal Control Problem Governed by Brinkman Equations

In this paper, we discuss virtual element method (VEM) approximation of optimal control problem governed by Brinkman equations with control constraints. Based on the polynomial projections and variational discretization of the control variable, we build up the virtual element discrete scheme of the optimal control problem and derive the discrete first order optimality system. A priori error estimates for the state, adjoint state and control variables in L2 and H1 norm are derived. The theoretical findings are illustrated by the numerical experiments.

ERROR ANALYSIS OF THE SECOND-ORDER SERENDIPITY VIRTUAL ELEMENT METHOD FOR SEMILINEAR PSEUDO-PARABOLIC EQUATIONS ON CURVED DOMAINS

The second-order serendipity virtual element method is studied for the semilinear pseudo-parabolic equations on curved domains in this paper.Nonhomogeneous Dirichlet boundary conditions are taken into account,the existence and uniqueness are investigated for the weak solution of the nonhomogeneous initial-boundary value problem.The Nitschebased projection method is adopted to impose the boundary conditions in a weak way.The interpolation operator is used to deal with the nonlinear term.The Crank-Nicolson scheme is employed to discretize the temporal variable.There are two main features of the proposed scheme:(i)the internal degrees of freedom are avoided no matter what type of mesh is utilized,and(ii)the Jacobian is simple to calculate when Newton’s iteration method is applied to solve the fully discrete scheme.The error estimates are established for the discrete schemes and the theoretical results are illustrated through some numerical examples.

Divergence-Free Virtual Element Method for the Stokes Equations with Damping on Polygonal Meshes

In this paper,we construct,analyze,and numerically validate a family of divergence-free virtual elements for Stokes equations with nonlinear damping on polygonal meshes.The virtual element method is H1-conforming and exact divergence-free.By virtue of these properties and the topological degree argument,we rigorously prove the well-posedness of the proposed discrete scheme.The con-vergence analysis is carried out,which imply that the error estimate for the velocity in energy norm does not explicitly depend on the pressure.Numerical experiments on various polygonal meshes validate the accuracy of the theoretical analysis and the asymptotic pressure robustness of the proposed scheme.

The Bulk-Surface Virtual Element Method for Reaction-Diffusion PDEs:Analysis and Applications

Bulk-surface partial differential equations(BS-PDEs)are prevalent in manyapplications such as cellular,developmental and plant biology as well as in engineeringand material sciences.Novel numerical methods for BS-PDEs in three space dimensions(3D)are sparse.In this work,we present a bulk-surface virtual elementmethod(BS-VEM)for bulk-surface reaction-diffusion systems,a form of semilinearparabolic BS-PDEs in 3D.Unlike previous studies in two space dimensions(2D),the3D bulk is approximated with general polyhedra,whose outer faces constitute a flatpolygonal approximation of the surface.For this reason,the method is restricted tothe lowest order case where the geometric error is not dominant.The BS-VEM guaranteesall the advantages of polyhedral methods such as easy mesh generation andfast matrix assembly on general geometries.Such advantages are much more relevantthan in 2D.Despite allowing for general polyhedra,general nonlinear reaction kineticsand general surface curvature,the method only relies on nodal values without needingadditional evaluations usually associated with the quadrature of general reactionkinetics.This latter is particularly costly in 3D.The BS-VEM as implemented in thisstudy retains optimal convergence of second order in space.

Serendipity Virtual Elements for General Elliptic Equations in Three Dimensions

The authors study the use of the virtual element method(VEM for short) of order k for general second order elliptic problems with variable coefficients in three space dimensions. Moreover, they investigate numerically also the serendipity version of the VEM and the associated computational gain in terms of degrees of freedom.

A MIXED VIRTUAL ELEMENT METHOD FOR THE BOUSSINESQ PROBLEM ON POLYGONAL MESHES

In this work we introduce and analyze a mixed virtual element method(mixed-VEM)for the two-dimensional stationary Boussinesq problem.The continuous formulation is based on the introduction of a pseudostress tensor depending nonlinearly on the velocity,which allows to obtain an equivalent model in which the main unknowns are given by the aforementioned pseudostress tensor,the velocity and the temperature,whereas the pressure is computed via a postprocessing formula.In addition,an augmented approach together with a fixed point strategy is used to analyze the well-posedness of the resulting continuous formulation.Regarding the discrete problem,we follow the approach employed in a previous work dealing with the Navier-Stokes equations,and couple it with a VEM for the convection-diffusion equation modelling the temperature.More precisely,we use a mixed-VEM for the scheme associated with the fluid equations in such a way that the pseudostress and the velocity are approximated on virtual element subspaces of H(div)and H^(1),respectively,whereas a VEM is proposed to approximate the temperature on a virtual element subspace of H^(1).In this way,we make use of the L^(2)-orthogonal projectors onto suitable polynomial spaces,which allows the explicit integration of the terms that appear in the bilinear and trilinear forms involved in the scheme for the fluid equations.On the other hand,in order to manipulate the bilinear form associated to the heat equations,we define a suitable projector onto a space of polynomials to deal with the fact that the diffusion tensor,which represents the thermal conductivity,is variable.Next,the corresponding solvability analysis is performed using again appropriate fixed-point arguments.Further,Strang-type estimates are applied to derive the a priori error estimates for the components of the virtual element solution as well as for the fully computable projections of them and the postprocessed pressure.The corresponding rates of convergence are also established.Finally,several numerical examples illustrating the performance of the mixed-VEM scheme and confirming these theoretical rates are presented.

A New Locking-Free Virtual Element Method for Linear Elasticity Problems

This paper devises a new lowest-order conforming virtual element method(VEM)for planar linear elasticity with the pure displacement/traction boundary condition.The main trick is to view a generic polygon K as a new one K with additional vertices consisting of interior points on edges of K,so that the discrete admissible space is taken as the V1 type virtual element space related to the partition{K}instead of{K}.The method is proved to converge with optimal convergence order both in H^(1)and L^(2)norms and uniformly with respect to the Lam´e constantλ.Numerical tests are presented to illustrate the good performance of the proposed VEM and confirm the theoretical results.

Shape optimization of plate with static and dynamic constraints via virtual laminated element

The virtual laminated element method (VLEM) can resolve structural shap e optimization problems with a new method. According to the characteristics of V LEM , only some characterized layer thickness values need be defined as design v ariables instead of boundary node coordinates or some other parameters determini ng the system boundary. One of the important features of this method is that it is not necessary to regenerate the FE(finite element) grid during the optimizati on process so as to avoid optimization failures resulting from some distortion grid elements. Th e thickness distribution in thin plate optimization problems in other studies be fore is of stepped shape. However, in this paper, a continuous thickness distrib ution can be obtained after optimization using VLEM, and is more reasonable. Fur thermore, an approximate reanalysis method named ″behavior model technique″ ca n be used to reduce the amount of structural reanalysis. Some typical examples are offered to prove the effectiveness and practicality of the proposed method.

RESEARCH ON VIRTUAL-PART-BASED CONNECTING ELEMENT MODELING

Based on the inner character analysis of interpart, detail modification andassembly relation of mechanical connecting element, the idea, which extends the feature modeling ofpart to the interpart feature modeling for assembly purpose, is presented, and virtual-part-basedconnecting element modeling is proposed. During the assembly modeling, base parts are modified bythe Boolean subtraction between the virtual part and the part to be connected. Dynamic matchingalgorithm, which is based on list database, is designed for dynamic extension and off-line editingof connecting part and virtual part, and design rules of connecting element is encapsulated by thevirtual part. A prototyped software module for rapid design of connecting elements is implementedunder self-developed CAD/CAM platform-SuperMan.

A novel virtual node method for polygonal elements

A novel polygonal finite element method （PFEM） based on partition of unity is proposed, termed the virtual node method （VNM）. To test the performance of the present method, numerical examples are given for solid mechanics problems. With a polynomial form, the VNM achieves better results than those of traditional PFEMs, including the Wachspress method and the mean value method in standard patch tests. Compared with the standard triangular FEM, the VNM can achieve better accuracy. With the ability to construct shape functions on polygonal elements, the VNM provides greater flexibility in mesh generation. Therefore, several fracture problems are studied to demonstrate the potential implementation. With the advantage of the VNM, the convenient refinement and remeshing strategy are applied.

Kinematics Analysis of Mechanisms Based on Virtual Assembly

Currently, virtual assembly technology has attracted increasing attention due to considerations of solving assembly problems in virtual environment before actual assembly in manufactory. Previous studies on kinematic analysis of mechanism only aim at analyzing motion law of single mechanism, but can not simulate the multi-mechanisms motion process at the same time, let alone simulating the automatic assembly process of products in a whole assembly workshop. In order to simulate the assembly process of products in an assembly workshop and provide effective data for analyzing mechanical performance after finishing assembly simulation in virtual environment, this study investigates the kinematics analysis of mechanisms based on virtual assembly. Firstly, in view of the same function of the kinematic pairs and the assembly constraints on restricting the motion of components （subassembly or part）, the method of identifying kinematic pairs automatically based on assembly constraints is presented. The information of kinematic pairs can be obtained through calculating the constraint degree of the assembly constraints. Secondly, the incidence matrix eliminating element method is proposed in order to search the information and establish the models of mechanisms automatically after finishing assembly simulation in virtual environment. Both methods have important significance for reducing the workload of pretreatment and promoting the level of automation of kinematics analysis. Finally, the method of kinematics analysis of mechanisms is presented. Based on Descartes coordinates, three types of kinematics equations are formed. The parameters, like displacement, velocity, and acceleration, can be obtained by solving these equations. All these data are important to analyze mechanical performance. All the methods are implemented and validated in the prototype system virtual assembly process planning（VAPP）. The mechanism models are established and simulated in the VAPP system, and the result curves are shown accurately. The proposed kinematics analysis of mechanisms based on virtual assembly provides an effective method for simulating product assembly process automatically and analyzing mechanical performance after finishing assembly simulation.

基于Virtual.Lab下消声器声固耦合的模型建立

论述了应用有限元法并借助于LMS Virtual.lab仿真软件分析了消声器声固耦合特性,并计算得出多种物理量值。从实体建模到声学性能计算分步进行,用有限元法得到的结果对软件模拟得到的数据进行校对,分析了消声器消声性能受声固耦合特性的影响。给消声器在考虑声固耦合时的性能分析提供了依据,并对指导之后的消噪。

基于S-R和分解定理的二维几何非线性问题的虚单元法求解

应变-旋转(Strain-Rotation,S-R)和分解定理为分析几何非线性问题提供了合理可靠的理论基础,但用有限元求解时会遇到大变形发生后的网格畸变问题。近年提出的虚单元法(Virtual element method,VEM)适用于一般的多边形网格,因此,该文尝试使用一阶虚单元求解基于S-R和分解定理的二维几何非线性问题,以克服网格畸变的影响。基于重新定义的多项式位移空间基函数,推演获得一阶虚单元分析线弹性力学问题时允许位移空间向多项式位移空间的投影表达式;按照虚单元法双线性格式的计算规则,分析处理基于更新拖带坐标法和势能率原理的增量变分方程;进而建立离散系统方程及其矩阵表达形式,并编制MATLAB求解程序;采用常规多边形网格和畸变网格,应用该文算法分析均布荷载下的悬臂梁和均匀内压下的厚壁圆筒变形。结果与已有文献和ANSYS软件的对比表明:该文算法在两种网格中均可有效执行且具备足够数值精度。总体该文算法为基于S-R和分解定理的二维几何非线性问题求解提供了一种鲁棒方法。

Kinematics and Dynamics of Deployable Structures with Scissor-Like-Elements Based on Screw Theory

Because the deployable structures are complex multi-loop structures and methods of derivation which lead to simpler kinematic and dynamic equations of motion are the subject of research effort, the kinematics and dynamics of deployable structures with scissor-like-elements are presented based on screw theory and the principle of virtual work respectively. According to the geometric characteristic of the deployable structure examined, the basic structural unit is the common scissor-like-element（SLE）. First, a spatial deployable structure, comprised of three SLEs, is defined, and the constraint topology graph is obtained. The equations of motion are then derived based on screw theory and the geometric nature of scissor elements. Second, to develop the dynamics of the whole deployable structure, the local coordinates of the SLEs and the Jacobian matrices of the center of mass of the deployable structure are derived. Then, the equivalent forces are assembled and added in the equations of motion based on the principle of virtual work. Finally, dynamic behavior and unfolded process of the deployable structure are simulated. Its figures of velocity, acceleration and input torque are obtained based on the simulate results. Screw theory not only provides an efficient solution formulation and theory guidance for complex multi-closed loop deployable structures, but also extends the method to solve dynamics of deployable structures. As an efficient mathematical tool, the simper equations of motion are derived based on screw theory.

砌体轴心和局部受压离散元仿真在教学中的应用

砌体是块体和砂浆的黏结组合材料,为了让学生更好地理解砖块体和砂浆对外力的分担作用,运用离散元方法建立了砖块体团簇模型、砂浆团簇模型,进而“砌筑”了普通砖砌体数值试件,对砖砌体分别开展轴心受压和局部受压仿真。仿真复现了砌体受压时的应力-应变关系和破坏模式,应力峰值处伴随大量砖颗粒-砖颗粒胶结接触破坏。砌体应力主要由胶结接触承担,其中砖-砖胶结接触>砖-砂浆胶结接触>砂浆-砂浆胶结接触,砂浆主要起到连接块体的作用;法向接触力承力大于切向接触力。通过仿真教学,有助于学生建立砌体宏观力学表现受控于微观结构和微观力学的认知,加深了学生对砌体受力机理和强度的理解。

虚拟视觉元素对消费者的创造力及新产品采纳意愿的影响

随着数字技术的进步,虚拟视觉元素的应用愈发广泛。本文通过3个线上实验和一个田野实验,系统探索了虚拟视觉元素对消费者的创造力及新产品采纳意愿的影响及其心理作用机制。实验一发现,相比于观看真实视觉元素,观看虚拟视觉元素后,消费者在有关创造力的任务中的表现显著提高。实验二采用调节检验中介的方法探究了该效应的心理机制,即当启动一种突破传统的思维模式后,真实视觉元素也能够提升消费者的创造力;而在控制组,只有虚拟视觉元素能提升消费者的创造力。实验三进一步将虚拟视觉元素提升消费者的创造力的主效应拓展至消费者决策领域,发现虚拟视觉元素能显著提高消费者采纳新产品的意愿,同时还直接测量并检验了突破传统思维模式的中介效应。实验四通过田野实验发现在观看虚拟(vs.真实)视觉元素后,更多消费者选择了创新(vs.传统)产品。本文的研究发现扩展了视觉设计和创造力等研究领域的相关文献,并对企业进行新产品推广等提供了有价值的启示。

融合中式元素的三维室内场景情绪化渲染

情绪具有主观性,利用计算机技术自动生成一个既满足真实性又与目标情绪匹配的虚拟室内场景是一项充满挑战的任务。目前缺乏对室内场景情感表达进行识别和评估的技术方法,且在充分考虑情感诉求的前提下,如何提升场景渲染结果真实性也是室内场景设计需要考虑的重要因素。针对上述问题,提出了一种融合中式元素的虚拟室内场景情绪化渲染算法。首先,利用深度学习算法从一个包含25 000张图片的家庭室内场景数据集中提取不同情绪的特征,训练情绪分类器,用于识别和评估渲染过程中虚拟室内场景的情绪表达。其次,为了保证渲染结果真实性,设计了一种场景物体纹理颜色真实性度量算法。然后,研究了根据目标情绪自动渲染虚拟室内场景的优化算法、融合中式元素的风格迁移算法,对场景中的物体进行细粒度的中式风格化处理,提升渲染结果的空间内涵、文化底蕴以及情感表达,增强视觉感染力。最后,在四个不同的室内场景中对该算法进行了实验,并通过对实验结果和用户调研数据的统计分析验证了该算法的正确性和有效性。

基于Virtual Lab研究影响空气滤芯消声能力的因素

进气系统噪声是汽车的主要噪声源之一,它直接影响着车内噪声和通过噪声,从而影响着驾乘人员的驾乘感受和能否满足通过噪声的法规要求。空气滤清器作为进气系统的关键零部件之一,它不仅仅起到保护发动机的能力,还具备着降低进气系统噪声的能力。空气滤芯作为多孔介质,不仅能吸收噪声,还可以通过多孔区域将声能转化为热能从而消除噪声,而影响空气滤芯降噪能力的因素主要为流阻率、孔隙率和结构因子,而三个因素是如何影响空气滤芯的消音能力就需要通过仿真分析进行验证。文章通过Hyper mesh和Virtual Lab软件进行传递损失联合仿真分析,验证各个因素对滤芯消声能力的影响。

基于数字孪生的装备维修保障平台

维修保障是装备运行使用的重要部分,装备的维修保障能力直接影响其效能的发挥。而基于历史故障数据的传统维修保障方式很难实现实时精确保障,使得装备效能发挥受到了影响。数字孪生技术的发展为装备运行使用过程中的全资可视化、装备状态实时感知、故障快速预测并诊断、维修方案智能化制定及验证、维修指导以及按需训练培训等提供了良好的实现条件。文中在研究装备维修保障对象、业务领域及寿命期保障内容的基础上,设计一种装备维修保障数字孪生模型,分析装备数字孪生体组成以及需要管理的元素;在分析装备维修保障孪生数据流的基础上,提出了装备维修保障数字孪生平台框架;最后针对装备维修保障数字孪生体的构建及使用,分析了数字孪生平台实现的关键技术。研究成果可指导装备维修保障数字孪生体建设工作的开展,实现装备实时、精确保障。