Hybrid Finite-Element, Spectral-Element Discretization for Translatory Symmetric Model Parts

The superior convergence properties of orthogonal polynomials are exploited along the direction of symmetry of a translatory symmetric model part. In the perpendicular directions and in the remaining model parts, standard finite elements are applied. The examples indicate a substantial saving of computational resources for both the 2D and 3D case.     

Stabilized global–local X‐FEM for 3D non‐planar frictional crack using relevant meshes

A stabilized global–local quasi‐static contact algorithm for 3D non‐planar frictional crack is presented in the X‐FEM/level set framework. A three‐field weak formulation is considered and allows an independent discretization of the bulk and the crack interface. Then, a fine discretization of the interface can be defined according to the possible complex contact state along the crack faces independently from the mesh in the bulk. Furthermore, an efficient stabilized non‐linear LATIN solver dedicated to contact and friction is proposed. It allows solving in a unified framework frictionless and frictional contact at the crack interface with a symmetric formulation, no iterations on the local stage (unilateral contact law with/without friction), no calculation of any global tangent operator, and improved convergence rate. 2D and 3D patch tests are presented to illustrate the relevance of the proposed model and an actual 3D frictional crack problem under cyclic fretting loading is modeled. Copyright © 2011 John Wiley & Sons, Ltd.     

Influence of non-axial magnetic field in a 3D3V Particle-In-Cell plasma model

In this article we report on results obtained using a newly developed self-consistent fully 3D Particle-In-Cell code for modelling of plasma-solid interaction.The model presented here involves a hollow cylindrical chamber opened to the plasma, with a thin cylindrical guard at the inlet and a strong external magnetic field limiting access of charged particles to the cylindrical wall. This model layout might provide more insight into processes taking place during magnetron deposition of thin films onto porous media. It is also a basis for probe diagnostics in fusion plasma research.The magnetic field is either parallel or slightly inclined with respect to the cylindrical axis. The results presented are axial and azimuthal ion current densities and cumulative distribution functions of ions impinging on the cylindrical surface for several angles of magnetic field inclination. They confirm the importance of proper alignment with magnetic field in certain geometries.Efficiency and possibilities of further extensions to the 3D model are also briefly discussed.     

Failure of heterogeneous materials: 3D meso‐scale FE models with embedded discontinuities

We present a meso‐scale model for failure of heterogeneous quasi‐brittle materials. The model problem of heterogeneous materials that is addressed in detail is based on two‐phase 3D representation of reinforced heterogeneous materials, such as concrete, where the inclusions are melt within the matrix. The quasi‐brittle failure mechanisms are described by the spatial truss representation, which is defined by the chosen Voronoi mesh. In order to explicitly incorporate heterogeneities with no need to change this mesh, some bar elements are cut by the phase‐interface and must be split into two parts. Any such element is enhanced using both weak and strong discontinuities, based upon the Incompatible Mode Method. Furthermore, a dedicated operator split solution procedure is proposed to keep local any additional computation on elements with embedded discontinuities. The results for several numerical simulations are presented to illustrate the capabilities of the proposed model to provide an excellent representation of failure mechanisms for any different macroscopic loading path. Copyright © 2010 John Wiley & Sons, Ltd.     

Application of the theory of representation to describe yielding of anisotropic aluminum alloys

In this paper a rigorous method to extend any isotropic yield criterion such as to describe any type of material symmetry is developed. Using this approach, extensions of Drucker’s [J. Appl. Mech. 16 (1949) 349] isotropic yield criterion to transverse isotropy, cubic symmetries, and orthotropy are presented. Comparison with representative sets of data show that the present theory can successfully describe anisotropy of both the plastic strain ratio and yield of aluminum thin sheets as well as the yield anisotropy of extruded bars.     

A new automatic adaptive 3D solid mesh generation scheme for thin‐walled structures

A new algorithm to generate three‐dimensional (3D) mesh for thin‐walled structures is proposed. In the proposed algorithm, the mesh generation procedure is divided into two distinct phases. In the first phase, a surface mesh generator is employed to generate a surface mesh for the mid‐surface of the thin‐walled structure. The surface mesh generator used will control the element size properties of the final mesh along the surface direction. In the second phase, specially designed algorithms are used to convert the surface mesh to a 3D solid mesh by extrusion in the surface normal direction of the surface. The extrusion procedure will control the refinement levels of the final mesh along the surface normal direction. If the input surface mesh is a pure quadrilateral mesh and refinement level in the surface normal direction is uniform along the whole surface, all hex‐meshes will be produced. Otherwise, the final 3D meshes generated will eventually consist of four types of solid elements, namely, tetrahedron, prism, pyramid and hexahedron. The presented algorithm is highly flexible in the sense that, in the first phase, any existing surface mesh generator can be employed while in the second phase, the extrusion procedure can accept either a triangular or a quadrilateral or even a mixed mesh as input and there is virtually no constraint on the grading of the input mesh. In addition, the extrusion procedure development is able to handle structural joints formed by the intersections of different surfaces. Numerical experiments indicate that the present algorithm is applicable to most practical situations and well‐shaped elements are generated. Copyright © 2004 John Wiley & Sons, Ltd.     

3D‐based hp‐adaptive first‐order shell finite element for modelling and analysis of complex structures—Part 2: Application to structural analysis

The paper presents a 3D‐based adaptive first‐order shell finite element to be applied to hierarchical modelling and adaptive analysis of complex structures. The main feature of the element is that it is equipped with 3D degrees of freedom, while its mechanical model corresponds to classical first‐order shell theory. Other useful features of the element are its modelling and adaptive capabilities. The element is assigned to hierarchical modelling and hpq‐adaptive analysis of shell parts of complex structures consisting of solid, thick‐ and thin‐shell parts, as well as of transition zones, where h, p and q denote the mesh density parameter and the longitudinal and transverse orders of approximation, respectively. The proposed hp‐adaptive first‐order shell element can be joined with 3D‐based hpq‐adaptive hierarchical shell elements or 3D hpp‐adaptive solid elements by means of the family of 3D‐based hpq/hp‐ or hpp/hp‐adaptive transition elements. The main objective of the first part of our research, presented in the first part of the paper, was to provide non‐standard information on the original parts of the element algorithm. Here we describe the second part of the research, devoted to the methodology and results of the application of the element to various plate and shell problems. The main objective of this part is to verify algorithms of the element and to show its usefulness in modelling and adaptive analysis of shell and plate parts of complex structures. In order to do that, there is a presentation of the results of a comparative analysis of model plate and shell problems using the classical and our elements, and equidistributed and integrated Legendre shape functions. For the plate problem a comparison of the results obtained from the adaptive and non‐adaptive analysis is also included. Additionally, some advantages of the application of our element are shown through a comparative analysis of p‐convergence of the thin plate problem and an adaptive analysis of the exemplary complex structure. Copyright © 2006 John Wiley & Sons, Ltd.     

Using symmetries of grating groove profiles to reduce computation cost of the C method

This work reduces the computation cost of the C method by taking into account the symmetries of grating grooves. All one-dimensionally periodic, single-interface, surface-relief gratings are classified into five categories according to the symmetries of the planar periodic curves describing the interface. The five categories are reflection symmetry, inversion symmetry, reflection-translation symmetry, complete symmetry (i.e., simultaneous existence of all three aforementioned symmetries), and no symmetry. Reductions of the eigenvalue problem in the C method are first carried out in real space and then in Fourier space by taking advantage of the four types of symmetries. The reflection-translation symmetry can be used without any restriction on the incident angle, but the other symmetries require a Littrow mounting; simultaneous use of the reflection-translation symmetry with any other symmetry further requires an even-order Littrow mounting. The types of eigenfunctions to be solved and boundary conditions to be matched, as well as the time reduction ratios in solving the eigenvalue problem, are given for all possible combinations of groove symmetries and incident configurations. The time reduction ratios range from 1/4 to 1/64.     

基于约束图的三维服装约束问题求解

采用样条曲线作为基本几何元素,建立了三维服装几何约束关系。以此为基础构造了三维服装的约束图,有效地表达了几何元素及其相互关系。提出了基于约束图的改进的三维服装几何约束求解方法,完成了构造服装和对服装的交互参数化修改问题。通过应用实例将参数化方法向高层次图素进行了推广,并成功应用于服装CAD系统中,运行效果良好。     

Mode-selective acoustic spectroscopy of trigonal piezoelectric crystals

A noncontacting electromagnetic-acousticresonance technique is presented for generating and detecting vibrational modes with prescribed symmetries in piezoelectric trigonal crystals with cylindrical geometry. This technique provides the experimental basis for determining all elastic constants from a single specimen, while overcoming difficulties in mode identification that can occur in traditional resonant-ultrasound spectroscopy. Narrow-band tone-burst excitation and piezoelectric coupling are employed with various geometrical configurations of electrodes near the surface of a quartz specimen. The geometries of the specimen and plates include all of the symmetry elements of the crystallographic point group, which enable selection of the irreducible representation of excited vibrational modes simply by switching electrical leads to the electrodes.     

Spatio-temporal symmetries in SN- and SN × 2-equivariant systems

This paper investigates the spatio-temporal symmetries of periodic trajectories in dynamical systems with S_N and S_N × ₂ symmetry. It turns out that trajectories in S_N-equivariant systems cannot exhibit spatio-temporal symmetries beyond the trivial symmetry of all periodic orbits. More complex symmetries in the trajectories require additional constraints on the dynamics. The possibilities offered by S_N × ₂ symmetric systems are considered and a specific S₃ × ₂-equivariant system is investigated numerically.     

A Cut‐and‐Paste Approach to 3D Graphene‐Oxide‐Based Architectures

Properly cut sheets can be converted into complex 3D structures by three basic operations including folding, bending, and pasting to render new functions. Folding and bending are extensively employed in crumpling, origami, and pop‐up fabrications for 3D structures. Pasting joins different parts of a material together, and can create new geometries that are fundamentally unattainable by folding and bending. However, it has been much less explored, likely due to limited choice of weldable thin film materials and residue‐free glues. Here it is shown that graphene oxide (GO) paper is one such suitable material. Stacked GO sheets can be readily loosened up and even redispersed in water, which upon drying, restack to form solid structures. Therefore, water can be utilized to heal local damage, glue separated pieces, and release internal stress in bent GO papers to fix their shapes. Complex and dynamic 3D GO architectures can thus be fabricated by a cut‐and‐paste approach, which is also applicable to GO‐based hybrid with carbon nanotubes or clay sheets.     

An integrated procedure for three‐dimensional structural analysis with the finite cover method

In this paper an integrated procedure for three‐dimensional (3D) structural analyses with the finite cover method (FCM) is introduced. In the pre‐process of this procedure, the geometry of a structure is modelled by 3D‐CAD, followed by digitization to have the corresponding voxel model, and then the structure is covered by a union of mathematical covers, namely a mathematical mesh independently generated for approximation purposes. Since the mesh topology in the FCM does not need to conform to the physical boundaries of the structure, the mesh can be regular and structured. Thus, the numerical analysis procedure is free from the difficulties mesh generation typically poses and, in this sense, enables us to realize the mesh‐free analysis. After formulating the FCM with interface elements for the static equilibrium state of a structure, we detail the procedure of the finite cover modelling, including the geometry modelling with 3D‐CAD and the identification of the geometry covered by a regular mesh for numerical integration. Prior to full 3D modelling and analysis, we present a simple numerical example to confirm the equivalence of the performance of the FCM and that of the standard finite element method (FEM). Finally, representative numerical examples are presented to demonstrate the capabilities of the proposed analysis procedure. Copyright © 2005 John Wiley & Sons, Ltd.     

High performance 3D-analysis of thermo-mechanically loaded composite structures

This paper considers the analysis of composite structures, simultaneously loaded by mechanical and thermal loads, as often found in aerospace applications. Typically a thermal analysis providing the temperature field must precede the stress analysis, which has to account for thermal as well as for additional mechanical loads. Presently, thermal analyses are mostly carried out by finite difference methods or by 3D finite elements, whereas the stress analysis is usually performed by the use of shell elements. Thus, the temperature field has to be transferred from a finite difference or 3D finite element model to a shell finite element model. This process often requires lots of manual user interaction and can get very time consuming. The paper suggests an integrated analysis process which uses a shell finite element model throughout. Thermal lamination theories and related finite elements developed by the first author are used for the 3D thermal analysis. This leads to a reduction of the computing time by two orders of magnitude as compared to 3D finite elements whereas the accuracy of the results is nearly unaffected. The stress analysis is carried out using the same geometry model but with different mesh density. Interpolation between the different meshes can be accomplished automatically since both discretizations are defined on the same geometry. Standard shell elements based on the First order shear deformation theory (FSDT) provide the three in-plane stress components. A novel postprocessing scheme is adopted for determining all transverse stress components from the in-plane stresses and the temperature field. The postprocessing methodology is based on the extended 2D-method which utilizes the material law for transverse shear and the 3D equilibrium conditions. It is computationally very efficient and can be applied in conjunction with any standard finite element package. The interaction of thermal and stress analysis is demonstrated by the example of a composite wing box for a future large airliner.     

基于Pro/E机构模块的齿轮三维实体建模研究

齿廓曲线尤其是齿根过渡曲线的构建是渐开线圆柱齿轮三维实体建模的难点,也是其关键问题。现在所采用的构建方法操作复杂,计算繁琐,且不适合不同刀具加工的齿轮模型的构建。以范成法加工齿轮的原理为理论基础,介绍在Pro/E平台下利用其机构模块的“轨迹曲线”(trace curve)功能精确构建各种刀具加工出来的渐开线圆柱齿轮齿廓曲线的方法,并以磨前滚刀加工直齿圆柱齿轮为例,详细介绍该方法的使用步骤,构建其精确的三维实体模型。该方法无需推导渐开线和过渡曲线的方程就能够方便、快捷地构建出任何刀具加工出来的齿轮模型,为基于啮合原理的复杂曲面零件的有限元建模提供了参考,特别是为复杂曲面零件的CAD/CAE建模与分析奠定了基础。     

基于映射理论的网格生成新方法及应用研究

基于映射函数理论提出二维/三维流场的网格生成新方法。针对实际应用中对场函数变密度的要求,提出可控制网格疏密度的插值公式,并以此对典型物体周围流场进行网格剖分,验证其有效性。针对圆形域(柱形域)流场网格生成质量的缺陷,提出在目标域中建立内置块的新策略,统计分析网格最小内角分布,并与原方法对比分析,以验证改进效果。运用自编程序,对具有复杂外形的空间膜结构进行流场网格剖分,并将该网格导入Ansys-CFX软件,进而数值模拟结构表面风压分布。经验证,该方法可有效地运用于流场网格剖分。     

Automatic adaptive FE analysis of thin‐walled structures using 3D solid elements

In this study, a new automatic adaptive refinement procedure for thin‐walled structures using 3D solid elements is suggested. This procedure employs a specially designed superconvergent patch recovery (SPR) procedure for stress recovery, the Zienkiewicz and Zhu (Z–Z) error estimator for the a posteriori error estimation, a new refinement strategy for new element size prediction and a special mesh generator for adaptive mesh generation. The proposed procedure is different from other schemes in such a way that the problem domain is separated into two distinct parts: the shell part and the junction part. For stress recovery and error estimation in the shell part, special nodal coordinate systems are used and the stress field is separated into two components. For the refinement strategy, different procedures are employed for the estimation of new element sizes in the shell and the junction parts. Numerical examples are given to validate the effectiveness of the suggested procedure. It is found that by using the suggested refinement procedure, when comparing with uniform refinement, higher convergence rates were achieved and more accurate final solutions were obtained by using fewer degrees of freedoms and less amount of computational time. Copyright © 2008 John Wiley & Sons, Ltd.     

Interior symmetry and local bifurcation in coupled cell networks

A coupled cell system is a network of dynamical systems, or 'cells', coupled together. Such systems can be represented schematically by a directed graph whose nodes correspond to cells and whose edges represent couplings. A symmetry of a coupled cell system is a permutation of the cells and edges that preserves all internal dynamics and all couplings. It is well known that symmetry can lead to patterns of synchronized cells, rotating waves, multirhythms, and synchronized chaos. Recently, the introduction of a less stringent form of symmetry, the 'symmetry groupoid', has shown that global group-theoretic symmetry is not the only mechanism that can create such states in a coupled cell system. The symmetry groupoid consists of structure-preserving bijections between certain subsets of the cell network, the input sets. Here, we introduce a concept intermediate between the groupoid symmetries and the global group symmetries of a network: 'interior symmetry'. This concept is closely related to the groupoid structure, but imposes stronger constraints of a group-theoretic nature. We develop the local bifurcation theory of coupled cell systems possessing interior symmetries, by analogy with symmetric bifurcation theory. The main results are analogues for 'synchrony-breaking' bifurcations of the Equivariant Branching Lemma for steady-state bifurcation, and the Equivariant Hopf Theorem for bifurcation to time-periodic states.     

Effect of Frictions on the Ballistic Performance of a 3D Warp Interlock Fabric: Numerical Analysis

3D interlock woven fabrics are promising materials to replace the 2D structures in the field of ballistic protection. The structural complexity of this material caused many difficulties in numerical modeling. This paper presents a new tool that permits to generate a geometry model of any woven fabric, then, mesh this model in shell or solid elements, and apply the mechanical properties of yarns to them. The tool shows many advantages over existing software. It is very handy in use with an organization of the functions in menu and using a graphic interface. It can describe correctly the geometry of all textile woven fabrics. With this tool, the orientation of the local axes of finite elements following the yarn direction facilitates defining the yarn mechanical properties in a numerical model. This tool can be largely applied because it is compatible with popular finite element codes such as Abaqus, Ansys, Radioss etc. Thanks to this tool, a finite element model was carried out to describe a ballistic impact on a 3D warp interlock Kevlar KM2? fabric. This work focuses on studying the effect of friction onto the ballistic impact behavior of this textile interlock structure. Results showed that the friction among yarns affects considerably on the impact behavior of this fabric. The effect of the friction between projectile and yarn is less important. The friction plays an important role in keeping the fabric structural stability during the impact event. This phenomenon explained why the projectile is easier to penetrate this 3D warp interlock fabric in the no-friction case. This result also indicates that the ballistic performance of the interlock woven fabrics can be improved by using fibers with great friction coefficients.     

Three‐dimensional immersed finite element methods for electric field simulation in composite materials

This paper presents two immersed finite element (IFE) methods for solving the elliptic interface problem arising from electric field simulation in composite materials. The meshes used in these IFE methods can be independent of the interface geometry and position; therefore, if desired, a structured mesh such as a Cartesian mesh can be used in an IFE method to simulate 3‐D electric field in a domain with non‐trivial interfaces separating different materials. Numerical examples are provided to demonstrate that the accuracies of these IFE methods are comparable to the standard linear finite element method with unstructured body‐fit mesh. Copyright © 2005 John Wiley & Sons, Ltd.