A triangular finite element with local remeshing for the large strain analysis of axisymmetric solids

In this work, a three-node triangular finite element with two degrees of freedom per node for the large strain elasto-plastic analysis of axisymmetric solids is presented. The formulation resorts to the adjacent elements to obtain a quadratic interpolation of the geometry over a patch of four elements from which an average deformation gradient is defined. Thus, the element formulation falls within the framework of assumed strain elements or more precisely of F-bar type formulations. The in-plane behavior of the element is similar to the linear strain triangle, but without the drawbacks of the quadratic triangle, e.g. contact or distortion sensitivity. The element does not suffer of volumetric locking in problems with isochoric plastic flow and the implementation is simple. It has been implemented in a finite element code with explicit time integration of the momentum equations and tools that allow the simulation of industrial processes. The widely accepted multiplicative decomposition of the deformation gradient in elastic and plastic components is adopted here. An isotropic material with non-linear isotropic hardening has been considered. Two versions of the element have been implemented based on a Total and an Updated Lagrangian Formulation, respectively. Some approximations have been considered in the latter formulation aimed to reduce the number of operations in order to increase numerical efficiency. To consider bulk forming, with large geometric changes, an automatic local remeshing strategy has been developed. Several examples are considered to assess the element performance with and without remeshing.     

Refined sandwich model for the vibration of beams with embedded shear piezoelectric actuators and sensors

This work extends a previously presented refined sandwich beam finite element (FE) model to vibration analysis, including dynamic piezoelectric actuation and sensing. The mechanical model is a refinement of the classical sandwich theory (CST), for which the core is modelled with a third-order shear deformation theory (TSDT). The FE model is developed considering, through the beam length, electrically: constant voltage for piezoelectric layers and quadratic third-order variable of the electric potential in the core, while mechanically: linear axial displacement, quadratic bending rotation of the core and cubic transverse displacement of the sandwich beam. Despite the refinement of mechanical and electric behaviours of the piezoelectric core, the model leads to the same number of degrees of freedom as the previous CST one due to a two-step static condensation of the internal dof (bending rotation and core electric potential third-order variable). The results obtained with the proposed FE model are compared to available numerical, analytical and experimental ones. Results confirm that the TSDT and the induced cubic electric potential yield an extra stiffness to the sandwich beam.     

2D and 3D finite element analysis of central incisor generated by computerized tomography

The purpose of this study was to compare the results of different hierarchical models in engineering analysis applied to dentistry with 2D and 3D models of a tooth and its supporting structures under 100 N occlusal loading at 45° and examine the reliability of simplified 2D models in dental research. Five models were built from computed-tomography scans: four 2D models with Plane Strain and Plane Stress State with linear triangular and quadratic quadrilateral elements and one 3D model. The finite element results indicated that the stress distribution was similar qualitatively in all models but the stress magnitude was quite different. It was concluded that 2D models are acceptable when investigating the biomechanical behavior of upper central incisor qualitatively. However, quantitative stress analysis is less reliable in 2D-finite element analysis, because 2D models overestimate the results and do not represent the complex anatomical configuration of dental structures. Therefore 3D finite element analyses of dental biomechanics cannot be simplified.     

Mixed least-squares finite element model for the static analysis of laminated composite plates

This paper presents a mixed finite element model for the static analysis of laminated composite plates. The formulation is based on the least-squares variational principle, which is an alternative approach to the mixed weak form finite element models. The mixed least-squares finite element model considers the first-order shear deformation theory with generalized displacements and stress resultants as independent variables. Specifically, the mixed model is developed using equal-order C⁰ Lagrange interpolation functions of high p-levels along with full integration. This mixed least-squares-based discrete model yields a symmetric and positive-definite system of algebraic equations. The predictive capability of the proposed model is demonstrated by numerical examples of the static analysis of four laminated composite plates, with different boundary conditions and various side-to-thickness ratios. Particularly, the mixed least-squares model with high-order interpolation functions is shown to be insensitive to shear-locking.     

A posteriori error estimates of finite element method for the time-dependent Darcy problem in an axisymmetric domain

We consider the time dependent Darcy problem in a three-dimensional axisymmetric domain and, by writing the Fourier expansion of its solution with respect to the angular variable, we observe that each Fourier coefficient satisfies a system of equations on the meridian domain. We propose a discretization of these equations in the case of general solution. This discretization relies on a backward Euler’s scheme for the time variable and finite elements for the space variables. We prove a posteriori error estimates that allow for an efficient adaptivity strategy both for the time steps and the meshes. Computations for an example with a known solution are presented which support the a posteriori error estimate.     

Processing of fiber architecture data for finite element modeling of 3D woven composites

An efficient procedure to process the textile simulation data and generate realistic finite element meshes of woven composites is proposed. The textile topology data in point cloud format is used to identify individual yarns, interpolate their cross-sectional contours, and generate smooth yarn surfaces. A robust algorithm to repair possible interpenetrations between yarn surfaces is developed and implemented in MATLAB. A 3D finite element mesh of the unit cell of composite material is generated based on the obtained yarn surfaces. The anisotropic material properties of the constituents are assigned with proper orientations.The procedure is successfully applied to generate four finite element models with 1–10 million degrees of freedom. The models are used to predict effective elastic properties of an orthogonal 3D woven composite. The sensitivity of results to the level of finite element discretization is investigated.     

三维渗流有限元软件GWSS开发与应用

针对复杂地质条件的三维地质建模、复杂建筑物的几何建模和复杂防渗排水系统作用下渗流场精细模拟等三维渗流场有限元分析的难点问题,采用IDL开发面向水工结构和岩土工程的渗流有限元分析软件GWSS（Ground Water Simulation System）.该软件包括系统控制模块、数据管理模块、前处理模块、计算模块、后处理模块和制图输出模块等六大模块.前处理模块具有基于钻孔和钻孔剖面的三维地质建模、几何建模与有限元网格生成等功能;计算模块主要用于各种闸坝、堤防、隧道和地下洞室等渗流问题的计算分析等;后处理模块可显示各渗流要素的三维云图和任意截面的二维云图等.GWSS已经在国内四十多个工程的渗流计算中得到应用和检验.     

An efficient 3D stochastic finite element method for failure probability analysis of high temperature components

The loadings on high temperature components are generally complex and the discreteness of the material strength is usually great. Therefore, the two-dimensional (2D) failure probability analysis model and the deterministic finite element method (DFEM) cannot be applied to evaluate the failure probability of asymmetrical three-dimensional (3D) components. To overcome the drawbacks of the 2D model and the DFEM, an efficient 3D stochastic finite element method (SFEM) is proposed in this paper. With this method, the failure probability of components subjected to complex loadings can be estimated by using the statistical analysis of the Von Mises stresses of element nodes. Meanwhile, ANSYS and MATLAB were employed to carry out 3D parametric modeling, solving and statistical analysis. The proposed method is efficient, as is verified for two cases, and it can also be easily applied in practical engineering.     

Space and time localization for the estimation of distributed parameters in a finite element model

In this paper we study the problem of estimating the possibly non-homogeneous material coefficients inside a physical system, from transient excitations and measurements made in a few points on the boundary. We assume there is available an adequate Finite Element (FEM) model of the system, whose distributed physical parameters must be estimated from the experimental data.We propose a space–time localization approach that gives a better conditioned estimation problem, without the need of an expensive regularization. Some experimental results obtained on an elastic system with random coefficients are given.     

A virtual stack facility for mini-computer and microcomputer implementation of the finite element method

In this paper, the efficient implementation of the finite element method on mini-computers and microcomputers is considered. The main limitations of memory and address space are overcome and a software solution proposed with the use of a virtual stack facility which is implemented and tested. A new replacement algorithm for a virtual stack is presented and shown to be more efficient than other known implementations.     

A 3D mathematical model for the prediction of mucilage dynamics

We illustrate a three-dimensional mathematical model for the prediction of biological processes that typically occur in a sea region with minor water exchange. The model accounts for particle transport due to water motion, turbulent diffusion and reaction processes and we use a fractional-step approach for discretizing the related different terms.     

A discrete layer beam finite element for the dynamic analysis of composite sandwich beams with integral damping layers

A discrete layer finite element is presented for the dynamic analysis of laminated beams. The element uses C⁰ continuous linear and quadratic polynominals to interpolate the in-plane and transverse displacement field, respectively, and is free from the effects of shear locking. Modal frequencies and damping are estimated using both the modal strain energy method and the complex modulus method. A forced response version of the model is also presented. The model predictions are compared with experimental data for composite sandwich beams with integral damping layers. Four damping configurations are considered, a constrained layer treatment, a segmented constrained layer treatment and two internal treatments.     

表面—体元一体化矿体三维模型算法研究及其实现

针对现有的矿体面-体混合建模方法要在表面模型和内部体元模型的边界处划分若干子块,存在子块的计算量随精度快速增加的问题,提出了一种基于矢量栅格一体化的矿体建模算法,重点研究了算法中表面与体元模型相交检测、ARTP体元剖切相交体元方法的实现。该算法采用剖分的体元代替子块,提高了计算精度,减少了数据冗余。     

A Simplified Model for Generating 3D Realistic Sound in the Multimedia and Virtual Reality Systems

It is a key feature to embed 3D realistic sound effect in the future multimedia and virtual reality systems.Recent research on acoustics and psychoacoustics reveals the important cues for sound localization and sound perception.One promising approach to generate 3D realistic sound effect uses two earphones by simulating the sound waveforms from sound source to eardrum.This paper summarizes two methods for generating 3D realistic sound and points out their inherent drawbacks.To overcome these drawbacks we propose a simplified model to generate 3D realistic sound at any positions in the horizontal plane based on the results of sound perception and localization.Experimental results show that the model is correct and efficient.     

A method for the analysis of the interaction between users and objects in 3D navigational space

Along with the improvement of eye-tracking technology, more and more distinct field of researches have introduced movements of the eye in relation to the head to understand user behavior. Most of current researches focus on the perception process of single 2-dimensional images by fixed eye-tracking devices or the head-mount devices. A method of applying eye-tracking on the analysis of the interaction between users and objects in 3D navigational space is proposed in this article. It aims to understand the visual stimulation of 3D objects and the user’s spatial navigational reactions while receiving the stimulation, and proposes the concept of 3D object attention heat map. It also proposes to construct a computational visual attention model for different geometric featured 3D objects by applying the method of feature curves. The VR results of this study also provide future assistance in the incoming immersive world. This study sets to promote eye-tracking from the mainstream of 2D field to 3D spaces and points to a deeper understanding between human and artificial product or natural objects. It would also serve an important role in the field of human-computer interaction, product usability, aids devices for cognition degenerative individuals, and even the field of visual recognition of daily human behavior.     

A novel method for 3D reconstruction: Division and merging of overlapping B-spline surfaces

B-spline surfaces, extracted from scanned sensor data, are usually required to represent objects in inspection, surveying technology, metrology and reverse engineering tasks. In order to express a large object with a satisfactory accuracy, multiple scans, which generally lead to overlapping patches, are always needed due to, inter-alia, practical limitations and accuracy of measurements, uncertainties in measurement devices, calibration problems as well as skills of the experimenter. In this paper, we propose an action sequence consisting of division and merging. While the former divides a B-spline surface into many patches with corresponding scanned data, the latter merges the scanned data and its overlapping B-spline surface patch. Firstly, all possible overlapping cases of two B-spline surfaces are enumerated and analyzed from a view of the locations of the projection points of four corners of one surface in the interior of its overlapping surface. Next, the general division and merging methods are developed to deal with all overlapping cases, and a simulated example is used to illustrate aforementioned detailed procedures. In the sequel, two scans obtained from a three-dimensional laser scanner are simulated to express a large house with B-spline surfaces. The simulation results show the efficiency and efficacy of the proposed method. In this whole process, storage space of data points is not increased with new obtained overlapping scans, and none of the overlapping points are discarded which increases the representation accuracy. We believe the proposed method has a number of potential applications in the representation and expression of large objects with three-dimensional laser scanner data.     

Coupled model for the non-linear analysis of anisotropic sections subjected to general 3D loading. Part 1: Theoretical formulation

A numerical model for the coupled analysis of arbitrary shaped cross sections made of heterogeneous-anisotropic materials under 3D combined loading is formulated. The theory is derived entirely from equilibrium considerations and based on the superposition of the 3D section’s distortion and the traditional plane section hypothesis. 3D stresses and strains fields are obtained as well as a section stiffness matrix reflecting coupling effects between normal and tangential forces due to material anisotropy. Traditional generalized strains and stresses are maintained as input and output variables. The proposed model is suitable as a constitutive law for frame elements in the analysis of complete structures.     

A 3D multi-grid algorithm for the Chan–Vese model of variational image segmentation

Variational segmentation models provide effective tools for image processing applications. Although existing models are continually refined to increase their capabilities, solution of such models is often a slow process, since fast methods are not immediately applicable to nonlinear problems. This paper presents an efficient multi-grid algorithm for solving the Chan–Vese model in three dimensions, generalizing our previous work on the topic in two dimensions, but this direct generalized method is low performance or unfeasible. So here, we first present two general smoothers for a nonlinear multi-grid method and then give our three new adaptive smoothers which can choose optimal a parameter of the smoothers automatically, also we analyse them using a local Fourier analysis and our theorem to inform how to obtain an optimal parameter and the best smoother selection. Finally, various advantages of our recommended algorithm are illustrated, using both synthetic and real images.     

Stereoscopic 3‐D display with optical correction for the reduction of the discrepancy between accommodation and convergence

Abstract— This paper describes a method for reducing the discrepancy between accommodation and convergence when viewing stereoscopic 3‐D images. The method uses a newly developed stereoscopic 3‐D display system with a telecentric optical system and a mobile LCD. The examination of a mono‐focal lens showed that a correction lens having the appropriate refractive power and conditions for presenting stereoscopic 3‐D images clearly reduces the discrepancy between accommodation and convergence. The authors also developed a stereoscopic 3‐D display that uses dynamic optical correction to reduce the discrepancy between accommodation and convergence. The display equalizes the theoretical points of accommodation and convergence. The purpose of the development was to expand the regeneration range of a stereoscopic 3‐D image having the appropriate accommodation. An evaluation of the developed display showed that it resolves the discrepancy between convergence and accommodation.     

Design of experiments and energy dissipation analysis for a contact mechanics 3D model of frictional bolted lap joints

Bolted lap joints allow structural assemblies to be made. The answer to requirements, both static and dynamic, depends on the joint behaviour. Bolted joints are a primary source of energy dissipation in dynamic built-up and space structures among others. This paper presents an analysis of a bolted lap joint, subjected to a relative displacement after applying a pre-stress on the bolt in order to characterise the joint behaviour. For this purpose a 3D modelling is made by means of finite elements, using design techniques of experiments (DOE) to fit constitutive contact parameters. The theoretical results relative to elasto-plastic hysteresis cycles of the joint are experimentally validated. Finally, the preload effect and the magnitude of the displacement on the non-linear joint behaviour are analysed to determine equivalent stiffness and dissipated energy in the hysterical loops of the joint.