Application of higher-order tensor theory for formulating enhanced continuum models

Summary In this paper attention is focussed on the derivation of higher-order isotropic tensors and their application in the formulation of enhanced continuum models. A mathematical theory will be discussed which relates formal orthogonal invariant polynomial functions to isotropic tensors. Using this theory, the second-order to the sixth-order isotropic tensor will be derived. When the tensor order increases, the derivation procedure clearly reveals a repeatable character. Thereafter, an example will be given of how the higher-order isotropic tensors can be used in the formulation of an enhanced continuum model. It will be demonstrated that symmetry conditions significantly reduce the number of material parameters.     

Algebraic methods in 3-d motion estimation from two-view point correspondences

We consider the problem of determining motion (3-D rotation and translation) of rigid objects from their images taken at two time instants. We assume that the locations of the perspective projection on the image plane of n points from the surface of the rigid body are known at two time instants. For n = 5, we show that there are at most ten possible motion values (in rotation and translation) and give many examples. For n ≥ 6, we show that the solution is generally unique. We derive a variety of necessary and sufficient conditions a solution must satisfy, show their equivalence, and use algebraic geometry to derive the bound on the number of solutions. A homotopy method is then used to compute all the solutions. Several examples are worked out and our computational experience is summarized.     

Seismic analysis of buried pipeline in a 3D soil continuum

An efficient numerical approach based on both boundary and finite element methods is developed in this work. This development is capable of realistic three dimensional analyses of soil-structure interaction problems in the real time domain and is specifically tailored to buried lifelines. In particular, boundary elements are used in a surface-only representation of the buried cavity problem for determining influence functions at the cavity/pipeline interface for the case of prescribed motions at the control point. Subsequently, these influence functions are converted into loads and are used as input to a finite element model of the pipeline. Following careful validation studies, the present methodology is applied to a real site with known seismological characteristics and the results are gauged against empirical design formulae. It is shown that the seismically induced stress state in a buried pipeline is more pronounced in the case of transverse vibrations than in the case of longitudinal vibrations.     

Application of fractional order theory of thermoelasticity to 3D time-dependent thermal shock problem for a half-space

A three-dimensional model of thermoelasticity with fractional order heat transfer is established. The resulting nondimensional coupled equations together with the Laplace and double Fourier transforms techniques are applied to a half space, which is assumed to be traction free and subjected to a thermal shock that is a function of time. The inverses of Fourier transforms and Laplace transforms are obtained numerically. Numerical results for the temperature, the stress, the strain, and the displacement distributions are represented graphically. The predictions of the theory are discussed and compared with those for the coupled and generalized theories of thermoelasticity.     

Simple shear in 3D DEM polyhedral particles and in a simplified 2D continuum model

We develop a discrete element model (DEM) simulation of mixed regular rounded polyhedra and spheres in simple shear with walls and periodic boundaries in 3-dimensions. The results show reasonably realistic behaviour developing shear and dilation or compaction depending on whether the initial state is dense or loose. Similarly non-coaxiality of principal stress direction and strain rate direction are shown. Polyhedra show more general realistic behaviour than spheres but take significantly longer to run. Particle forces include normal elastic, damping, and tangential friction and rolling friction. No cohesion or interstitial fluid is modelled. A separate simplified dynamic implicit finite difference Eulerian continuum model is developed and its parameters are used to fit the DEM results. This uses mass and momentum balances, a non-linear constitutive model and Mohr–Coulomb failure criterion. It runs in 2D with periodic boundaries effectively making it pseudo-1D. The model can reproduce the general trend of the DEM results and is a good basis for further development and understanding the physics.     

3D Imaging of particle motion during penetrometer testing

We present the results of direct observation of material rearrangement due to penetration of a solid rod (penetrometer) through a granular medium. Two different techniques and their advantages are discussed in this paper. We investigate the motion of material within the bulk around the rod. Transparent, polydisperse, and irregularly shaped silica particles immersed in index matching fluid are used for detailed imaging of the interior of a granular pile. Motion of material is observed by confocal microscopy from the bottom boundary up to 100 particle diameters in height. Image analysis indicates that rearrangements spread furthest not directly under the penetrometer but in a ring around the penetrometer. In addition, the direction of preformed stress chains in the material influences the particle rearrangements. Material compressed from one side exhibits anisotropic particle rearrangements under penetrometer testing. Laser sheet scanning allows for direct imaging of individual particle motion with greater accuracy, but works best for spherical particles only.     

Spectrum analysis of motion parallax in a 3D cluttered scene and application to egomotion

Previous methods for estimating observer motion in a rigid 3D scene assume that image velocities can be measured at isolated points. When the observer is moving through a cluttered 3D scene such as a forest, however, pointwise measurements of image velocity are more challenging to obtain because multiple depths, and hence multiple velocities, are present in most local image regions. We introduce a method for estimating egomotion that avoids pointwise image velocity estimation as a first step. In its place, the direction of motion parallax in local image regions is estimated, using a spectrum-based method, and these directions are then combined to directly estimate 3D observer motion. There are two advantages to this approach. First, the method can be applied to a wide range of 3D cluttered scenes, including those for which pointwise image velocities cannot be measured because only normal velocity information is available. Second, the egomotion estimates can be used as a posterior constraint on estimating pointwise image velocities, since known egomotion parameters constrain the candidate image velocities at each point to a one-dimensional rather than a two-dimensional space.     

A continuum theory of degrading elastic solids with application to stress corrosion

A mechanical constitutive relationship is developed for a material-corrodant system that includes the effects of corrosion, stress corrosion, and fatigue corrosion. The constitutive theory is based on observed macroscopic material behavior and the principles of continuum mechanics. The development is for a fixed material-corrodant system and for arbitrary stress, temperature, and corrodant concentration histories. The framework of the theory is that of aging materials; however, the real time is replaced by an intrinsic material time coordinate that depends on the relevant constitutive parameters.     

ShockWave3D技术在工程图学CAI中的应用

文章讨论了3D技术在图学教育CAI中的应用状况,介绍了Shockwave3D技术的开发环境和技术特点,讨论了Shockwave3D对于制作CAI 3D交互动画的优势,简介了在Director中几种常见的CAI元素和3D交互动画的创作方法,最后给出一个截交线的课件实例.     

画法几何在三维设计中的应用

对某些空间几何问题，采用画法几何的方法进行解题比用其它方法解题要简单快捷得多。但在三维设计环境中，采用传统的画法几何方法进行解题却有很大的局限性．针对三维设计中的一些难以解决的空间几何问题，尝试采用画法几何的方法，并应用三维造型中几何约束、基准平面等基本理论，将画法几何的应用领域拓展到三维设计环境中，探讨了“三维设计环境中的画法几何”的问题，从而避免了二维空间和三维空间的数据交换问题，提高了设计的效率。     

Application of localized meshless methods to 2D shallow water equation problems

This study aims to apply the meshless local radial-basis-function differential quadrature (LRBFDQ) method to solve the shallow water equations (SWE). This localized approach is developed from the differential quadrature (DQ) method by employing the radial-basis functions (RBFs) as the trial functions. Comparing with global-type meshless methods, the present method is more appropriate to large-scale problems with complex shapes. Moreover the drawbacks rising from the poor selection of shape parameter and also the full resultant matrix with high condition number are reduced. For real hydraulic-engineering applications located in irregular domains, the LRBFDQ method is very suitable to solve these kinds of shallow-water problems. In this work, the numerical models are applied to simulate three typical 2D SWE problems: (1) a tidal-wave propagation, (2) a dam-break problem and (3) an inverse engineering problem: the numerical analysis of the inflow discharge of the Yuanshantze Flood Diversion (YFD) project in Taiwan. As a result, the adopted meshless method not only shows its algorithm superiority over other mesh-dependent numerical schemes, but also brings more efficiency than several conventional mesh or meshless methods. The application of YFD project also delivers its applicability of this meshless scheme to solve real-world engineering projects.     

Pathways to controlled 3D deformation of graphene: Manipulating the motion of topological defects

Functional properties of 2D materials like graphene can be tailored by designing their 3D structure at the Angstrom to nanometer scale. While there are routes to tailoring 3D structure at larger scales, achieving controllable sub-micron 3D deformations has remained an elusive goal since the original discovery of graphene. In this contribution, we summarize the state-of-the-art in controllable 3D structures, and present our perspective on pathways to realizing atomic-scale control. We propose an approach based on strategic application of mechanical load to precisely relocate and position topological defects that give rise to curvature and corrugation to achieve a desired 3D structure. Realizing this approach requires establishing the detailed nature of defect migration and pathways in response to applied load. From a computational perspective, the key needed advances lie in the identification of defect migration mechanisms. These needed advances define new forward and inverse problems: when a fixed stress or strain field is applied, along which pathways will defects migrate?, and vice versa. We provide a formal statement of these forward and inverse problems, and review recent methods that may enable solving them. The forward problem is addressed by determining the potential energy surface of allowable topological configurations through Monte Carlo and Gaussian process models to determine defect migration paths through dynamic programming algorithms or Monte Carlo tree search. Two inverse models are suggested, one based on genetic algorithms and another on convolutional neural networks, to predict the applied loads that induce migration and position defects to achieve desired curvature and corrugation. The realization of controllable 3D structures enables a vast design space at multiple scales to enable new functionality in flexible electronics, soft robotics, biomimetics, optics, and other application areas.     

The development and evaluation of Syco3D: a real-time collaborative 3D CAD system

This paper describes the development and evaluation of a real-time collaborative 3D CAD system, Syco3D, which allows distributed designers in a small team to work together to build and edit virtual 3D models. A shared 3D workspace, Shared Stage, is incorporated in a conventional CAD interface and provides a number of real-time collaborative features in two main interface elements: Synchronised Stage View and Data Structure Diagram. This paper also reports on a usability experiment with two versions of the system, one with the Shared Stage module and the other without, and discusses the issues raised from the development and experiments with the real-time collaborative 3D CAD system.     

Application of Clifford algebra {C ell_3(mathbb{C})} to continuum and engineering mechanics

Multivectorial algebra is of both academic and technological interest. Its application, however, is not always easy. A distinction must be made between polar and axial vectors and between scalars and pseudo-scalars. Eight element types are often considered even if they are not always identified as multivectors. In some cases, for simplicity’s sake, only vectorial algebra or quaternion algebra is explicitly used for physical and mechanical applications. It would, however, be more convenient to use more complex algebra directly in order to have a wider range of mechanical applications. The aim of this paper is to examine one particular type of Clifford algebra that could solve this problem. The present study focusses on showing how these quantities can be used to model mechanical and engineering problems. First, continuum mechanics in a Cauchy medium is investigated for elastic transformations. Second, a specific type of shot-peening application is studied. Applications are then used to illustrate the scope and efficiency of this type of modeling based on geometric algebra.     

A continuum theory of chemically reacting mixtures of fluids and solids

In this work, a continuum theory of a chemically reacting mixture composed of solids and fluids is presented. Following a different line of localization, a set of balance equations applicable to every component in the mixture is obtained. These are: conservation of mass, balance of momenta, conservation of energy and the principle of entropy which is also given for every species in the mixture. The localization is so applied that the individual energy equations are form invariant under time dependent motions of the spatial frame of reference and every state variables appearing explicitly in these equations can be considered as objective quantities. By use of the concept of reactive mass density for solid continuum and modifying the axiom of equipresence, originally developed for single bodies, a set of thermodynamically admissible constitutive relations is derived for a reacting mixture composed of a solid and a non-Newtonian fluid. Finally, utilizing the linearized field and constitutive equations, the propagation of simple harmonic waves in such a medium is studied and several particular cases are discussed.     

Application of the material force method to isotropic continuum damage

 The objective of this work is the exploitation of the notion of material forces in computational continuum damage mechanics. To this end we consider the framework of isotropic geometrically non–linear continuum damage and investigate the spatial and material settings that lead to either spatial or material forces, respectively. Thereby material forces essentially represent the tendency of material defects to move relative to the ambient material. In this work we combine an internal variable approach towards damage mechanics with the material force method. Thus the appearance of distributed material volume forces that are conjugated to the damage field necessitates the discretization of the damage variable as an independent field in addition to the deformation field. Consequently we propose a monolithic solution strategy for the corresponding coupled problem. The underlying kinematics, strong and weak forms of the coupled problem will be presented and implemented within a standard Galerkin finite element procedure. As a result in particular global discrete nodal quantities, the so–called material node point (surface) forces, are obtained and are studied for a number of computational examples. Received: 19 August 2002 / Accepted: 16 October 2002