3D Solids Research Articles

A marching cubes based failure surface propagation concept for three‐dimensional finite elements with non‐planar embedded strong discontinuities of higher‐order kinematics

SUMMARYThis paper presents an advanced failure surface propagation concept based on the marching cubes algorithm initially proposed in the field of computer graphics and applies it to the embedded finite element method. When modeling three‐dimensional (3D) solids at failure, the propagation of the failure surface representing a crack or shear band should not exhibit a strong sensitivity to the details of the finite element discretization. This results in the need for a propagation of the discrete failure zone through the individual finite elements, which is possible for finite elements with embedded strong discontinuities. Whereas for two‐dimensional calculations the failure zone propagation location is easily predicted by the maximal principal stress direction, more advanced strategies are needed to achieve a smooth failure surface in 3D simulations. An example for such method is the global tracking algorithm, which predicts the crack path by a scalar level set function computed on the basis of the solution of a simplified heat conduction like problem. Its prediction may though lead to various scenarios on how the failure surface may propagate through the individual finite elements. In particular, for a hexahedral eight‐node finite element, 256 such cases exist. To capture all those possibilities, the marching cubes algorithm is combined with the global tracking algorithm and the finite elements with embedded strong discontinuities in this work. In addition, because many of the possible cases result in non‐planar failure surfaces within a single finite element and because the local quantities used to describe the kinematics of the embedded strong discontinuities are physically meaningful in a strict sense only for planar failure surfaces, a remedy for such scenarios is proposed. Various 3D failure propagation simulations outline the performance of the proposed concept. Copyright © 2013 John Wiley & Sons, Ltd.

On the Importance of Work-Conjugacy and Objective Stress Rates in Finite Deformation Incremental Finite Element Analysis

This paper is concerned with two issues that arise in the finite element analysis of 3D solids. The first issue examines the objectivity of various stress rates that are adopted in incremental analysis of solids. In doing so, it is revealed that large errors are incurred by an improper choice of stress rate. An example problem is presented to show the implications of the choice of stress rate. The second issue addresses the need to maintain work-conjugacy in formulating and solving bifurcation buckling problems of 3D elastic solids. Four popular commercial codes are used to obtain buckling loads of an axially compressed thick sandwich panel, and it is shown that large errors in buckling load predictions are incurred as a result of violating the requirement of work-conjugacy. Remedies to fix the errors in the numerical solution strategy are given.

Design and Two-Photon Polymerization of Complex Functional Micro-Objects for Lab-on-a-Chip: Rotating Micro-Valves

Two-Photon Polymerization is a powerful technology that can be used to fabricate complex functional microobjects in lab-on-a-chip platforms. It is a laser-based prototyping technique with full tri-dimensional capability and sub-micron resolution. We report on the development of a computer-assisted design and fabrication process based on Q-switched Nd:YAG microlasers and AutoCAD environment. Microlasers with sub-nanosecond pulses of visible light are efficient and low cost lasers for two-photon microfabrication. Polymerization is easily obtained with sub-milliwatt average powers (12 kHz repetition rate). The microfabrication software has been developed to design the micro-objet models and to calculate their laser trajectories using AutoCAD. It is open platform for the design of 3D solids with full access to entities information, and an efficient slicing command that can cut solids from any orientation plane. As a typical example of complex functional micro-object, we report on the fabrication of laser-driven rotating micro-valves. The design parameters have been optimized to allow a free movement of the valve around its axis using the optical force of a laser tweezers.

Lamellar zeolites: an oxymoron?

“Lamellar zeolites” can be considered as an oxymoron. Zeolites, by definition, are three-dimensional structures displaying pores of a molecular dimension. Lamellar materials, contrarily, are bidimensional materials that, in some cases, can be delaminated, that is, have their lamella separated. It is exactly the combination of these properties that is so attractive in lamellar zeolites. They are zeolites whose precursors are/can be prepared in such a way as to display bidimensional organization where parts of the structure, the lamella, interact with one another by weak forces through the interactions of organic/inorganic ions and/or molecules housed in the “interlayer” spaces. From these precursors, calcination procedures lead to the 3D zeolitic structures, delamination in solutions provides individual or groups of lamella, pillarization processes conduct to mesoporous molecular sieves. Naturally, all these procedures eliminate the shape selectivity typical of zeolites in all cases of lamellar zeolites known so far, except one particular structure. However, providing that the resulting layers keep the original structure of the precursor, most of the zeolite acidity remains in the final material. In this way, pore sizes that limit the access of larger molecules to the active sites in the zeolites are not formed, the surface area of the material is increased and large molecular weight molecules are free to react in surface sites made available by the delamination or pillaring of layered zeolites. Finally, 3D fully connected zeolites can be deconstructed into layered zeolites from which all the above procedures are foreseen to provide modified solids. This recent discovery opens up a wealth of interesting structures from which to extract lamella with surface exposed active sites. Lamellar zeolites may be considered a true link between 2D and 3D solids and allow us to really determine which properties derive from one or the other structural dimensions, thus allowing us to precisely design structure-based properties for use in a range of technological applications.

Analysis of Piezoelectric Solids through Boundary Element Method

Boundary element method (BEM) is a powerful computational tool for analysing piezoelectric problems. The BEM has been so well developed during the past 40 years that it has been considered as a very popular computational tool. This method consists of formulating the engineering problem in terms of an integral equations relating only boundary values and determining its solutions numerically. Thus, it requires only a surface discretization, rather than a full-domain discretization with “domain-type techniques, such as the finite element method. If interior domain values are needed, however, it can be subsequently calculated from boundary data. Remarkable advances in this area during last decades can be found, for example, in Manolis and Beskos[1] and Qin [2,3]. For piezoelectric problems, BEM, as an important complementary tool for analytical method [4-8], has been the subject of fruitful scientific attention by many a distinguished researcher e.g. Lee and Jiang [9], Denda and Mansukh [10], Sanz, Ariza and Dominguez [11], Lee and Jiang [9] derived the boundary integral equation of piezoelectric media by the method of weighted residuals for plane piezoelectricity. Lu and Mahrenholtz [12] presented a variational boundary integral equation for the same problem. Ding, Wang and Chen [13] developed a boundary integral formulation which is efficient for analysing crack problems in piezoelectric material. Xu and Rajapakse [14,15] presented the formulations for problems of piezoelectric solids with various defects (cavities, inclusions, cracks, etc.). Pan [16] derived a single domain BE formulation for 2D static crack problems. Denda and Lua [17] developed a BEM formulation using Stroh’s formalism to derive the fundamental solution without numerical results. Qin [18] presented a BEM formulation for cracked piezoelectric materials with half-plane boundary. Later, Qin and Lu [19] extended the model presented in [18] to the case of piezoelectric materials containing both crack and inclusion problems. Davi and Molazo [20] used the known sub domain method to formulate a multi-domain BEM, well suited for crack problems, by modelling crack faces as boundaries of the different sub domains. Groh and Kuma [21] developed a direct collocation boundary element code with a sub domain technique for analysing crack problems and calculating stress intensity factors. Qin an Mai [22] investigate crack-hole interaction of piezoelectric materials using BEM. Zhao et al. [23], presented a boundary integral-differential model for interfacial cracks in 3D piezoelectric solids. Qin [24,25] imbedded BEM into micromechanics model for evaluating effective properties of piezoelectric solids. Analysis of Piezoelectric Solids through Boundary Element Method

3103 Isogeometric解析用3D NURBSソリッドの生成方法

3103 Isogeometric解析用3D NURBSソリッドの生成方法

Development and validation of a novel Digital Image Analysis method for fluidized bed Particle Image Velocimetry

Abstract Particle Image Velocimetry (PIV) is a widely applied non-intrusive, optical experimental technique to measure characteristics of the solids motion in pseudo 2D fluidized beds. However, the majority of the research that concerns the use of PIV on granular systems focused thus far on either particle velocities or on particle fluxes with a very rudimentary implementation for the correction for the presence of bubbles. A reliable correlation between the 2D image intensity and the true 3D solids fraction in fluidized beds is required to obtain more accurate information on the solid particle flux profiles in granular systems. Using only experimental data, it is difficult – if not impossible – to obtain such a correlation, but by using data from Discrete Particle Model (DPM) simulations to create artificial 2D-images, we reconstructed this 2D–3D correlation for the solids fraction correction. In this paper the influence of particle size, fluidization velocity, bed depth and intensity distribution function on the 2D–3D correlation has been investigated, in particular for the application in gas-solid fluidized beds in the bubbling regime. It was found that the particle size and fluidization velocity have no influence on the correlation and the intensity distribution function only slightly affects the results for dilute regions, but the bed depth shows the most prominent effect. A detailed comparison between the DPM velocity field as a reference and the conventional and newly introduced Digital Image Analysis (cDIA/ nDIA) techniques shows that the error in the solids flux decreases from 18.7% to 12.3%. Also, we used PIV software to reconstruct the solids velocity field, based on a pair of artificial images from DPM simulations (as done for experimentally acquired data based on a pair of real images), and showed that the largest error is introduced in the determination (cross-correlation) of the particle velocity field.

Boundary element method for thermoelastic analysis of three-dimensional transversely isotropic solids

Thermal effects are well known to manifest themselves as additional volume integral terms in the direct formulation of the boundary integral equation (BIE) for linear elastic solids when using the boundary element method (BEM). This domain integral has been successfully transformed in an exact manner to surface ones only in isotropy and in 2D anisotropy, thereby restoring the BEM as a truly boundary solution technique. The difficulties with extending it to 3D general anisotropic solids lie in the mathematical complexity of the Green’s function and its derivatives for such materials. These quantities are required items in the BEM formulation. In this paper, the exact, analytical transformation of the volume integral associated with thermal effects to surface ones is achieved for a transversely isotropic material using a similar approach which the authors have previously employed for the same task in BEM for 2D general anisotropy. A numerical scheme, however, needs to be employed to evaluate some of the new terms introduced in the surface integrals that arise from this process here. The mathematical soundness of the formulation is demonstrated by a few examples; the numerical results obtained are checked by alternative means, including those obtained from the commercial FEM code, ANSYS.

Boundary element method applied to three dimensional thermoelastic contact

In this paper we present a boundary element method to analyze and solve three dimensional frictionless thermoelastic contact problems. Although many problems in engineering can be solved with one-dimensional or two-dimensional models, those simplifications there are not possible in many others, such as the design of microelectronics packages. We calculate the stresses, movements, temperatures and thermal gradients on 3D solids. A thermal resistance at the contact zone depends on the local pressure is considered. The problem is solved by a double iterative method, so that in the final solution do not appear tensions in the contact zone or penetrations between the two solids. The solutions are compared with other works, where possible, to validate the method.

Using Bendable and Rigid Manipulatives in Primary Mathematics: Is One More Effective Than the Other in Conceptualising 3D Objects from Their 2D Nets?

The usefulness of manipulatives in the primary maths classroom has been frequently asserted. The purpose of this study was to compare the effectiveness of two different types of manipulatives, bendable and rigid, as aids for the conceptualisation of 3D solids from 2D nets (fold-outs of solid geometrical shapes) within the NSW Stage 2 Mathematics Curriculum. Contrary to initial expectations, the bendable nets, although more attractive to pupils, did not prove superior to the rigid variety. In fact, the most noticeable advances in conceptualisation followed teaching experiences using the rigid nets. Although this was a preliminary study and the sample sizes were too small to support solid conclusions, it is suggested that the data were sufficiently robust to warrant further investigation. We suggest that the lower than expected results for the bendable nets may be explained, partially, by the reduced conceptual demands made by these more ‘obvious’ shapes. Correspondingly, the greater mental visualisation required when working with the rigid nets may have produced heightened student conceptualisation.

Decagonal Quasicrystals and Approximants: Two‐Dimensional or Three‐Dimensional Solids?

AbstractCrystallographic structures of decagonal quasicrystals (d‐QCs) are traditionally described as a periodic stacking of atomic planes with quasiperiodic in‐plane atomic order, so that d‐QCs are considered to be two‐dimensional (2D) quasicrystals, whereas they are periodic crystals in the third dimension. Similar stacked‐layer structures are observed also in the periodic decagonal approximant phases. In this review paper, we consider the dimensionality of the chemical bonding network in the d‐QCs and their approximants on the basis of electrical resistivity. By comparing the anisotropic resistivity along the stacking‐ and the in‐plane directions of a series of decagonal approximants with different numbers of atomic layers within one periodicity unit (the two‐layer Y‐Al‐Co‐Ni, the four‐layer o‐Al13Co4, Al13Fe4 and Al13(Fe,Ni)4, and the six‐layer Al4(Cr,Fe) and T‐Al3(Mn,Fe)) and of a two‐layer d‐Al‐Co‐Ni decagonal quasicrystal, we show that universally, the stacking direction perpendicular to the atomic planes is always the most conducting one. Since the in‐plane electrical resistivities are of the same order of magnitude as the resistivity along the stacking direction, this confirms the 3D character of the investigated solids. The stacked‐layer description in terms of 2D atomic planes should therefore be regarded as a convenient geometrical approach to describe the complex structures of the d‐QCs and their approximants, whereas their physical properties are those of true 3D solids.

Calculation of the number of atoms displaced during the irradiation of monolayer graphene

The irradiation of monolayer graphene, combined with chemical functionalization, could be an effective method for modifying its electronic structure and for achieving specific physical properties adjusted to different applications. A difficulty arising during planning and studying the irradiation in this system is that many of the models of interaction of the radiation with the substance cannot be applied to the two-dimensional structure of graphene. In particular, the mathematical expressions available to calculate the number of atoms displaced during the bombardment with particles can be applied only to 3D isotropic solids. In the present work, an alternative analytic expression is presented for the irradiation of graphene with heavy ions or with protons and other light charged particles. The expression was obtained on the basis of the classic theory of dispersion, using a Coulomb potential for the light charged particles and one of Inverse Square for heavy ions. For medium values of the energy of the incident particle a decreasing dependence of the number of displaced atoms with energy is obtained. This behavior, related with the two-dimensional structure of the target, had been observed in other authors’ works using computational simulation.

A new method for identifying and validating features from 2D sectional views

Feature identification is one of the key steps for 3D solids reconstruction from 2D vector engineering drawings using the volume-based method. In this paper, we propose a novel method to identify and validate features from sectional views. First, features are classified as explicit features (EPFs) and implicit features (IPFs), which are then identified in an order of priority using heuristic hints. We show that the problem of constructing EPFs can be formulated as a 0-1 integer linear program (ILP), and the IPFs are generated based on the understanding of semantic information of omitted projections in sectional views. Then, the Loop-Relation Graph (LRG) is introduced as a multi-connected-subgraph representation for describing the relations between loops and features. According to the LRG, a reasoning technique based on confidence is implemented to interactively validate features. This method can recover features without complete projections, and the level of understanding sectional views is improved. Full sections, partial sections, offset sections as well as revolved sections can be handled by our method. Several examples are provided to demonstrate the practicability of our approach.

Effects of Hydrophobic Chain Length on Temperature Dependence of Monolayer Behavior of Ester-type Tartaric Geminis

Ester-type tartaric gemini amphiphiles bearing two carboxyl groups and two hydrophobic alkanoyl groups were prepared from L-tartaric acid, and the pressure-area (π-A) isotherms for a series of symmetric tartaric gemini amphiphiles were measured by the conventional film-balance technique. The effects of the length of the hydrophobic alkanoyl chains and of the subphase temperature (T(sub)) on the π-A isotherms for these compounds were examined. As the length of the hydrophobic alkyl chain increased, a more tightly packed monolayer was formed at the air-water interface. The melting temperature (T(m)) of the monolayer on the water surface was evaluated from the subphase temperature (T(sub)) dependence of the monolayer static elasticity ε(s), based on a π-A isotherm. A clear relationship between T(m) and hydrophobic carbon number (n) was observed for 2D monolayers of tartaric geminis on water surfaces, as well as for fatty acids and/or 3D solids.

Atomistic simulation studies of size effects in plasticity: compression of single- and polydomain crystals in two dimensions

We perform atomistic Monte Carlo simulations of a Lennard-Jones crystal under uniaxial compression on single crystal and polycrystalline samples in two dimensions. In single crystals, we observe a size effect in initial yield: smaller samples yield at higher stress. We also find a size effect in the plastic regime which is accounted for by dislocation starvation. Two-dimensional polycrystalline samples are generated using a statistical physics model, and studied under uniaxial compression. The resulting microstructures show higher stress within the grain boundary regions relative to that in the bulk, consistent with theoretical models and experimental results. We also examine the broad distribution of stresses within the polydomain sample and compare with recent experimental observations. While 2D simulations cannot predict behavior of real 3D solids, they are valuable for exploring some of the fundamental mechanisms controlling mechanical response and serve as a testing ground for theories of size effects in plasticity.

Mott and Efros-Shklovskii Variable Range Hopping in CdSe Quantum Dots Films

The model of variable range hopping conductivity predicts a crossover between Mott and Efros-Shklovskii as a function of temperature and density of states. This is observed using monodispersed CdSe colloidal quantum dot 3D solids where the density of states at the Fermi level is varied by electrochemistry. At low density of states, both below the lowest state (<0.4e(-)/dot) and in the conductivity gap between the first and second state (2e(-)/dot), the temperature dependence of the conductivity shows the 1/4 exponent of Mott hopping. At other fillings up to 6e(-)/dot, the conductivity shows the 1/2 exponent of Efros-Shklovskii hopping. The non-Ohmic conductivity is also found to be explained quantitatively by the variable range hopping model.

A node-based smoothed finite element method (NS-FEM) for upper bound solution to visco-elastoplastic analyses of solids using triangular and tetrahedral meshes

A node-based smoothed finite element method (NS-FEM) was recently proposed for the solid mechanics problems. In the NS-FEM, the system stiffness matrix is computed using the smoothed strains over the smoothing domains associated with nodes of element mesh. In this paper, the NS-FEM is further extended to more complicated visco-elastoplastic analyses of 2D and 3D solids using triangular and tetrahedral meshes, respectively. The material behavior includes perfect visco-elastoplasticity and visco-elastoplasticity with isotropic hardening and linear kinematic hardening. A dual formulation for the NS-FEM with displacements and stresses as the main variables is performed. The von-Mises yield function and the Prandtl–Reuss flow rule are used. In the numerical procedure, however, the stress variables are eliminated and the problem becomes only displacement-dependent. The numerical results show that the NS-FEM has higher computational cost than the FEM. However the NS-FEM is much more accurate than the FEM, and hence the NS-FEM is more efficient than the FEM. It is also observed from the numerical results that the NS-FEM possesses the upper bound property which is very meaningful for the visco-elastoplastic analyses which almost have not got the analytical solutions. This suggests that we can use two models, NS-FEM and FEM, to bound the solution, and can even estimate the global relative error of numerical solutions.

DEVELOPMENT OF 3D NUMERICAL MANIFOLD METHOD

The numerical manifold method (NMM) is a combination of the finite element method (FEM) and discontinuous deformation analysis (DDA) method. It provides a robust numerical solution to a solid medium with dense discontinuities. This paper extends NMM to the three-dimensional domain based on the 2D fundamentals. The general framework of the 3D NMM is introduced, including the cover geometry patterns (GP) with division structure from hexahedron to tetrahedron, and general formulations based on the virtual work principle. The block cutting process to generate discrete blocks are discussed through the topological structure description of blocks, and the operation rule of blocks is explained. The proposed 3D block generation algorithm allows for any arbitrary discrete structure or block system. Three numerical examples are presented to demonstrate that the developed 3D numerical manifold code is effective and applicable to 3D continuum solids. Further developments aim to incorporate contact models to simulate complicated discrete block system.

The first 3D framework based on Dawson-like [SbW 18O 60] 9− polyoxoanions

Two new 3D framework solids based on tungstoantimonate [H 2bpy] 2[Ni(bpy)(Hbpy) 2HSbW 18O 60]·4H 2O ( 1) and [H 2bpy] 2[Cu(bpy)(Hbpy) 2HSbW 18O 60]·5H 2O ( 2) (bpy = 4,4′-bipyridine) have been synthesized hydrothermally and structurally characterized by elemental analyses, IR spectra, thermal stability analyses, and single-crystal X-ray diffraction analysis. Structure analysis reveals that both of the structures exhibit 3D host frameworks constructed from the non-classical Dawson-like [SbW 18O 60] 9− polyoxoanions building units and 1D coordination cationic chains ([Ni(bpy)(Hbpy) 2] n 4 n + for 1 or [Cu(bpy)(Hbpy) 2] n 4 n + for 2), which represent the first 3D frameworks composed of Dawson-like [SbW 18O 60] 9− polyoxoanions. Furthermore, the compound 2-modified carbon paste electrode ( 2-CPE) displays good electrocatalytic activity toward the reduction of nitrite.

OPTIMIZATION OF THREE-DIMENSIONAL MODELING IN ENGINEERING AND BUILDING DESIGN IN THE EDUCATIONAL PROCESS

AutoCAD possibilities of 3D solid modeling are described in the article. The optimum methods of designing for construction and machine drawing applying are analyzed. The choice of methods for 3D solids drawing is proved by samples.