Three-dimensional Formulation Research Articles

Determination of Interlaminar Shear Properties of Fibre-Reinforced Composites under Biaxial Loading: A New Experimental Approach.

The complexity of biaxial tests and analysis of their results makes it difficult to study the interlaminar shear properties of fibre-reinforced composites, particularly under through-thickness compression, which occurs in thick-walled composite elements. The improvements in experimental methods to study the features of the nonlinear behaviour of composites under biaxial loading is now an important and relevant task in the development aircraft structural elements made of carbon fibre-reinforced polymers. This study aimed to develop a new experimental approach for the reliable determination of the interlaminar shear properties of laminates under through-thickness compression using a standard testing machine. An appropriate V-notched specimen was developed based on the configuration of well-known Iosipescu and butterfly-shaped specimens. The approach is demonstrated using woven carbon/epoxy laminates. Both the preliminary assessment of the stress fields under combined compression/shear loading and the analysis of fracture mechanisms were performed with finite-element modelling in a three-dimensional formulation. The digital image correlation (DIC) method was used to obtain experimental, full-field deformations of the specimens and to estimate the uniformity of the strain distribution in the gauge section. The stress–strain curves were obtained under biaxial loading, and the corresponding features of the composite failure behaviour were analysed in detail. It was found that the maximum compression strain on the stress–strain curves, in some cases, corresponded to the discontinuity in the composite structure. In these cases, the disproportionate changes in through-thickness strains in the gauge section of the specimens were recorded at the maximum load. With the increase in through-thickness compression stresses, the difference between the shear strength values, determined by the maximum load and the maximum compressive strain, increased by up to 20%. It was shown that the assessment of the composite strength at maximum load at the design stage significantly increased the risk of premature failure of the composite elements during exploitation.

Numerical Study on Thermal Performance of Water Flow in a Twisted Duct Heat Exchanger

This paper presents a numerical study of heat transfer through a downstream annulus using water as the working fluid within the laminar flow region. The annulus consisted of an outer twisted square duct and an inner circular pipe. A three-dimensional formulation was used to solve the Navier-Stokes equations numerically for the laminar flow system with a low Reynolds number. Three parameters were used in the numerical simulation: the length of the twisted square (<i>a</i>: <i>6.6</i>, <i>8.2 10.2, 12.6 mm</i>) the inner diameter of the inner circular pipe (<i>d</i>: <i>19, 21, 23 and 25 mm</i>); and the twist angle (θ: <i>0</i>° (smooth), <i>45</i>°, <i>60</i>°, <i>and 90</i>°). Numerical calculations were conducted on sixteen twisted square duct heat exchangers, with water flowing within a Reynolds number range of <i>220</i> – <i>1100</i>. The results were illustrated as a profile of the thermal enhancement factor, the friction factor and the Nusselt number. The results show that the twisted outer duct of the heat exchanger can create a swirl flow along the length of the heat exchanger. It also caused a boundary layer separation-reattachment on the wall of the inner pipe. Moreover, an increase in the twist angle increased the Nusselt number by <i>20</i> %, and the friction factor was also increased as the annular gap of the heat exchanger decreased.

Novel asymmetric space vector pulse width modulation for dead-time processing in three-phase power converters

<p>This research analyzes the asymmetric control strategies in multilevel inverters, including asymmetric techniques in space vector modulation of power converters. Modulation parameters such as reference voltage vector (Vref), switching time, and duty cycle are derived in the three-dimensional spatial vector geometry formulation. Asymmetric space vector pulse width modulation (SVPWM) is unique in specifying modulation parameters, has unequal tetrahedron patterns, accompanied by application examples for the upper and lower sector pairs of a tetrahedron. The combination of the switch in the form of an inclined cylinder produces twelve pairs of asymmetric tetrahedrons where the voltage vector positions are in the other twenty-four tetrahedrons. The calculation shows processing dead-time in switching, which is used for current compensation in three-phase power converters.</p>

DETERMINATION OF STRESSES IN A CYLINDRICAL SHELL TAKING INTO ACCOUNT HOLES

Perforated elements are widely used in collectors of nuclear power plants, chemical devices, construction equipment. Perforation allows to reduce the material consumption of an expensive product, to facilitate the design and is performed for design reasons. At the same time, there is a concentration of stresses near the holes, which significantly reduces the durability of the perforated parts of the products, as well as determines the relevance of the study of the stress-strain state in the perforated parts. The paper presents an analytical description of the problem of the theory of elasticity for a perforated thick-walled cylinder in thermomechanical formulation. The problem of cylindrical bodies of rotation was considered in the axisymmetric three-dimensional formulation in displacements with the definition of stress and strain tensors. It is shown that numerical methods, in particular the finite element method, must be used to solve problems on the stress-strain state of perforated cylinders. For thick-walled perforated cylinders, it is advisable to use finite three-dimensional elements. Problems for homogeneous thick-walled and perforated cylinders were solved using three-dimensional and shell finite elements. Both four-node shell and three-dimensional eight-node prismatic finite elements were used in the numerical solution of this problem. The loading of the cylinder with holes was internal pressure. From the comparison of the results it follows that in the absence of holes it is enough to use two-dimensional shell finite elements, but in the presence of holes in perforated thick-walled shells there is a concentration of stress, so in this case it is advisable to consider the problem in three-dimensional form. It is shown in the paper that the solution of the problem taking into account the consolidated stiffness for the shell model gives an underestimated value of stresses, because it does not take into account the stress concentration on the inner surface of the shell. The coefficient of stress concentration obtained in the work due to the presence of holes was equal to two.

A three-dimensional weak formulation for stress, deformation, and free vibration analyses of functionally graded microscale plates based on the consistent couple stress theory

A three-dimensional (3D) weak formulation based on the consistent couple stress theory (CCST) is developed for displacement, stress, and free vibration analyses of simply-supported, power-law-/exponential-type functionally graded (FG) microscale plates. In the formulation, the microscale plate is artificially divided into numerous finite microscale layers, where Fourier functions and Lagrange/Hermite polynomials are used to interpolate the in- and out-of-plane variations in the displacement variables for each individual layer, respectively. Based on the weak formulation, the authors develop layer-wise C0 quadratic and cubic finite element methods (FEMs), as well as layer-wise C1 two- and three-node FEMs to address the current issue. The accuracy and convergence of these layer-wise C0 and C1 FEMs are validated by comparing their solutions with the 3D exact and the quasi-3D results available in the literature. A 3D weak formulation based on the modified couple stress theory (MCST) is also developed for comparison purposes. The similarity and differences between the results obtained using the CCST- and MCST-based weak formulations are examined and discussed. Some key effects on stress, deformation, and free vibration characteristics of the FG microscale plate are examined, including the material length scale, the material-property gradient index, and the length-to-thickness ratio effects, which are shown to be significant for the FG microscale plate.

Convection-Enhanced Delivery In Silico Study for Brain Cancer Treatment.

Brain cancer therapy remains a formidable challenge in oncology. Convection-enhanced delivery (CED) is an innovative and promising local drug delivery method for the treatment of brain cancer, overcoming the challenges of the systemic delivery of drugs to the brain. To improve our understanding about CED efficacy and drug transport, we present an in silico methodology for brain cancer CED treatment simulation. To achieve this, a three-dimensional finite element formulation is utilized which employs a brain model representation from clinical imaging data and is used to predict the drug deposition in CED regimes. The model encompasses biofluid dynamics and the transport of drugs in the brain parenchyma. Drug distribution is studied under various patho-physiological conditions of the tumor, in terms of tumor vessel wall pore size and tumor tissue hydraulic conductivity as well as for drugs of various sizes, spanning from small molecules to nanoparticles. Through a parametric study, our contribution reports the impact of the size of the vascular wall pores and that of the therapeutic agent on drug distribution during and after CED. The in silico findings provide useful insights of the spatio-temporal distribution and average drug concentration in the tumor towards an effective treatment of brain cancer.

Studies about Solution Convergence of the Spline Version of the Finite Element Method in Two-Dimensional and Three-Dimensional Formulations

Studies about Solution Convergence of the Spline Version of the Finite Element Method in Two-Dimensional and Three-Dimensional Formulations

Numerical Investigation of High-Order Solid Finite Elements for Anisotropic Finite Strain Problems

In this paper, a hierarchic high-order three-dimensional finite element formulation is studied for hyperelastic and anisotropic elastoplastic problems at finite strains. The element formulation allows for anisotropic ansatz spaces supporting efficient discretizations of beam-, plate-, and shell-like structures. Several benchmark examples are investigated and the results of the high-order formulation are compared to analytic solutions and different mixed finite element formulations. Special emphasis will be placed on locking effects, robustness with respect to high aspect ratios and element distortion as well as anisotropies related to the material model. Furthermore, the interplay between the chosen ansatz space for the displacement field and mapping function in the context of geometrically nonlinear problems are studied.

Comparative analysis of the lattice Boltzmann method and the finite difference technique of thermal convection in closed domains with heaters

PurposeThe purpose of this paper is to investigate numerically thermal convection heat transfer in closed square and cubical cavities with local energy sources of various geometric shapes.Design/methodology/approachThe analyzed regions are square and cubical cavities with two isothermally cold opposite vertical walls, whereas other walls are adiabatic. A local energy element of rectangular, trapezoidal or triangular shape is placed on the lower surface of the cabinet. The lattice Boltzmann technique has been used as the main method for the problem solution in two-dimensional (2D) and three-dimensional (3D) formulations, whereas the finite difference technique with non-primitive parameters such as stream function and vorticity has been also used.FindingsThe velocity and temperature fields for a huge range of Rayleigh number 104–106, as well as for various geometry shapes of the heater have been studied. A comparative analysis of the results obtained on the basis of two numerical techniques for 2D and 3D formulations has been performed. The dependences of the energy transfer strength in the region on the shape of energy source and Rayleigh number have been established. It has been revealed that the triangular shape of the energy source corresponds to the maximum values of the velocity vector and temperature within the cavity, and the rectangular shape corresponds to the minimum values of these mentioned variables. With the growth of the Rayleigh number, the difference in the values of these mentioned variables for rectangular and triangular shapes of heaters also increases.Originality/valueThe originality of this work is to scrutinize the lattice Boltzmann method and finite difference method for the problem of natural convection in 2D and 3D closed chambers with a local heated element.

Modeling the process of mixing the coolant in the lower section and pressure mixing chamber of VVER-1200 (V-491)

The most representative accident scenario is determined and a physical and mathematical model is developed for studying the mixing of non-isothermal coolant flows in the structural elements of the V-491 reactor facility (VVER-1200), in which the motion of the medium is described in a three-dimensional non-stationary formulation. Based on the analytical estimates of the list of initiating events, a scenario was chosen with the connection of an idle loop of the main circulation pipeline to three operating ones without a preliminary power reduction. A computational algorithm and a numerical method have been developed for the computational analysis of the selected accident scenario and the justification of the safety of operation of the V-491 reactor facility (VVER-1200). During the numerical simulation, the RANS method was used, which consists in solving the Reynolds-averaged Navier–Stokes equations, the continuity equation and the energy equation. The SST k–ω model of turbulence by Florian Menter is used to close the equations. The verification of the developed physical and mathematical model and calculation procedure was carried out by modeling thermohydraulic processes in models with both a relatively simple geometric design (tee connection) and in a scale model of the reactor vessel (ROCOM experiment), including a lowering section and a pressure mixing chamber. The qualitative agreement of the numerical simulation results with the available data of physical experiments is shown. The results of numerical simulation of the mixing process of non-isothermal coolant flows in the section from the branch pipe of the “cold” thread of the main circulation pipeline to the lower boundary of the fuel of the VVER-1200 core (V-491) are presented. It is shown that the heterogeneity in the temperature distribution at the entrance to the core manifests itself up to 15.5 s of the calculated accident scenario. For calculations the following code coupling were used: Ansys Fluent/Rainbow-TPP.

Spline-based space-time finite element approach for fluid-structure interaction problems with a focus on fully enclosed domains

Non-Uniform Rational B-Spline (NURBS) surfaces are commonly used within Computer-Aided Design (CAD) tools to represent geometric objects. When using isogeometric analysis (IGA), it is possible to use such NURBS geometries for numerical analysis directly. Analyzing fluid flows, however, requires complex three-dimensional geometries to represent flow domains. Defining a parametrization of such volumetric domains using NURBS can be challenging and is still an ongoing topic in the IGA community.With the recently developed NURBS-enhanced finite element method (NEFEM), the favorable geometric characteristics of NURBS are used within a standard finite element method. This is achieved by enhancing the elements touching the boundary by using the NURBS geometry itself. In the current work, a new variation of NEFEM is introduced, which is suitable for three-dimensional space-time finite element formulations. The proposed method makes use of a new mapping which results in a non-Cartesian formulation suitable for fluid-structure interaction (FSI).This is demonstrated by combining the method with an IGA formulation in a strongly-coupled partitioned framework for solving FSI problems. The framework yields a fully spline-based representation of the fluid-structure interface through a single NURBS.The coupling conditions at the fluid-structure interface are enforced through a Robin-Neumann type coupling scheme. This scheme is particularly useful when considering incompressible fluids in fully Dirichlet-bounded and curved problems, as it satisfies the incompressibility constraint on the fluid for each step within the coupling procedure.The accuracy and performance of the introduced spline-based space-time finite element approach and its use within the proposed coupled FSI framework are demonstrated using a series of two- and three-dimensional benchmark problems.

GCM-motivated Multidimensional Temperature Parametrization Scheme for Phase-curve Retrieval

Abstract We present a novel physically motivated, parametrized temperature model for phase-curve retrieval, able to self-consistently assess the variation in thermal structure in multidimensions. To develop this approach, we drew motivation from both full three-dimensional general circulation models and analytic formulations, accounting for the dominant dynamical feature of tidally locked planets, the planetary jet. Our formulation shows notable flexibility. It can generate planetary jets of various characteristics and redistribution efficiencies seen in the literature, including both standard eastward and unusual westward offset hotspots, as well as more exotic configurations for potential future observations. In our modeling scheme we utilize a tractable set of parameters efficient enough to enable future Bayesian analysis and, in addition to the resolved temperature structure, we return physical insights not yet derived from retrievals: the amplitude and the phase offset, and the location and the extent of the equatorial jet.

THE CALCULATION OF THE MAIN CHARACTERISTICS OF A TURBOMOLECULAR VACUUM PUMP WITH BLADES OF VARIABLE THICKNESS

The calculated dependences and the results of modeling the process of the flow of a rarefied gas through the flow part of a turbomolecular vacuum pump with blades of variable thickness in a three-dimensional formulation of the problem solution are presented. The Monte Carlo method was used for modeling. The calculations trace the movement of each gas molecule from the inlet to the outlet of the pump with the calculation of the probabilities of their passage in the forward and reverse directions. The gas flow mode is molecular.

DYNAMIC MODEL OF A RAILWAY LIFTING CRANE

Introduction: Currently, mobile boom cranes equipped with telescopic boom equipment are widely used in construction, loading and unloading, as well as installation. Purpose of the study: We aimed to develop a dynamic model for a railway lifting crane, taking into account the interaction of its structural elements with each other and the bearing soil surface in a three-dimensional formulation. Methods: In the course of the study, we used Simulation and Motion modules of the SolidWorks software package, Klepikov’s non-linearly deformable soil model, and Lagrange’s equation of the second kind. Results: As a result, we developed a numerical analytical 3D model describing dynamic loading and deformation of the “mobile boom crane – foundation” system in a three-dimensional formulation. The model takes into account the following: the internal bending deformation and the interaction of the mating structural elements of a crane (telescopic sections, telescoping hydraulic cylinders, and outriggers), hoist rope rigidity, grillage (framework of sleepers) influence, elastic and plastic properties of the base platform soil, and action of inertial loads on the structural elements of the lifting crane.

On the role of heat source location and multiplicity in topographically controlled Marangoni–Rayleigh–Bénard convection

Periodically distributed wall-mounted hot blocks with a cubic shape located at the bottom of a layer of liquid with a free top interface tend to create patterns in their surrounding fluid that are reminiscent of the classical modes of Marangoni–Rayleigh–Bénard convection. Through direct numerical solution of the governing equations in their complete three-dimensional unsteady and nonlinear formulation, we investigate this specific subject giving much emphasis to understanding how ensemble properties arise from the interplay of localized effects. Through the used numerical framework, we identify the emerging planforms and connect the statistics of the associated heat transport mechanisms with the spatially averaged behaviour of the underlying thermal currents. In some cases, all these features can be directly mapped into the topography at the bottom of the layer. In other circumstances, these systems contain their own capacity for transformation, i.e. intrinsic evolutionary mechanisms are enabled, by which complex steady or unsteady patterns are produced. It is shown that self-organization driven by purely surface-tension or mixed buoyancy–Marangoni effects can result in ‘quantized states’, i.e. aesthetically appealing solutions that do not depend on the multiplicity of wall-mounted elements.

Wave propagation in a non-linearly elastic bar with phase transformations

There exist considerable difficulties in studying the wave propagation problems of the kind of phase transforming materials with non-monotone material responses due to the lack of uniqueness of solution for a moving phase boundary. An admissibility condition, which is named the Maxwell equal-area criterion, was established from a three-dimensional (3D) internal-variable formulation in the previous study to supplement the one-dimensional (1D) dynamical system of the bars/rods made of the special materials to determine the phase boundary uniquely. In this paper, we employ this criterion to investigate the wave propagation in the bar made of the special kind of phase transforming materials, which are associated with trilinear non-monotone stress–strain responses. The Riemann problem for different boundary states that arises from wave encounters are analyzed by the method of wave curves. Based on the construction of the Riemann solution, we explicitly study the wave propagation in a semi-infinite bar under an impulsive stress impact to explore the dynamical features of the special materials. The wave structures in the entire spatial and temporal domain for two different impact levels are obtained, as well as the state profiles. Detailed analyses and discussions of the wave patterns and wave encounters occurring during the wave propagation process are given for a deep understanding of dynamical phase transitions of the materials. These results are further compared with those obtained using the artificially adopted maximal dissipation rate criterion. The similarities and differences are discussed. The comparisons further confirmed that the special phase transforming material can be used for designing wave-absorption/impact-protection devices.

Numerical analysis of soot emissions from gasoline-ethanol and gasoline-butanol blends under gasoline compression ignition conditions

In the present work, computational fluid dynamics (CFD) simulations of a single-cylinder gasoline compression ignition (GCI) engine were performed to investigate the impact of blending two biofuels, ethanol and n-butanol, with gasoline on the trade-off between combustion phasing and soot emissions under low load conditions. In order to represent market gasoline (RD5-87), a four-component toluene primary reference fuel (TPRF) + ethanol (ETPRF) surrogate (with 20% ethanol by mole; E20) was formulated using a neural network based octane predictor such that the surrogate had the same ethanol content, Research Octane Number (RON) and Octane Sensitivity (S). In addition, a novel skeletal kinetic mechanism for ETPRF and TPRF + n-butanol (BTPRF) blends, incorporating polycyclic aromatic hydrocarbon (PAH) chemistry, was developed. A three-dimensional (3D) engine CFD formulation employing the skeletal mechanism, adaptive mesh refinement (AMR), finite-rate chemistry approach, and hybrid method of moments (HMOM) was adopted to capture the in-cylinder combustion phenomena and soot emissions. The engine CFD model was validated against RD5-87 experimental data for a broad range of start-of-injection (SOI) timings (-21/-27/-36/-45 crank angle degrees (CAD) after top-dead-center (aTDC)), with respect to in-cylinder pressure, heat release rate, combustion phasing, and soot emissions. The closed-cycle simulation results were analyzed to elucidate the non-monotonic trend of soot emissions versus SOI timing: SOI-36 > SOI-45 > SOI-21 > SOI-27. Thereafter, the validated CFD model was employed to simulate the combustion of a gasoline-ethanol blend with 45% (by mole) ethanol (E45) and a gasoline-butanol blend with 45% (by mole) n-butanol (B45) under the same operating conditions to study the effects of fuel composition and SOI timing on combustion phasing and soot emissions. The sooting propensity followed the trend: B45 > E20 > E45 at all SOI timings. Overall, it was observed that the autoignition propensity was primarily related to fuel chemistry. On the other hand, sooting propensity showed strong coupling with both fuel chemistry and physical properties, with greater impact of fuel physical properties at advanced SOI timings.

Constitutive modelling of plastically deformable self-healing materials

A novel elasto-plastic constitutive model of self-healing materials is proposed coupling continuum damage–healing mechanics (CDHM) framework with kinematic and isotropic hardening cases. A novel secondary damage internal variable is presented, eliminating an assumption in the existing literature that the healed area does not undergo damage again, thus improving the existing CDHM framework. The necessity of the proposed secondary damage variable is successfully demonstrated by a four spring material model. The improved CDHM framework is coupled with the three-dimensional elasto-plastic formulation containing nonlinear kinematic hardening and isotropic strain hardening effects. The proposed formulation is finally numerically implemented by return mapping approach employing the strain energy equivalence hypothesis from CDHM, and the macro-scale stress update is performed applying several different strain histories. A continuum tangent modulus expression is also derived, and a boundary value problem is successfully solved employing an in-house developed plane strain nonlinear finite element code. It is finally demonstrated, by the numerical results, that the secondary damage variable is crucial while obtaining the physically realistic stress–strain response of self-healing materials leading to the complete failure upon exhaustion of the healing capabilities.

A Three-Dimensional Printable Hydrogel Formulation for the Local Delivery of Therapeutic Nanoparticles to Cervical Cancer.

Cervical cancer is the fourth most common malignancy among women. Compared to other types of cancer, therapeutic agents can be administrated locally at the mucosal vaginal membrane. Thermosensitive gels have been developed over the years for contraception or for the treatment of bacterial, fungal, and sexually transmitted infections. These formulations often carry therapeutic nanoparticles and are now being considered in the arsenal of tools for oncology. They can also be three-dimensionally (3D) printed for a better geometrical adjustment to the anatomy of the patient, thus enhancing the local delivery treatment. In this study, a localized delivery system composed of a Pluronic F127-alginate hydrogel with efficient nanoparticle (NP) release properties was prepared for intravaginal application procedures. The kinetics of hydrogel degradation and its NP releasing properties were demonstrated with ultrasmall gold nanoparticles (∼80% of encapsulated AuNPs released in 48 h). The mucoadhesive properties of the hydrogel formulation were assayed by the periodic acid/Schiff reagent staining, which revealed that 19% of mucins were adsorbed on the gel's surface. The hydrogel formulation was tested for cytocompatibility in three cell lines (HeLa, CRL 2616, and BT-474; no sign of cytotoxicity revealed). The release of AuNPs from the hydrogel and their accumulation in vaginal membranes were quantitatively measured in vitro/ex vivo with positron emission tomography, a highly sensitive modality allowing real-time imaging of nanoparticle diffusion (lag time to start of permeation of 3.3 h, 47% of AuNPs accumulated in the mucosa after 42 h). Finally, the potential of the AuNP-containing Pluronic F127-alginate hydrogel for 3D printing was demonstrated, and the geometrical precision of the 3D printed systems was measured by magnetic resonance imaging (<0.5 mm precision; deviation from the design values <2.5%). In summary, this study demonstrates the potential of Pluronic F127-alginate formulations for the topical administration of NP-releasing gels applied to vaginal wall therapy. This technology could open new possibilities for photothermal and radiosensitizing oncology applications.

Simulating Lagrangian Subgrid-Scale Dispersion on Neutral Surfaces in the Ocean.

To capture the effects of mesoscale turbulent eddies, coarse‐resolution Eulerian ocean models resort to tracer diffusion parameterizations. Likewise, the effect of eddy dispersion needs to be parameterized when computing Lagrangian pathways using coarse flow fields. Dispersion in Lagrangian simulations is traditionally parameterized by random walks, equivalent to diffusion in Eulerian models. Beyond random walks, there is a hierarchy of stochastic parameterizations, where stochastic perturbations are added to Lagrangian particle velocities, accelerations, or hyper‐accelerations. These parameterizations are referred to as the first, second and third order “Markov models” (Markov‐N), respectively. Most previous studies investigate these parameterizations in two‐dimensional setups, often restricted to the ocean surface. On the other hand, the few studies that investigated Lagrangian dispersion parameterizations in three dimensions, where dispersion is largely restricted to neutrally buoyant surfaces, have focused only on random walk (Markov‐0) dispersion. Here, we present a three‐dimensional isoneutral formulation of the Markov‐1 model. We also implement an anisotropic, shear‐dependent formulation of random walk dispersion, originally formulated as a Eulerian diffusion parameterization. Random walk dispersion and Markov‐1 are compared using an idealized setup as well as more realistic coarse and coarsened (50 km) ocean model output. While random walk dispersion and Markov‐1 produce similar particle distributions over time when using our ocean model output, Markov‐1 yields Lagrangian trajectories that better resemble trajectories from eddy‐resolving simulations. Markov‐1 also yields a smaller spurious dianeutral flux.