Mesh Algorithm Research Articles

Effect of microstructural variations on the failure response of a nano-enhanced polymer: a homogenization-based statistical analysis

Statistical Volume Elements (SVEs) are employed to evaluate homogenized mesoscopic ductile failure response of a carbon nanofiber reinforced composite under uniaxial tensile and compressive loadings. In the mesoscale analysis, after virtual reconstruction of the material microstructure, 2D finite element models are generated for each SVE using a non-iterative meshing algorithm named CISAMR, which fully automates the modeling process. The ductile damage response of each SVE is then simulated to derive its homogenized stress-strain curve. Corresponding initiation, maximum, and failure turning points, together with local fiber volume fraction and homogenized bulk modulus, are defined as mesoscopic Quantities of Interest (QoIs). While compressive loadings have slightly higher strength and nearly twice higher strains at failure compared to similar tensile cases, both loadings yield similar coefficients of variance for most QoIs. Further, a stochastic bulk damage model is calibrated from mesoscopic responses, which takes bilinear and linear forms versus strain for tensile and compressive loadings, respectively. Finally, cross-correlations are made between different QoIs, showing lower strain-based QoIs and higher strengths correspond to either higher local fiber volume fractions or more fibers being aligned with the loading direction.

On mesh geometries of root Coxeter orbits and mesh algorithms for corank two edge-bipartite signed graphs

Following a Coxeter spectral analysis problems for positive edge-bipartite graphs (signed multigraphs with a separation property) introduced in Simson (2013) [41] and Simson (2013) [42], we study analogous problems for loop-free corank two edge-bipartite graphs Δ=(Δ0,Δ1), i.e., for edge-bipartite graphs Δ, with n+2=|Δ0|≥3 vertices such that its rational symmetric Gram matrix GΔ:=12(GˇΔ+GˇΔtr)∈Mn+2(Q) is positive semi-definite of rank n. We study such connected edge-bipartite signed graphs (bigraphs, for short), up to the strong Gram congruence Δ≈ZΔ′, by means of the non-symmetric Gram matrix GˇΔ∈Mn+2(Z), the Coxeter matrix CoxΔ:=−GˇΔ⋅GˇΔ−tr∈Mn+2(Z), its complex spectrum speccΔ⊆C, and an associated simply laced Dynkin diagram DynΔ∈{An,Dn,E6,E7,E8}, with n≥1 vertices. It is known that if the congruence holds Δ≈ZΔ′ (i.e., there exists B∈Mn+2(Z) such that det⁡B=±1 and GˇΔ′=Btr⋅GˇΔ⋅B) then (speccΔ,DynΔ)=(speccΔ′,DynΔ′).The inverse implication is proved in [Fund. Inform. 152 (2017) 185–222] for all pairs of non-negative corank two bigraphs Δ, Δ′ without loops with n+2≤6 vertices. One of the main aims of the paper is to find algorithms that construct the set Cong(Δ,Δ′) of all Z-invertible matrices B∈Mn+2(Z) defining the congruence Δ≈ZΔ′, for any pair of corank two bigraphs Δ and Δ′ such that (speccΔ,DynΔ)=(speccΔ′,DynΔ′). We do it in case when Δ and Δ′ have at most six vertices in three steps: (i) to any such Δ, we associate algorithmically a ΦΔ-mesh translation quiver ΓΔ•=Γ(RˆΔ,ΦΔ) in Zn+2 (called ΦΔ-mesh geometry of roots of Δ, in the sense of Simson (2013) [42]), where ΦΔ:Zn+2→Zn+2, v↦v⋅CoxΔ, is the Coxeter transformation of Δ; (ii) we define an injective contravariant map h˜•:Cong(Δ,Δ′)→Iso(ΓΔ′•,ΓΔ•), where Iso(ΓΔ′•,ΓΔ•) is the set of all mesh translation quiver isomorphisms h˜B:ΓΔ′•→ΓΔ•, and (iii) a numerical algorithm computing a required matrix B∈Cong(Δ,Δ′) is constructed by means of the shape of the ΦΔ-mesh translation quiver ΓΔ•, its toroidal-tubular structure, and an analysis of admissible isomorphisms h˜B:ΓΔ′•→ΓΔ•.

자동격자생성 알고리듬을 이용한 주름관을 갖는 배관계의 효율적 진동 분석

In this study, an automatic mesh generation algorithm was developed for efficient finite shell element modeling of piping systems with bellows. For pre-processing of finite element analysis, a pipe geometry should be modeled using meshing software. However, the finite element meshing process requires time-consuming efforts for complicated piping systems such as bellows. Therefore, this study proposed an algorithm that can efficiently generate finite shell elements automatically. To generate the finite shell element model of the pipe, this algorithm only needs the information of the centerline of the pipe and the corresponding radius that is identical to the finite beam element. Additionally, effects of bellows on the dynamic characteristics of a curved pipe were discussed. The variation of the natural frequencies and dynamic stiffness of the piping system with respect to the change of the location, height and width of the bellows were investigated. The suggested automatic mesh algorithm is advantageous for the modeling of pipes having complex shapes such as bellows. Hence, it has the potential to be useful in designing optimal bellows in piping systems that require numerous finite element analysis calculations.

Analysis of the effects of finite element type within a 3D biomechanical model of a human optic nerve head and posterior pole

Background and objectiveBiomechanical stresses and strains can be simulated in the optic nerve head (ONH) using the finite element (FE) method, and various element types have been used. This study aims to investigate the effects of element type on the resulting ONH stresses and strains. MethodsA single eye-specific model was constructed using 3D delineations of anatomic surfaces in a high-resolution, fluorescent, 3D reconstruction of a human posterior eye, then meshed using our simple meshing algorithm at various densities using 4- and 10-noded tetrahedral elements, as well as 8- and 20-noded hexahedral elements. A mesh-free approach was used to assign heterogeneous, anisotropic, hyperelastic material properties to the lamina cribrosa, sclera and pia. The models were subjected to elevated IOP of 45 mmHg after pre-stressing from 0 to 10 mmHg, and solved in the open-source FE package Calculix; results were then interpreted in relation to computational time and simulation accuracy, using the quadratic hexahedral model as the reference standard. ResultsThe 10-noded tetrahedral and 20R-noded hexahedral elements exhibited similar scleral canal and laminar deformations, as well as laminar and scleral stress and strain distributions; the quadratic tetrahedral models ran significantly faster than the quadratic hexahedral models. The linear tetrahedral and hexahedral elements were stiffer compared to the quadratic element types, yielding much lower stresses and strains in the lamina cribrosa. ConclusionsPrior studies have shown that 20-noded hexahedral elements yield the most accurate results in complex models. Results show that 10-noded tetrahedral elements yield very similar results to 20-noded hexahedral elements and so they can be used interchangeably, with significantly lower computational time. Linear element types did not yield acceptable results.

Probabilistic Modeling for Frequency Vectors Using a Flexible Shifted-Scaled Dirichlet Distribution Prior

Burstiness and overdispersion phenomena of count vectors pose significant challenges in modeling such data accurately. While the dependency assumption of the multinomial distribution causes its failure to model frequency vectors in several machine learning and data mining applications, researchers found that by extending the multinomial distribution to the Dirichlet Compound multinomial (DCM), both phenomena modeling can be addressed. However, Dirichlet distribution is not the best choice, as a prior, given its negative-correlation and equal-confidence requirements. Thus, we propose to use a flexible generalization of the Dirichlet distribution, namely, the shifted-scaled Dirichlet, as a prior to the multinomial, which grants the model a capability to better fit real data, and we call the new model the Multinomial Shifted-Scaled Dirichlet (MSSD). Given that the likelihood function plays a key role in statistical inference, e.g., in maximum likelihood estimation and Fisher information matrix investigation, we propose to improve the efficiency of computing the MSSD log-likelihood by approximating its function based on Bernoulli polynomials where the log-likelihood function is computed using the proposed mesh algorithm. Moreover, given the sparsity and high-dimensionality nature of count vectors, we propose to improve its computation efficiency by approximating the novel MSSD as a member of the exponential family of distribution, which we call EMSSD. The clustering is based on mixture models, and for learning a model, selection approach is seamlessly integrated with the estimation of the parameters. The merits of the proposed approach are validated via challenging real-world applications such as hate speech detection in Twitter, real-time recognition of criminal action, and anomaly detection in crowded scenes. Results reveal that the proposed clustering frameworks offer a good compromise between other state-of-the-art techniques and outperform other approaches previously used for frequency vectors modeling. Besides, comparing to the MSSD, the approximation EMSSD has reduced the computational complexity in high-dimensional feature spaces.

A Simple Approach for Generating Random Aggregate Model of Concrete Based on Laguerre Tessellation and Its Application Analyses.

Generating random aggregate models (RAMs) plays a key role in the mesoscopic modelling of concrete-like composite materials. The arbitrary geometry, wide gradation, and high volume ratio of aggregates pose a great challenge for fast and efficient numerical construction of concrete meso-structures. This paper presents a simple strategy for generating RAMs of concrete based on Laguerre tessellation, which mainly consists of three steps: tessellation, geometric smoothing, and scaling. The computer-assisted design (CAD) file of RAMs obtained by the proposed approach can be directly adopted for the construction of random numerical concrete samples. Combined with the image-based octree meshing algorithm, the scaled boundary finite element method (SBFEM) was adopted for an automatic stress analysis of mass concrete samples, and a parametric study was conducted to investigate the meso-structural effects on concrete elasticity properties. The modelling results successfully reproduced the increasing trend of concrete elastic modulus with the grading of coarse aggregates in literature test data and demonstrate the effectiveness of the proposed strategy.

A modification of the hexahedral mesh generator based on voxel geometry representation

We consider a modification of the previously developed voxel-based mesh algorithm to generate models given in STL-geometry format. Proposed hexahedral mesh generator belongs to the family of grid methods, and is general-purpose in terms of a capability to use as source data both volume (voxel) and STL-surface representation of model geometry. For now, the algorithm works with CAD models described in the well-known STL format. However, it also allows to handle higher-order surface patches defined in an arbitrary format if appropriate procedures for projection and intersection operations will be specified. To define the initial position of mesh nodes, a “signed distance field” volume data file, obtained from the STL-geometry, is used. A special projection technique was developed to adapt constructed orthogonal mesh on the model's boundary. It provides an approximation of sharp edges and corners and is performed before running any other operations with the mesh. Finally, to improve the quality of the mesh, additional procedures were implemented, including boundary layers insertion, bad quality cells splitting, and optimization-based smoothing technique. The algorithm has been tested on a sufficient number of models, some of which are given as examples.

A new auxiliary volume-based gradient algorithm for triangular and tetrahedral meshes

To have a second-order accurate centroid-based finite volume method, the gradients at the cell-centroids need to be evaluated with at least first-order accuracy. This again requires the cell face-center solution values to be interpolated with second-order accuracy when using Green-Gauss methods. It is not always possible to obtain the second-order accuracy in face interpolations with simple averaging or linear interpolation by Traditional Green-Gauss methods when the meshes are irregular in nature. In this paper, a simple and novel way to calculate first-order accurate gradients on any tri and tetra type meshes is proposed. The new method, referred to as the Circle Green-Gauss (CGG) reconstruction, is based on constructing an auxiliary volume around the cell of interest from the neighboring cells. The solution values at the faces of the constructed auxiliary volume of the cell can then be easily estimated to second-order accuracy, thereby making the gradients first-order accurate. Qualitative comparison of the proposed method with Traditional Green-Gauss (TGG) reconstruction and the Least-Squares (LS) reconstruction (used in most commercial solvers) is shown on different mesh topologies that are irregular in nature. The stability and applicability of CGG are discussed in detail through representative test problems including the method of manufactured solutions that demonstrate that the gradients are first-order accurate (so that the overall method is second-order accurate) on triangular and tetrahedral meshes.

Exact and efficient polyhedral envelope containment check

We introduce a new technique to check containment of a triangle within an envelope built around a given triangle mesh. While existing methods conservatively check containment within a Euclidean envelope, our approach makes use of a non-Euclidean envelope where containment can be checked both exactly and efficiently. Exactness is crucial to address major robustness issues in existing geometry processing algorithms, which we demonstrate by integrating our technique in two surface triangle remeshing algorithms and a volumetric tetrahedral meshing algorithm. We provide a quantitative comparison of our method and alternative algorithms, showing that our solution, in addition to being exact, is also more efficient. Indeed, while containment within large envelopes can be checked in a comparable time, we show that our algorithm outperforms alternative methods when the envelope becomes thin.

Efficient meshing technique for textile composites unit cells of arbitrary complexity

Meso-scale unit cell models are often used to simulate mechanical behaviour of textile composites. Apart from reliable ways to create meso-scale geometries, such simulations require reliable meshing algorithms. While the former is made possible via dedicated textile pre-processors or high-fidelity weaving simulations, the meshing remains quite problematic for complex textiles and geometries. Even though, with a lot of user input, it is possible to create very complex meshes using meshing pre-processors, this approach remains infeasible for cases when a large number of models need to be analysed.This paper presents a meshing approach based on the combination of local octree-refinement with surface smoothing. This allows nearly conformal meshes to be generated for geometries of any complexity which achieve accuracy comparable to that of conformal meshes. A range of unit cells was analysed using the new approach and it was shown that the error in local stresses is within 10% of the reference solution and the average error is below 7%. It was found that the computational cost of the analysis using the new meshing technique is not considerably higher than for an analysis which uses a conventional conformal mesh yet the new approach allows analysis of any geometry.

Condition numbers of finite element methods on a class of anisotropic meshes

We study the behavior of the finite element condition numbers on a class of anisotropic meshes. These newly-developed mesh algorithms can produce numerical approximations with optimal convergence to isotropic and anisotropic singular solutions of elliptic boundary value problems in two- and three-dimensions. Despite the simplicity and fewer geometric constraints in implementation, these meshes can be highly anisotropic and do not maintain the maximum angle condition. We formulate a unified refinement principle and establish sharp estimates on the growth rate of the condition numbers of the stiffness matrix from these meshes. These results are important for effective applications of these meshes and for the design of fast numerical solvers. Numerical tests validate the theoretical analysis.

Numerical simulation of crust freezing in processed meat: A fully coupled solid–fluid approach

We present a numerical model for the simulation of continuous impingement freezing of processed food products. This model is capable of fully describing the fluid dynamics of the non-isothermal flow field, including turbulence with conjugate heat transfer (CHT). The motion of the solid region is captured by advecting the solid rathe than employing a moving mesh algorithm, resulting in a model that is more computationally efficient. This methodology is implemented as a numerical solver using the well-known open-source library OpenFOAM. Our results confirm that the proposed model can provide detailed insight on the freezing process at a minimum computational cost.

A dynamic phase field model with no attenuation of wave speed for rapid fracture instability in hyperelastic materials

Numerical experiments on phase field modeling of the fracture in pre-strained hyperelastic materials reveal that the classical mechanical-based dynamic phase field model is ineffective in the framework of non-linear deformation. The aspiration to gain insight into rapid fracture instability motivated us to develop a novel dynamic phase field model characterized by wave velocity invariance, enabling crack propagation at a velocity approach to the asymptotic limit. Given that the numerical treatment of rapid fractures involves extremely high spatiotemporal resolution, robust explicit dynamics and a tried-and-tested multi-level hybrid adaptive mesh algorithm are invoked. More crucially, an original adaptive distorted mesh removal scheme (ADMR) was developed to cope with the intractable finite element mesh distortion problem in large deformation fractures. The detailed numerical implementation for entire procedures is outlined, and its reliability is verified by two quasi-static fracture benchmarks. Utilizing the proposed model and innovative algorithms, the arresting ultrahigh-speed crack oscillation and tip-splitting instabilities captured in the fracture experiments of brittle gels were successfully reproduced. The critical crack velocity at the onset of the instability is also identified, close to the experimental measurements.

An unstructured mesh algorithm for simulation of hydraulic fracture

The paper describes a flexible computational method that can be used to represent the complex geometric evolution of a fluid-driven fracture front using an unstructured triangular element mesh. A specific motivation for the method is to allow subsequent treatment of non-planar fracture growth problems. Elastic interactions between the crack opening displacements and the surrounding medium are calculated using displacement discontinuity boundary element influence functions. A novel feature of the approach is the use of an adjustable region of tip elements to accommodate both time-dependent crack edge movements and to ensure correct velocity-dependent asymptotic behavior for viscous and viscous-toughness flow conditions. The adjustable tip element region is represented using a special-purpose data structure that allows the iteration of the moving edge element vertices to be linked directly to the flow rate and the crack opening solution values that are determined in each time step. The fringe region is periodically replaced with a set of fixed vertex elements as the fracture surface evolves. The proposed scheme has been evaluated using available analytic and experimental results for planar fracture propagation. The method is found to be both accurate and robust for a range of choices of geometric fracture shapes and time step sizes.

Numerical Prediction of the Vertical Responses of Planing Hulls in Regular Head Waves

The evaluation of the hydrodynamic performance of planing vessels has always been one of the most attractive study fields in the maritime agenda. Resistance and self-propulsion studies have been performed using experimental and numerical methods by researchers for a long time. As opposed to this, the seakeeping performance of planing hulls is assessed with 2D approximation methods, but limitedly, while the experimental campaign is not cost-effective for several reasons. With this motivation, pitch and heave transfer functions and accelerations were obtained for a monohedral hull and a warped hull using a state of art commercial Reynolds-averaged Navier–Stokes (RANS) solver, in this study. Moreover, 2-DOF (degree of freedom) dynamic fluid–body interaction (DFBI) equations were solved in a coupled manner with an overset mesh algorithm, to find the instantaneous motion of the body. After verification, obtained numerical results at three different Froude numbers and a sufficiently large wave frequency range were compared with the experiments. The results showed that the employed RANS method offers a very accurate prediction of vertical motions and accelerations for planing hulls.

Natural Ventilation Design: Predicted and Measured Performance of a Hostel Building in Composite Climate of India

Natural ventilation is recognized for improving the thermal comfort of the built environment and indoor air quality. It provides comfortable conditions for building occupants and reduces energy consumption for air-conditioning. Therefore, it is important to study and explore effective means of ventilation to improve the building designs. This study investigates the thermal comfort of a naturally ventilated hostel operational building in the composite climate of Jaipur, India using Computational Fluid Dynamics (CFD) simulation tool ‘Cradle scSTREAM’. A 3D building model has been developed to analyze the thermal comfort for different natural ventilation strategies with advanced mesh algorithms which generate fewer mesh elements and maintain good mesh quality. A field study was carried out to collect the actual data and to validate the model which was further used to evaluate the thermal comfort range based on the ASHRAE-55 standard. Several design strategies have been applied to enhance thermal comfort. It was found that an increase in air velocity up to 0.5 m/s was achieved by Cross Ventilation while a drop of 2.0–2.5°C in the air temperature was found using Night Ventilation. It can be stated that cross ventilation increases the air movement while night ventilation gives comparatively higher comfort regarding air temperature and relative humidity.

A new topology optimization framework for stiffness design of beam structures based on the transformable triangular mesh algorithm

Abstract This paper presents an explicit topology optimization method based on the so called Transformable Triangular Mesh (TTM) approach. It improves a general weakness of the traditional explicit approaches in the sense that the genus of initial geometry no longer affects the design result. In the proposed method, we first triangulate the initial geometry and organize it with the halfedge data structure. Then we employ the Laplacian energy controlled mesh deformation algorithm to realize smooth transition from the initial TTM. Furthermore, three geometrical mesh processing techniques (mesh subdivision, mesh split, and mesh refinement) are adopted to realize surface genus change. Respectively, the mesh subdivision is beneficial for the increase of mesh control hot points to obtain more degree of freedoms, the mesh split is able to rip connected triangles such that holes can be generated both inside a mesh and on the border, and the mesh refinement unifies the sizes and shapes of each triangle in the mesh such that no large distortion and self-intersection exist. To enhance the computational efficiency, we realize the above algorithm parallelly using CUDA. Finally, some benchmark examples (a cantilever beam, an MBB beam, and a cantilever beam with a fixed hole) are used to validate the algorithm. By comparing with state-of-the-art algorithms, our method proves to be reliable, accurate, and advanced.

Semitractability of optimal stopping problems via a weighted stochastic mesh algorithm

AbstractIn this paper, we propose a Weighted Stochastic Mesh (WSM) algorithm for approximating the value of discrete‐ and continuous‐time optimal stopping problems. In this context, we consider tractability of such problems via a useful notion of semitractability and the introduction of a tractability index for a particular numerical solution algorithm. It is shown that in the discrete‐time case the WSM algorithm leads to semitractability of the corresponding optimal stopping problem in the sense that its complexity is bounded in order by with being the dimension of the underlying Markov chain. Furthermore, we study the WSM approach in the context of continuous‐time optimal stopping problems and derive the corresponding complexity bounds. Although we cannot prove semitractability in this case, our bounds turn out to be the tightest ones among the complexity bounds known in the literature. We illustrate our theoretical findings by a numerical example.

Robust control volume finite element methods for numerical wave tanks using extreme adaptive anisotropic meshes

SummaryMultiphase inertia‐dominated flow simulations, and free surface flow models in particular, continue to this day to present many challenges in terms of accuracy and computational cost to industry and research communities. Numerical wave tanks and their use for studying wave‐structure interactions are a good example. Finite element method (FEM) with anisotropic meshes combined with dynamic mesh algorithms has already shown the potential to significantly reduce the number of elements and simulation time with no accuracy loss. However, mesh anisotropy can lead to mesh quality‐related instabilities. This article presents a very robust FEM approach based on a control volume discretization of the pressure field for inertia dominated flows, which can overcome the typically encountered mesh quality limitations associated with extremely anisotropic elements. Highly compressive methods for the water‐air interface are used here. The combination of these methods is validated with multiphase free surface flow benchmark cases, showing very good agreement with experiments even for extremely anisotropic meshes, reducing by up to two orders of magnitude the required number of elements to obtain accurate solutions.

Gas-liquid mass transfer and hydrodynamics in a vertically-oscillating multiphase reactor

Gas-liquid mass transfer and hydrodynamics were studied experimentally and numerically in a vertically-oscillating vessel with an internal diameter of 33 mm and a height of 114 mm. The amplitude was 57 mm and frequency ranged from 2.8 to 3.7 Hz. The dissolution of pressurized oxygen into water was measured between 3 and 6 MPa. Simulations were performed using a computational fluid dynamics (CFD) model with partial interface capturing by a compressive-interface volume-of-fluid method. A new surface area reconstruction algorithm for unstructured meshes was developed and implemented into OpenFOAM. Predicted radial phase distributions were within one standard deviation of experimental values, while predicted axial distributions at high oscillation frequencies matched more closely than when approaching the onset of splashing. Mass transfer predictions performed without the use of a sub-grid model were underpredicted. Sub-grid mass transfer predictions using an eddy cell model were more scalable than a model based on penetration theory.