Aspect Ratio Of Elements Research Articles

Cutout effects on the vibration of sandwich auxetic cylindrical shells with an experimental validation

This study investigates the influence of auxetic core layers on the vibrational characteristics of sandwich cylindrical shells with cut-outs. The analysis utilizes the First-order Shear Deformation Theory (FSDT) and analytical techniques. The irregular behavior of auxetic re-entrante honeycomb cells necessitates the exploration of their effects on various systems. Additionally, the proposed method offers advantages over Finite Element Method (FEM). FEM modeling suffers from increased computational time and reduced accuracy with a large number of elements or high aspect ratio elements. These challenges are particularly significant for shells with geometric features of disparate scales, such as large cylinders with tiny cutouts or cutouts with low aspect ratios. However, the present research addresses these challenges by employing a method that integrates five panels with varying dimensions. Consequently, each section can utilize specific Two-Dimensional Generalized Differential Quadrature (2D-GDQ) grid points, tailored to the size of each side, enabling rapid and accurate prediction of displacement and stress parameters, particularly for shorter sides. The proposed method excels at precisely modeling cutouts while preserving their realistic properties. This is achieved by avoiding geometric and material simplifications and by assigning distinct boundary conditions to each region, including critical areas like corners, internal, and external sides. Moreover, Frequency Response Functions (FRFs) obtained from accelerometer and laser signals, alongside vibration-induced sound wave signals captured by electroacoustic microphones, validate the precision of the numerical calculations.

Modulation of Standing Spin Waves in Confined Rectangular Elements

Magnonics is an emerging field within spintronics that focuses on developing novel magnetic devices capable of manipulating information through the modification of spin waves in nanostructures with submicron size. Here, we provide a confined magnetic rectangular element to modulate the standing spin waves, by changing the saturation magnetisation (MS), exchange constant (A), and the aspect ratio of rectangular magnetic elements via micromagnetic simulation. It is found that the bulk mode and the edge mode of the magnetic element form a hybrid with each other. With the decrease in MS, both the Kittel mode and the standing spin waves undergo a shift towards higher frequencies. On the contrary, as A decreases, the frequencies of standing spin waves become smaller, while the Kittel mode is almost unaffected. Moreover, when the length-to-width aspect ratio of the element is increased, standing spin waves along the width and length become split, leading to the observation of additional modes in the magnetic spectra. For each mode, the vibration style is discussed. These spin dynamic modes were further confirmed via FMR experiments, which agree well with the simulation results.

Comparing flows of FENE-P, sPTT, and Giesekus model fluids in a helical static mixer

Helical static mixers are used widely for mixing of non-Newtonian fluid flows in the laminar regime. We study flows of three viscoelastic constitutive models (sPTT, FENE-P, and Giesekus) in the helical static mixer using computational fluid dynamics. These three models have similarities in steady viscometric flows in that they all exhibit shear thinning and their planar extensional viscosities can be matched, but their responses can differ in complex geometries. We observe flow distribution asymmetries at the element intersections for all three models, which hinders the mixing performance of the device. These have previously been observed with the constant shear viscosity FENE-CR model. The asymmetry behaves similarly between the sPTT and Giesekus models, however the FENE-P model behaves in a distinct manner; beyond a critical degree of elasticity, the asymmetry sharply changes direction. This was also observed previously with the FENE-CR model. These results suggest that shear thinning and second-normal stress differences (present in the Giesekus model) do not significantly influence mixing performance in the range of conditions studied. We show that increasing the aspect (length/diameter) ratio of the mixer elements mitigates the poor mixing caused by elasticity. Overall, this study provides insight into the behaviour of these well-used constitutive models in complex, industrially-relevant flows.

Computational modeling of cracking in cortical bone microstructure using the mesh fragmentation technique

The cortical bone is a hierarchical composite material that, at the microscale, is segmented in an interstitial matrix, cement line, osteons, and Haversian canals. The cracking of the structure at this scale directly influences the macro behavior, and, in this context, the cement line has a protagonist role. In this sense, this work aims to simulate the crack initiation and propagation processes via cortical bone microstructure modeling with a two-dimensional mesh fragmentation technique that captures the mechanical relevance of its constituents. In this approach, high aspect ratio elements are inserted between the regular constant strain triangle finite elements to define potential crack paths a priori. The crack behavior is described using a composed damage model with two scalar damage variables, which is integrated by an implicit-explicit (Impl-Ex) scheme to avoid convergence problems usually found in numerical simulations involving multiple cracks. The approach’s capability of modeling the failure process in cortical bone microstructure is investigated by simulating four conceptual problems and one example based on a digital image of an experimental test. The results obtained in terms of crack pattern and failure mechanisms agree with those described in the literature, demonstrating that the numerical tool is promising to simulate the complex failure mechanisms in cortical bone, considering the properties of its distinct phases.

The Behaviour of Building Frames on Raft Foundation using Dynamic Analysis

When designing building frames for seismic reasons, the effect of soil flexibility is typically disregarded, and the design is executed using the outcomes of dynamic analysis with a fixed base condition. Because the overall lateral stiffness of the structure decreases as a result of soil flexibility, the lateral natural period lengthens. The building frames situated on the Raft foundation may experience a significant change in seismic response due to this extension of the lateral natural period (T). Therefore, it is imperative to consider the soil's flexibility, also known as soil structure interaction, when doing analysis on the foundation's supporting layer.
 This paper examines how asymmetric building frames with raft footings behave dynamically when subjected to seismic forces that involve soil-structure interaction. The analysis is performed with SAP 2000*V21 FEM software. The structure is idealized as a three-dimensional space frame, with slabs modeled as a thin shell with four noded plate elements and six degrees of freedom at each node, and beams and columns modeled as two noded line elements. The soil is represented as equivalent springs with one (Winkler) and six (Modified Winkler) degrees of freedom; the stiffness of these springs varies depending on the type of soil and is determined by its dynamic shear modulus and poissons ratio. The Modified Winkler and Winkler raft foundations are modeled as thin shells with four noded plate elements, each with six degrees of freedom, and are criticized so that the element aspect ratios are equal to one.
 
 To assess the impact of soil structure interaction on building frames, the response is compared for a range of building frames with and without consideration of soil flexibility in terms of fundamental Natural Period, Seismic Base Shear, and Max. Lateral Displacement. The parametric study for Zone V takes into account the influence of various parameters, including the number of bays, stories, span lengths, and soil types (i.e., soft, medium, and stiff).
 
 It is discovered that the fundamental lateral natural period and seismic base shear of the system are significantly altered by the influence of soil flexibility on building frames. As soil stiffness decreases, the lateral natural period and seismic base shear increase as a result of soil flexibility. Additionally, it has been noted that as the number of bays increases, so do the building's base shear and lateral period. As the number of bays and stories increases, so does the maximum lateral displacement. 

Hybrid mesh for magnetotelluric forward modeling based on the finite element method

Unstructured tetrahedral grids have been applied in magnetotelluric (MT) forward modeling using the finite element (FE) method because of their adaptability to complex anomalies. However, high-quality results require an extreme refinement of the near-surface area, which leads to excessive meshes and an increased degree of freedom (DoF) of the governing equation of the finite element system. To reduce the computational cost, we have developed a hybrid mesh based on triangular prisms and tetrahedrons. The required elements in the near-surface area are reduced because the quality of the triangular prism is not limited by the element aspect ratio. The deep area is discretized by tetrahedral elements to ensure the flexibility of the unstructured grids. The superiority of this hybrid mesh has been tested on a layered model, the DTM1 model and terrain relief models. The results show that the modeling efficiency has been improved, especially for high-frequency data. The accuracy of the modeling using the hybrid mesh is significantly higher than that of the tetrahedral mesh with a similar DoF. Usage of the hybrid mesh can be easily adapted to complex geoelectric models with strong terrain fluctuations, which requires less computational cost than using conventional unstructured elements.

Vortex structure and small scale characteristics in turbulent Rayleigh–Bénard convection with mixed isothermal–adiabatic bottom boundary

Turbulent Rayleigh–Bénard convection with a mixed isothermal–adiabatic bottom boundary is simulated to investigate the effect of a nonideal thermal boundary on vortex structure and small-scale characteristics in turbulent convection. Simulations of convection with element aspect ratios of the mixed isothermal–adiabatic boundary cell ranging from 116 to 14 are performed at fixed Rayleigh and Prandtl numbers. Within the parameters adopted in this paper, the large-scale circulation under the mixed boundary condition is found to be consistent with that under the classical isothermal condition. However, the shape characteristics and distribution of plumes are strongly affected by the presence of a mixed isothermal–adiabatic boundary. Compared with the isothermal system, the mixed boundary breaks up the corner vortex structures and reduces the vortex intensity at the corners. Some complex vortex structures, such as a horseshoe vortex, appear in the case of a mixed isothermal–adiabatic thermal boundary. The vortices in side and face regions are governed by an enhancement rule that is related to the ratio of the element width to the typical plume size. The structure functions of scales above the element scale are greatly affected by the presence of a mixed boundary. The temperature structure function exhibits discrete characteristics, especially in the near-bottom region. However, the velocity structure function of the velocity retains continuous characteristics in all regions. The small-scale characteristics observed here help provide better understanding of the effect of a discrete boundary on buoyancy-driven turbulent convection.

2D mesoscale modeling of compressive fracture in concrete using a mesh fragmentation technique

The computational prediction of the failure processes of concrete under compression is still a challenge. Several researchers have proposed mesoscale models to have a better understanding of the influence of the distinct phases of the concrete on the fracture process. In this sense, this work proposes an extension of the mesoscale model proposed by Rodrigues et al. (2016) to describe the complex failure behavior of concrete under compression. In the proposed 2D approach, two layers of interface elements are inserted into the standard finite element mesh to define the potential crack paths using the mesh fragmentation technique. Each layer is formed by a pair of high aspect ratio elements and is responsible for modeling the tensile or frictional shear failure behavior. According to this approach, the compressive failure is a consequence of the combination between tensile and shear failure modes in the mesoscopic scale. The use of these two damage models allows to represent the debonding (opening) between the aggregates and matrix due to local tensile stress concentration, i.e. the fracture propagation in mode-I, as well as the sliding process corresponding to the fracture propagation in mode-II. Furthermore, adopting adequate parameters, these models allow representing the friction condition between the concrete specimen and the steel loading plates. The failure behavior of compression tests with different specimen slenderness as well as the different friction restraints between loading platen and concrete specimen is predicted. The numerical results are compared qualitatively and quantitatively against the experimental results found in the literature, demonstrating that the proposed approach is able to describe the failure process of concrete in compression.

Strain-induced shape anisotropy in antiferromagnetic structures

We demonstrate how shape-induced strain can be used to control antiferromagnetic order in NiO/Pt thin films. For rectangular elements patterned along the easy and hard magnetocrystalline anisotropy axes of our film, we observe different domain structures and we identify magnetoelastic interactions that are distinct for different domain configurations. We reproduce the experimental observations by modeling the magnetoelastic interactions, considering spontaneous strain induced by the domain configuration, as well as elastic strain due to the substrate and the shape of the patterns. This allows us to demonstrate and explain how the variation of the aspect ratio of rectangular elements can be used to control the antiferromagnetic ground state domain configuration. Shape-dependent strain does not only need to be considered in the design of antiferromagnetic devices, but can potentially be used to tailor their properties, providing an additional handle to control antiferromagnets.

Consolidation theory of slurry dewatered by permeable geotextile tube with distributed prefabricated drains

Introducing the prefabricated horizontal drains (PHDs) into the permeable geotextile tubes has been reckoned as an efficient and economical method of dewatering slurries with high water contents. However, its application is limited by the poor understanding of the fundamental consolidation mechanism, often resulting in overconservative designs. With the proposed two-dimensional plane-strain consolidation model, a semi-analytical solution calibrated by laboratory test results is obtained. Furthermore, parametric analyses, for example, PHD pave rate, and element aspect ratio, along with the soil anisotropy coefficient, are also conducted to achieve the optimum design requirement. A critical condition corresponding to the optimum effectiveness of this consolidation technique is found, beyond which the consolidation efficiency decreases gradually. The greater the abovementioned parameters are, the later and milder the efficiency reduction occurs. The consolidation efficiency can keep at a high level until the end of consolidation when the values of these parameters are great enough. In the end, design charts and design recommendations are provided with immediate benefits for practical engineers.

A mixed finite element formulation for elastoplasticity

AbstractThe present article, provides a novel mixed finite element formulation for elastoplasticity which is suitable for the discretization of thin‐walled structures using highly anisotropic volume elements. We present a thermodynamically consistent framework for the modeling of elastoplastic stress response, where dissipative effects are considered through a dissipation function instead of explicit flow rules. Along these lines, a mixed incremental principle, in which stresses are included as independent unknowns, is derived. We propose to employtangential‐displacement normal‐normal‐stress(TDNNS) elements for a Galerkin discretization of the underlying variational problem. These elements were originally developed for linear elasticity, where it could be shown that they do not suffer from shear locking if the element's aspect ratio deteriorates. Excellent computational performance and accuracy of the proposed method are demonstrated in several benchmark problems.

An automated mesh generation algorithm for simulating complex crack growth problems

In this manuscript, we expand the conforming to interface structured adaptive mesh refinement (CISAMR) algorithm for modeling complex two-dimensional (2D) crack growth problems involving contact/friction along the crack surface and interaction between multiple cracks. The CISAMR algorithm transforms a structured mesh into a high-quality conforming mesh non-iteratively, which is an attractive feature for modeling the evolution of the crack geometry with minimal changes to the underlying mesh structure. To model such problems, the mesh structure is first adaptively refined and updated near the crack tip to form a spider-web pattern of elements for the accurate approximation of the energy release rate and thereby predicting the new crack path. In each step of the crack advance simulation, a small subset of elements in the vicinity of the crack tip is detected using a tree data structure and then deleted/regenerated to simulate the crack growth. The construction of a high-quality mesh with appropriate element aspect ratios in the algorithm allows the use of an explicit dynamic solver, which is essential to simulate the nonlinear response of the problem caused by contact forces along crack faces. Several benchmark fracture problems are presented to study the accuracy of the proposed algorithm, as well as two more complex problems to demonstrate its ability for modeling interaction of multiple growing cracks with one another and with embedded heterogeneities in the domain.

Innovative Sensor Design Method of Industrial Ceramic Product Modeling Based on Immune Optimization Algorithm

A new method based on immune optimization algorithm was proposed for modeling and design of industrial ceramic products. Based on the joint coding of fuzzy rules and membership function parameters, an improved immune optimization algorithm was used to realize the synchronous optimization of industrial ceramic product modeling. A superheated steam temperature control system is taken as an example to carry out simulation tests. The results show that the ratio of the unit volume to the side length is between 0 and 1, which is called the mass of the grid element. Zero is the worst quality and one is the best. Element aspect ratio and distortion degree are also basic inspection indexes. The average mass of vacuum glass is 0.86, the aspect ratio is 1.71, and the element distortion degree is 0.13, indicating that the grid quality is well divided. It is proved that using the improved immune genetic algorithm to optimize fuzzy control can overcome the defects of the traditional genetic algorithm and ensure the faster and more stable search for the optimal rule base and membership function.

The incorporation of mesh quality in the stabilization of virtual element methods for nonlinear elasticity

This work constitutes a further contribution to developing convergent, locking-free virtual element formulations for problems of large-deformation nonlinear elasticity. Earlier work by the authors and others has introduced simple and effective forms of stabilization. This work investigates the approximation properties of the virtual element method for problems with domains having a high aspect ratio, and for alternative forms of stabilization: an existing approach, and two modifications, which account for high element aspect ratio and element distortion. The results in all cases demonstrate the locking-free convergence of the approach, with the newer modifications leading to improvements in accuracy.

Approaches for the RCWA-based non-destructive characterization of subwavelength-structured gratings

Nano-structuring enables us to add additional degrees of freedom to the design of optical elements. Especially the possibility of controlling the polarization is of great interest in the field of nano-structured optics. For being able to exploit the whole range of form-birefringent phase shifts, the aspect ratios of the resulting element are typically much higher than the aspect ratios of conventional diffractive optical elements (DOEs), which does not only pose a challenge on fabrication but also on characterization. We evaluate several well-established approaches for the nondestructive characterization, including Müller-Matrix-Ellipsometry, measurement of the diffraction efficiencies, scattering measurements and calibration with rigorous coupled-wave modelling. The goal is to understand the challenges with all these techniques and combine them to a reliable method for structural reconnaisance of high aspect ratio nanostructures.

The Influence of Deterministic Surface Roughness and Freestream Turbulence on Transitional Boundary Layers: Heat Transfer Distributions and a New Transition Onset Correlation

AbstractHeat transfer measurements in transitional flat plate boundary layers subjected to surface roughness, strong pressure gradients, and freestream turbulence are presented. The surfaces considered consist of a smooth reference and 26 deterministic surface topographies that vary in roughness element aspect ratio, height, and density. They are designed to cover the full range of roughness regimes from smooth over transitionally rough to fully rough. For each surface, two pressure distributions, characteristic for a suction and a pressure side turbine vane, are investigated. Inlet Reynolds numbers range from 3.0 × 105 to 6.0 × 105 and inlet turbulence intensity is varied between 1% and 8%. Furthermore, different turbulence Reynolds numbers, i.e., turbulence length scales, are realized while the incident turbulence intensity is kept constant. Additionally, the turbulence intensity and Reynolds stress distributions in the freestream along the flat plate are measured using x-wire probes. Results show a strong influence of roughness and turbulence intensity on the onset of transition. The new data set is used to develop an improved correlation considering the roughness height, density, and shape as well as the turbulence intensity and turbulent length scales.

Surface discretization considerations for the boundary-element method applied to three-dimensional ellipsoidal particles in Stokes flow

The boundary-element method has often been used for simulating particle motion in Stokes flow, yet there is a scarcity of quantitative studies examining local errors induced by meshing highly elongated particles. In this paper, we study the eigenvalues and eigenfunctions of the double layer operator for an ellipsoid in an external linear or quadratic flow. We examine the local and global errors induced by changing the interpolation order of the geometry (flat or curved triangular elements) and the interpolation order of the double layer density (piecewise-constant or piecewise-linear over each element). Our results show that local errors can be quite large even when the global errors are small, prompting us to examine the distribution of local errors for each parameterization. Interestingly, we find that increasing the interpolation orders for the geometry and the double layer density does not always guarantee smaller errors. Depending on the nature of the meshing near high curvature regions, the number of high aspect ratio elements, and the flatness of the particle geometry, a piecewise-constant density can exhibit lower errors than piecewise-linear density, and there can be little benefit from using curved triangular elements. Overall, this study provides practical insights on how to appropriately discretize and parameterize three-dimensional boundary-element simulations for elongated particles with prolate-like and oblate-like geometries.

Free Vibration Analysis of Hybrid Laminated Composite Plate

In past decade a new manufacturing and Design technology developed across the globe because of that it possible to manufacture and analyses a hybrid laminated composite plate which is used in the various applications like aerospace, marine, spacecraft application were its subjected to dynamic loading so it is necessary estimate the response of the system under free vibration. Aim of this paper is Dynamic analysis of laminated composite plate which is made of hybridization of carbon epoxy and glass epoxy material. Natural frequencies are evaluated by FEM with the help of abaqus software for of hybrid laminated composite plate. The Parameter like aspect ratio, fiber orientation, boundary condition and mesh size of the FEA elements and stacking sequence affects natural frequencies of the plate. A hybrid laminated composite in which carbon fiber on top as well as bottom and glass fiber in inters layer gives maximum natural frequency at any boundary condition. FEM uses first order shear deformation theory.

STUDY THE BEHAVIOR OF ELASTIC MODULUS FOR ZIGZAG AND ARMCHAIR SINGLE WALL CARBON NANOTUBE STRUCTURE WITH FEM

A three-dimensional finite element (FE) model for single-walled carbon nanotubes with armchair and zigzag shapes is proposed in this paper (SWCNTs). Nodes are positioned at the locations of carbon atoms to design the FE models. And three-dimensional elastic beam components are used to model the bonds between them. The effect of the diameter length/diameter ratio on the diameter length/diameter ratio, cross sectional aspect ratio and number of elements on the Young’s modulus of SWCNTs has been considered herein. From the conducted experiments it can be observed that, the larger tube diameter can lead to higher Young’s modulus for carbon nanotubes. Such that, maximum elastic modulus for the armchair and the zigzag models has been obtained to be 1.0285TPa and 1.0396TPa when the diameters for the armchair and the zigzag models were 2.034nm and 1.957nm respectively. Increasing the length/diameter ratio has led the Young’s modulus to be increased for armchair and zigzag models such that its values can reach 1.0451TPa and 1.0191TPa respectively. The cross sectional aspect ratio of SWCNTs showed an inversely proportional effect on the elastic modulus in this work. As a result of rising the cross sectional aspect ratio to be2, the Young's modulus for armchair and zigzag models has decreased to 0.7991TPa and 0.8873TPa, accordingly. The change in geometry has been observed to be a defect and it is in general can decrease the modulus of elasticity. The number of elements in the armchair model considered as prominent factor that increases the young’s modulus to be 1.0280TPa when the number of element is 10836. In zigzag model, the number of element has no effect on the elastic modulus since the number of nodes that exposed to the applied load is fixed in this case. The findings showed that the proposed FE model may be useful for studying carbon nanotube mechanical action in the future.

An efficient automatic adaptive algorithm for cohesive crack propagation modeling of concrete structures using matrix-free unstructured Galerkin Finite Volume Method

Using Galerkin Finite Volume method, a 2D adaptive algorithm is developed for crack propagation simulation of concrete structures under mixed mode loading. The matrix free Finite Volume formulation is applied to implement a crack propagation model in a fully automatic adaptive mesh refinement framework for unstructured meshes. Cohesive cracks are implemented using nonlinear interface elements with bilinear softening constitutive equation. On contrary to existing cohesive crack models where the Newton-Raphson techniques are required to simulate the nonlinear behavior in the fracture process zone, the need for such a computational costly technique is relaxed. The matrix-free Finite Volume formulation method can provide better computational performance than the matrix-base methods. The introduced Method can also relax the problems of the standard Finite Element base methods with high aspect-ratio elements. The present Finite Volume model accurately predicts the crack propagation path and correctly evaluates the load-displacement curve while consumes low computational CPU time.