Finite Element Type Research Articles

Understanding the machined material’s behaviour in electro-discharge machining (EDM) using a multi-phase smoothed particle hydrodynamics (SPH) modelling

Electro-discharge machining (EDM) has been extensively employed for machining hard alloys, and its simulations have been widely conducted using finite element analysis (FEA). However, the majority of mesh-based models depended on forecasting the crater profile only based on the temperature gradient, without offering detailed data regarding the machined material properties. It is crucial to understand the behaviour of the machined material in order to accurately assess the flushing efficiency, analyse the wear on the electrode, and examine the interaction between the debris generated during machining and the remaining workpiece. This is done to ensure that no recast material is left behind after the EDM process. For the first time, a meshless smoothed particle hydrodynamics multi-phase model was implemented to gain practical insights and comprehensively understand a very intricate phenomenon that occurs within a very short time. Additionally, this approach is utilised to investigate the characteristics of the materials being machined. We utilised our SPH model to simulate both the capacitance- and transistor-based EDM of Ti–6Al–4V and AISI304 steel. Our simulation considered the temperature-dependent thermal properties and latent heats of the materials. The accuracy of our model was confirmed by comparing its results with experimental, analytical, and finite element analysis (FEA) results. The machined material was observed during its removal from the surface, and the dimensions of the resulting crater, as well as its aspect ratio and the rate at which the material was removed, were predicted with an error ranging from 2 to 22%. This error is far lower than that of the typical finite element (FE) prediction. This model lays the groundwork for a more complex model that will more accurately represent EDM and other similar manufacturing processes.

An Unfitted Finite Element Poisson-Boltzmann Solver with Automatic Resolving of Curved Molecular Surface.

So far, the existing Poisson-Boltzmann (PB) solvers that accurately take into account the interface jump conditions need a pregenerated body-fitted mesh (molecular surface mesh). However, qualified biomolecular surface meshing and its implementation into numerical methods remains a challenging and laborious issue, which practically hinders the progress of further developments and applications of a bunch of numerical methods in this field. In addition, even with a molecular surface mesh, it is only a low-order approximation of the original curved surface. In this article, an interface-penalty finite element method (IPFEM), which is a typical unfitted finite element method, is proposed to solve the Poisson-Boltzmann equation (PBE) without requiring the user to generate a molecular surface mesh. The Gaussian molecular surface is used to represent the molecular surface and can be automatically resolved with a high-order approximation within our method. Theoretical convergence rates of the IPFEM for the linear PB equation have been provided and are well validated on a benchmark problem with an analytical solution (we also noticed from numerical examples that the IPFEM has similar convergence rates for the nonlinear PBE). Numerical results on a set of different-sized biomolecules demonstrate that the IPFEM is numerically stable and accurate in the calculation of biomolecular electrostatic solvation energy.

Micromechanical analysis of fiber-reinforced ceramic matrix composites by a geometrically nonlinear hierarchical quadrature element model

The stress fields of fiber-reinforced ceramic matrix composites (CMCs) under longitudinal tension are predicted using a non-linear hierarchical quadrature element method (HQEM) in this work. The HQEM combines the differential quadrature method (DQM) with the hierarchical finite element method (HFEM), which is a typical p-version finite element method (FEM). High-order interpolation functions of the HQEM allow accurate evaluation of stress distribution. Fiber, matrix, and interfaces of the CMCs are modeled as linear elastic materials that may have large displacements. The nonlinear HQEM estimation of CMCs stress distributions are validated by comparing with analytical results obtained using classical BHE shear-lag model. Stress distribution in three characteristic stages in the damage evolution process, namely, interface perfectly bonded, interface debonding, and fiber failure are investigated. It is shown that when fiber failure happens, geometric non-linearity must be considered to avoid excessive stress concentration. Furthermore, the stress distribution within three-dimensional cylindrical CMCs cell is studied, which sheds light on the future exploration of three-dimensional CMCs analyses.

Adjoint sensitivity kernels for free oscillation spectra

SUMMARY We apply the adjoint method to efficiently calculate sensitivity kernels for long-period seismic spectra with respect to structural and source parameters. Our approach is built around the solution of the frequency-domain equations of motion using the direct solution method (DSM). The DSM is currently applied within large-scale mode coupling calculations and is also likely to be useful within finite-element type methods for modelling seismic spectra that are being actively developed. Using mode coupling theory as a framework for solving both the forward and adjoint equations, we present numerical examples that focus on the spectrum close to four eigenfrequencies (the low-frequency mode, 0S2, and higher frequency modes, namely 2S2, 0S7 and 0S10 for comparison). For each chosen observable, we plot sensitivity kernels with respect to 3-D perturbations in density and seismic wave speeds. We also use the adjoint method to calculate derivatives of observables with respect to the matrices occurring within mode coupling calculations. This latter approach points towards a generalization of the two-stage splitting function method for structural inversions that does not rely on inaccurate self-coupling or group-coupling approximations. Finally, we verify through direct calculation that our sensitivity kernels correctly predict the linear dependence of the chosen observables on model perturbations. In doing this, we highlight the importance of non-linearity within inversions of long-period spectra.

The distribution law of shock wave pressure in typical trenches

Trenches, as important practical military facilities, have important theoretical and military value in evaluating the damage power of ammunition, operational application, and effective safety protection of personnel on the battlefield through the spatiotemporal evolution of explosive shock waves within them. At present, there is a lack of in-depth research on the distribution and impact of overpressure inside the trench. The paper constructed a typical finite element simulation model of a trench, numerically calculated the shock wave overpressure inside the trench and on the wall, analyzed the spatiotemporal distribution of shock wave pressure in various parts of the trench, conducted on-site explosion tests, and installed shock wave pressure sensor measurement points in the trench. The pressure time history curve was obtained, and verified and compared with the simulation calculation results. Research data shows that the peak overpressure of the shock wave in the trench increases sequentially from the front wall to the back wall. The peak overpressure of the shock wave at the front wall attenuates by 10 % to 20 % compared to the inside of the trench, and increases by 40 % to 60 % at the back wall; The peak overpressure in the trench exhibits a “V-shaped” distribution at different depths, decreasing first and then increasing as the depth increases. The maximum overpressure peak increases by 40 % to 50 % compared to the minimum; Based on simulation and measured data in the trench, as well as the distribution law of shock wave pressure, safety protection suggestions for on-site combat personnel in the trench are provided.

Stable and locally mass- and momentum-conservative control-volume finite-element schemes for the Stokes problem

We introduce new control-volume finite-element discretization schemes suitable for solving the Stokes problem. Within a common framework, we present different approaches for constructing such schemes. The first and most established strategy employs a non-overlapping partitioning into control volumes. The second represents a new idea by splitting into two sets of control volumes, the first set yielding a partition of the domain and the second containing the remaining overlapping control volumes required for stability. The third represents a hybrid approach where finite volumes are combined with finite elements based on a hierarchical splitting of the ansatz space. All approaches are based on typical finite element function spaces but yield locally mass and momentum conservative discretization schemes that can be interpreted as finite volume schemes. We apply all strategies to the inf-sub stable MINI finite-element pair. Various test cases, including convergence tests and the numerical observation of the boundedness of the number of preconditioned Krylov solver iterations, as well as more complex scenarios of flow around obstacles or through a three-dimensional vessel bifurcation, demonstrate the stability and robustness of the schemes.

Composite anisogrid lattice toroidal shell: Application to a load-carrying rim of the spacecraft reflectarray antenna

A novel design of the composite transformable/foldable rim of the spacecraft reflectarray antenna is presented in the paper. The rim is made in the form of anisogrid lattice toroidal shell split into six parts that are jointed using hinges containing helical springs. The springs create the moments required to deploy the antenna in orbit. A dielectric flexible flat membrane with reflective radiating elements generating a radio signal with required directivity is stretched on the rim. An algorithm of the finite-element model generation is developed for the toroidal rim using a typical finite-element unit cell of lattice structure. The lattice toroidal shell is modelled as a three-dimensional frame composed of curvilinear ribs. The results of design analysis of the lattice rim delivering a minimal mass to its structure subject to constraints imposed on the fundamental frequency, values of stress, and the buckling load factor are presented in this work. The corresponding set of design parameters of lattice structure, including the angle of orientation of helical ribs, number of helical ribs of one orientation, and size of the ribs’ cross section are identified based on these results.

Thermal metasurface with tunable narrowband absorption from a hybrid graphene/silicon photonic crystal resonance.

We report the design of a tunable, narrowband, thermal metasurface that employs a hybrid resonance generated by coupling a tunable permittivity graphene ribbon to a silicon photonic crystal. The gated graphene ribbon array, proximitized to a high quality factor Si photonic crystal supporting a guided mode resonance, exhibits tunable narrowband absorbance lineshapes (Q > 10,000). Actively tuned Fermi level modulation in graphene with applied gate voltage between high absorptivity and low absorptivity states gives rise to absorbance on/off ratios exceeding 60. We employ coupled-mode theory as a computationally efficient approach to elements of the metasurface design, demonstrating an orders of magnitude speedup over typical finite element computational methods.

Comparison of Monte Carlo and bootstrap analyses for residual life and confidence interval

Abstract Failure starts with creation of a crack, then the propagation of the crack and eventually the fracture of the material. Furthermore, material selection, geometry, processing and residual stresses are critical factors that may contribute to uncertainty and prospective failure mechanisms in engineering. These issues may also arise in computational analysis, a problematic model, for instance, a three-dimensional surface fracture that may necessitate numerous degrees of freedom during analysis. However, considering the multiple incidents of material failure, detailed analysis and efforts to prevent premature material failure for safety and engineering integrity can be carried out. Thus, the objective of this study is to model crack growth in a surface-cracked structure. Aluminium alloy 7075-T6 was the material of interest in this study. The S-version finite element method (SFEM) was used to study fracture propagation. The numerical approach developed in this research was the probabilistic SFEM. Instead of mesh rebuilding, a typical finite element approach, the SFEM uses global–local element overlay method to create a fatigue crack growth model, which was then used for crack research. Empirical computation and previous experimental data were used to evaluate the stress intensity factor (SIF), surface crack growth and fatigue life. The SIF was determined using a virtual crack closure method (VCCM). In addition, the probabilistic approach is also a critical method to generate random parameters, such as Monte Carlo and bootstrap methods. The SIF, fatigue life and surface crack growth were validated and deemed to be within the acceptable range.

Towards high frequency boundary element methods for multiple scattering

Standard Boundary Element Methods (BEM) for time-harmonic acoustics, using piecewise polynomial finite-element type approximation spaces, have a computational cost that grows rapidly with frequency, to ensure at least a fixed number of degrees of freedom per wavelength. Hybrid Numerical-Asymptotic (HNA) BEMs, based on enriched approximation spaces consisting of the products of piecewise polynomials with carefully chosen oscillatory functions, have a computational cost that is almost frequency-independent for some problem classes (e.g. Chandler-Wilde, Graham, Langdon, Spence, Acta Numerica 2012), but the technology is largely undeveloped for problems where multiple scattering is important. In this paper we present computational experiments, supported by mathematical analysis, which suggest that multiple scattering configurations may be within reach. Specifically, we solve, by a HNA BEM, scattering by a pair of screens in an arbitrary configuration, which we anticipate may serve as a building block towards algorithms for general multiple scattering problems with computational cost independent of frequency. The specific configuration considered, as we discuss, is relevant to the efficient simulation of multiple outdoor noise barriers.

Seismic fragility analysis using stochastic polynomial chaos expansions

Within the performance-based earthquake engineering (PBEE) framework, the fragility model plays a pivotal role. Such a model represents the probability that the engineering demand parameter (EDP) exceeds a certain safety threshold given a set of selected intensity measures (IMs) that characterize the earthquake load. The-state-of-the art methods for fragility computation rely on full non-linear time–history analyses. Within this perimeter, there are two main approaches: the first relies on the selection and scaling of recorded ground motions; the second, based on random vibration theory, characterizes the seismic input with a parametric stochastic ground motion model (SGMM). The latter case has the great advantage that the problem of seismic risk analysis is framed as a forward uncertainty quantification problem. However, running classical full-scale Monte Carlo simulations is intractable because of the prohibitive computational cost of typical finite element models. Therefore, it is of great interest to define fragility models that link an EDP of interest with the SGMM parameters — which are regarded as IMs in this context. The computation of such fragility models is a challenge on its own and, despite a few recent studies, there is still an important research gap in this domain. This comes with no surprise as classical surrogate modeling techniques cannot be applied due to the stochastic nature of SGMM. This study tackles this computational challenge by using stochastic polynomial chaos expansions to represent the statistical dependence of EDP on IMs. More precisely, this surrogate model estimates the full conditional probability distribution of EDP conditioned on IMs. We compare the proposed approach with some state-of-the-art methods in two case studies. The numerical results show that the new method prevails over its competitors in estimating both the conditional distribution and the fragility functions.

Experimental and Numerical Investigation of an Innovative 3DPC Thin-Shell Structure

The development and application of new Fiber Reinforced Polymer (FRP) material and 3D printing construction technology provide a basis for making up for the shortcomings of traditional thin-shell structures and building new thin-shell structures with better performance. In this paper, a new 3D Printing Composite (3DPC) thin-shell structure is proposed, which is prepared using a FRP plate as a permanent base mold and combining it with 3D printing cement technology. Both the typical experiment and finite element numerical simulation analysis of the 3DPC thin-shell structure are carried out. The results show that the maximum load capacity of the 3DPC thin-shell structure is increased by 53.3% as compared with the corresponding traditional concrete thin-shell structure. The presence of the FRP sheet effectively delays the generation of initial cracks and enhances the ductility of components.

Prediction of Surface Location Error Considering the Varying Dynamics of Thin-Walled Parts during Five-Axis Flank Milling

Surface location error (SLE) caused by forced vibration is a key factor to determine the quality of the finished part. When machining thin-walled structures with sculptured surfaces, the complicated milling process is significantly influenced by the vibration due to the flexibility of the part. The dynamics of the part are dominant and vary with the material removal during machining. This paper presents a prediction method of SLE considering the varying dynamics of thin-walled parts in five-axis flank milling. The in-process part is decomposed into unmachined and machined portions, which are both modelled based on the thin-plate theory. The dynamics models of the two portions are coupled using the substructure method. Coordinate transformation based on the screw theory and the general cutting dynamics model for five-axis flank milling is employed to transform the cutting force vectors and frequency response function (FRF) to the same coordinate system for the prediction of SLE. The proposed method is validated with five-axis flank milling tests and SLE measurements on a thin-walled twisted part. It is shown that the average error of the proposed method for SLE prediction is less than 5 μm, and the calculation is almost 8 times faster than the typical finite element method.

Mechanical Calculation of Stator Core Vibration of Rotating Electric Machines Using an Analytical Beam Element Model

The stator core vibration caused by electromagnetic forces is an important topic in the design of electric machines. A crucial task for the comprehensive analysis of this issue is to accurately estimate the eigenmodes and eigenfrequencies of the mechanical system, which allows the calculation of the forced mechanical response. This paper presents a new analytical model based on beam elements as an alternative to the typical finite-element (FE) and classical analytical models applied for this purpose assuming a 2D simplification of the system. The proposed model takes the stator yoke and teeth into account and is able to predict the eigenmodes, eigenfrequencies and forced response of the stator core of rotating electric machines, such as synchronous and induction motors. The results are compared to FE and analytical calculations and validated based on measurements on the stator core of a permanent magnet synchronous motor.

Effect of fines content on soil moisture responses to wetting & drying cycles

Studies of soil moisture responses to climatic conditions are essential for understanding the mechanism of rainfall-induced landslide. This study aims to investigate the effects of fines content on soil moisture responses under repetitive wetting and drying cycles. Remoulded residual soil samples were prepared at 5 different fines contents, i.e. 15%, 30%, 45%, 60% and 75%. The soils were instrumented with soil moisture sensors and they were subjected to 2 cycles of wetting and drying. Results showed that all the soil specimens experienced faster reductions in soil moisture during the second cycle of drying than the first cycle. During wetting, the recovery of soil moisture, however, was less affected by the repetitive wetting and drying cycles. The fines content has a significant influence on the soil moisture reduction during drying. The degree of saturation of the specimen with 15% fines was found to be 3.5–6 times lower than that of 75% fines. The response of soil moisture to wetting was only marginally affected by the fines content. Results from numerical seepage analyses showed that the wetting soil moisture responses can be simulated to a reasonable accuracy. However, the simulated drying soil moisture responses showed relatively large discrepancies with the actual measurements. The results implied that the soil may have experienced changes in soil structure, void ratio or formation of desiccated crack during the repetitive wetting and drying cycles which cannot be captured by a typical finite element seepage analysis.

Analysis of the drainage effect of different incisions for high complex anal fistula based on FLUENT hydrodynamic simulation.

PurposeThe biomechanical characteristics of the trauma size and postoperative drainage of different incisions for high complex anal fistula surgery were compared by numerical simulation analysis to provide a theoretical basis for the clinical selection of minimally invasive incisions for surgery.MethodsUsing FLUENT finite element software, a typical incision finite element model was established to obtain incision areas, and the total mass outlet flow within 200 s was calculated to evaluate the drainage effect of each incision.ResultsThe incisions with the largest to smallest areas were the curved, spindle, and curved plus extended groove incision, indicating that the curved plus extended groove incision caused the least damage to the perianal skin muscles. Conversely, the incisions with the largest to smallest total outlet flow were as follows: curved plus extended groove, spindle, curved, and straight incision, suggesting that the curved plus extended groove model had the best diversion effect, and the curved incision had better diversion effect than that of the straight incision.ConclusionThe curved plus extended groove surgical incision had the smallest incision area, minimized damage to the perianal skin and muscle tissue, conformed to the concept of minimally invasive surgery, ensured adequate drainage of exudate, maintained the normal growth of granulation tissue on the wound surface, preserved the original form of the anus, and thus better protected the function of the anus. This improved the quality of life of patients requiring high complex anal fistulas.

Analysis of relationship between loading condition and cranial cracking pattern using a three-dimensional finite element model

BackgroundA hairline crack on the cranium can occur even under a small external load or impact and are thus often observed in patients who have experienced an accidental fall or collision. Typical finite element analysis is useful to analyze the stress concentration or the propagation of stress waves. However, a stress propagation model does not accurately reproduce the features of hairline cracks on the cranium. The objective in this study was to reproduce cranial hairline cracks.MethodsA three-dimensional finite element model of the cranial bone was developed from a patient CT images. The model consists of the frontal, parietal, occipital and temporal bones, and the bones are connected with the sutures. Additionally, the model comprised three layers; the external and internal tables and the diploe. The model was analyzed using the extended finite element method (X-FEM), and a forming limit diagram (FLD) was embedded in the model. In this study, the model was symmetrized bilaterally using the model developed from the left side of the skull. The FLD in this study was assumed to be a relationship between the maximum and minimum strains when a fracture occurs. A total of 13 typical loadings were applied to the model: loading points on the top, left, and back of the cranium were considered, and at each loading point, loads were applied with four or five different directions, namely perpendicular to the cranium and inclined in the anterior, posterior, superior, or inferior at an angle of 45∘.ResultsUnder all loading conditions, many small cracks formed radially at the loading points. Moreover, some large cracks formed under the certain loading conditions. The crack shapes on the top and left side could be associated with the specific loading directions, whereas cracks on the back did not show distinguishing characteristics depending on the loading directions. The present model was reproduced anatomically and morphologically, and the results were similar to those obtained in previous cadaver experiments.ConclusionsThrough X-FEM analysis of the FE model embedded with an FLD, hairline cracks in the cranium were reproduced, and a few crack shapes were identified as potential markers for estimating the loading conditions.

A practical numerical model for thin-walled steel connections and built-up members

The interaction between the cold-formed steel members and fasteners in a structural assembly often involves complex stress states, material plasticity, significant in-plane deformations and curling, rendering computational modelling of the resulting structural system challenging. In addition, the presence of initial geometric imperfections and the susceptibility of cold-formed steel members to local instabilities adds a further degree of complexity to the numerical modelling. The behaviour of bolted connections between cold-formed steel members has traditionally been assessed based on physical tests, though these can be time consuming and expensive. In this paper, a practical numerical approach to the simulation of bolted cold-formed steel connections, capturing all the key behavioural features including bolt preload, slippage and bearing, is introduced. Starting from a typical shell finite element (FE) model of a cold-formed steel plate, a small number of solid elements is introduced around the bolt holes, to allow accurate replication of the bolt-ply interaction, with contact pairs defined between the bolts and the surrounding material. An explicit dynamic solver is then employed to solve the geometrically and materially nonlinear problem, both with and without bolt slippage. Validation of the FE model is conducted using benchmark tests reported in the literature. It is shown that the proposed numerical method can accurately capture the structural behaviour of bolted cold-formed steel connections and cold-formed steel built-up sections, while being computationally efficient and numerically stable; the proposed approach is therefore recommended for the numerical modelling of cold-formed steel systems assembled using fasteners.

СИМУЛЯЦИЯ ТЕРМОДЕФОРМАЦИОННОГО ПОВЕДЕНИЯ ДВУСТОРОННИХ ТОРЦЕШЛИФОВАЛЬНЫХ СТАНКОВ

The paper presents the result of modeling the thermal deformation behavior of the bearing system of a double-sided face grinder. Two modes of its operation is considered: idling and working strokes. Spindle bearings, heat fluxes from coolant, and heat fluxes from motors are considered as the main heat sources. The preliminary values of heat and convective fluxes are assigned according to well-known methods used in engineering calculations of machine tools. Refinement of the values of heat and convective fluxes is carried out according to the results of experimental values of temperatures and temperature displacements. In the thermal model, convective heat transfer is assigned to 450 surfaces. Heat flows are assigned to 161 surfaces. The simulation is run in Ansys for 6 hours of machine tool operation. Ansys uses a ten-node Solid227 element as a typical finite element. The problem of thermoelasticity is solved in a related setting. The error in modeling thermal processes did not exceed 0,5 degree, the error in modeling temperature displacements did not exceed 5 microns. The results of computer simulation confirmed the relative experimental positions of the left and right grinding wheels characteristic of this range of machines. At idle, the relative position of the grinding wheels represented the state «wider at the bottom», and during the working stroke, the state «at the bottom narrower» is recorded. The illustrations of the FEM model and contour plots for the temperature field and temperature displacements of the bearing system of the machine tool for two modes of its operation are presented.

The Influence of anisotropy on the vibration behaviour of S600Mc sheet metal

Sheet metal anisotropy is the directional dependence of mechanical properties. It is a critical factor that must be considered when using numerical simulation to predict any plastic deformation manufacturing process. Sheet metals prove anisotropic plastic behaves due to crystallographic texture caused by progressive rolling steps, Banabic D. et al. (2000). Cold bending of steel sheets is a widely used manufacturing process in the automotive industry due to its cost efficiency. By avoiding line heating, the oxidative process of steel is thus avoided. The automotive industry's primary application of sheet metal includes doors, fenders, bumpers, roof panels, and seat frames. In this paper, test specimens were laser cut at orientations θ = 0°, 45°, and 90° to the rolling direction. The specimens were subjected to forced vibration on an electromechanical shaker, and the frequency response amplitude was measured using accelerometers. Natural frequency and Q-factors were discussed. Experimental data are used for viscous damping coefficients (alpha and beta) for each direction of the specimen. The measured coefficients are then used to validate each type's finite element, numerical models. The results show the level of dependency between the structural damping and anisotropy of the laminated sheet metal and the influence on the high cycle fatigue performance.