For Finite Element Method Research Articles

Advancing Structural Optimization of an Electric Motor Rotor through Mesh Morphing Techniques

The electric motor has been one of the most important inventions of the last two centuries and has become increasingly important in the last 10 years thanks to its efficiency and its ability to reduce pollution. Given this increasing importance of electrical motors, an interest in design and optimization approaches for motor components is arising. Given the different physics involved in the transformation from electrical to mechanical energy, a valuable and reliable approach has to be applied in the optimization process. In past years, Mesh Morphing based on Radial Basis Functions (RBF) has largely proved its validity in generating shape modification for Finite Element Method (FEM) models. In this work, authors will demonstrate the advantages in applying two opposite approaches for shape optimization using RBF Mesh Morphing applied to electrical motors rotors. These components need to be accurately designed in order to guarantee an adequate life duration by reducing stresses in the rotating components. The two approaches that will be described are the parameter based one, in which a set of design parameters will be varied to generate shape modification used to feed a meta-model that will be used to identify an optimal configuration, and a parameter-less approach, in which the shape modification will be driven by FEM analysis results, with the aim to reduce stress hot-spots.

Finite element models for radiation effects in nuclear fusion applications

Deuterium-tritium fusion reactions produce energy in the form of 14.1 MeV neutrons, and hence fusion reactor components will be exposed to high energy neutron irradiation while also being subjected to thermal, mechanical and magnetic loads. Exposure to neutron irradiation has numerous consequences, including swelling and dimensional changes, comparable in magnitude to the peak transient thermal deformations occurring in plasma-facing components. Irradiation also dynamically alters the various thermo-mechanical properties, relating temperature, stress and swelling in a strongly non-linear way. Experimental data on the effect of neutron exposure spanning the design parameter space are very sparse and this highlights the relevance of computer simulations. In this study we explore the equivalence between the body force/surface traction approach and the eigenstrain formalism for treating anisotropic irradiation-induced swelling. We find that both commercial and massively parallelised open source software for finite element method (FEM) simulations are suitable for assessing the effect of neutron exposure on the mechanically loaded reactor components. We demonstrate how two primary effects of irradiation, radiation swelling and the degradation of thermal conductivity, affect the distributions of stress and temperature in the divertor of the ITER tokamak. Significant uncertainties characterising the magnitude of swelling and models for treating it suggest that on the basis of the presently available data, only an order of magnitude estimate can be given to the stress developing in reactor components most exposed to irradiation during service.

Reduction of Numerical Model in Some Geotechnical Problems

Abstract The concept of equivalence of the realistic, initial reference model and the simplified, reduced model is proposed. In reduced models, the action of the soil on the structure is replaced by the action of a layer with prescribed properties, defined by a set of parameters. The main difficulty here is to find the parameter values required by the simplified theory. The subject of this work is to find the dependence of the parameters of the reduced model on the parameters of the full model, including realistic soil behavior, in order to ensure the equivalence of both models. We show the potential of the method by presenting two examples: Winkler and Pasternak's model of a plate on the ground. We assume that both models are equivalent if they give identical results (displacements) at a finite number of observation points. An artificial neural network (ANN) is built in order to approximate and record the dependence of the parameters of the reduced model (at the network output) from the parameters of the full model (given at the network input). The complex network acts as a formula that assigns the parameters of the reduced model to a realistic description of the soil structure that is used for finite element method (FEM) modeling. The formalism we propose is quite general and can be applied to many engineering problems. The presented procedure is entirely numerical; it allows to calculate the parameters of the reduced model without resorting to symbolic calculations or additional theoretical considerations.

Development of an empirical model for the prediction of the airflow resistivity of thin and low-density fibrous materials

This study develops an empirical model to predict the airflow resistivity of thin and low-density sound-absorbing materials. Airflow resistivity is a key input parameter for Finite Element Method (FEM) simulations of sound pressure levels (SPLs) in vehicle cabins. However, existing models for determining the airflow resistivity of thin and low-density fibrous materials are inaccurate. Therefore, this study proposes a simple and reliable model based on multiple linear regression analysis of polypropylene fibrous nonwoven samples. The samples were tested using equipment designed according to ISO standards 9053-1. The model selection was performed using stepwise techniques to identify the most relevant predictors. The final model, along with its coefficients and goodness of fit statistics, is presented and discussed. The results of this study offer a practical tool for design engineers to estimate the airflow resistivity of thin and low-density materials, which can improve the accuracy of FEM simulations of SPLs in vehicle cabins.

Predictive Modeling of Spring-Back Behavior in V-Bending of SS400 Steel Sheets under Elevated Temperatures Using Combined Hardening Laws

This research presents an innovative methodology for accurately predicting spring-back tendencies in V-bending of SS400 steel sheets under elevated temperatures. The study leverages extensive tensile test data to determine parameters for pure isotropic and kinematic hardening laws at varying temperatures, crucial inputs for Finite Element Method (FEM) simulations. While using pure isotropic or kinematic hardening laws alone has limitations, especially at elevated temperatures, a hybrid approach is recommended for robust predictive models in ABAQUS 6.13 software. To address this challenge, a novel method is introduced, utilizing flow stress curve ratios between elevated and room temperatures as a function of equivalent strain to derive combined hardening law parameters. Rigorous comparison of simulation and experimental results confirms the model’s effectiveness in predicting spring-back in the V-bending of SS400 steel sheets, particularly under elevated temperatures. This innovative approach enhances understanding of material behavior at high temperatures and improves predictive capabilities for designing and optimizing complex V-bending processes.

3D Multi-Ion Corrosion Model in Hierarchically Structured Cementitious Materials Obtained from Nano-XCT Data.

Corrosion of steel reinforcements in concrete constructions is a worldwide problem. To assess the degradation of rebars in reinforced concrete, an accurate description of electric current, potential and concentrations of various species present in the concrete matrix is necessary. Although the concrete matrix is a heterogeneous porous material with intricate microstructure, mass transport has been treated in a homogeneous material so far, modifying bulk transport coefficients by additional factors (porosity, constrictivity, tortuosity), which led to so-called effective coefficients (e.g., diffusivity). This study presents an approach where the real 3D microstructure of concrete is obtained from high-resolution X-ray computed tomography (XCT), processed to generate a mesh for finite element method (FEM) computations, and finally combined with a multi-species system of transport and electric potential equations. This methodology allows for a more realistic description of ion movements and reactions in the bulk concrete and on the rebar surface and, consequently, a better evaluation of anodic and cathodic currents, ultimately responsible for the loss of reinforcement mass and its location. The results of this study are compared with a state-of-the-art model and numerical calculations for 2D and 3D geometries.

Application of G-N high-order boundary condition on time harmonic analysis of concrete gravity dam-reservoir systems

PurposeThe response of an idealized triangular concrete gravity dam is studied due to horizontal and vertical ground motions for both fully reflective and absorptive reservoir bottom conditions. For each combination, in this paper different orders of Givoli-Neta (G-N) high-order truncation condition are aimed to be evaluated from accuracy point of view by comparing the results against corresponding exact solutions which relies on utilizing a two-dimensional fluid hyper-element.Design/methodology/approachIn present study, the dynamic analysis of concrete gravity dam-reservoir systems is formulated by Finite Element (FE)-(FE-TE) approach. In this technique, dam and reservoir are discretized by plane solid and fluid finite elements. Moreover, the G-N high-order condition imposed at the reservoir truncation boundary. This task is formulated by employing a truncation element at that boundary. It is emphasized that reservoir far-field is excluded from the discretized model.FindingsIt was observed that trend in gaining accuracy with increase in the order of G-N condition were basically the same for both horizontal and vertical ground motions under full reflective reservoir bottom condition. Moreover, convergence rate increases for absorptive reservoir bottom condition cases in comparison with fully reflective cases. It is also noticed that in certain cases, the responses are hardly distinguishable from corresponding exact responses. This reveals that proposed FE-(FE-TE) analysis technique based on G-N condition is quite successful, and one may fully rely on that for accurate and efficient analysis of concrete gravity dam-reservoir systems.Originality/valueDynamic analysis of concrete gravity dam-reservoir systems are formulated by a new method. The salient aspect of the technique is that it utilizes G-N high-order condition at the truncation boundary. This is achieved by developing a special truncation element which its generalized matrices are derived for Finite Element Method (FEM) programmers. The method is discussed for all types of excitation and reservoir bottom conditions. It must be emphasized that although time harmonic analysis is considered in the present study, the main part of formulation is explained in the context of time domain. Therefore, the approach can easily be extended for transient type of analysis.

Experimental study on the constitutive model of optically clear adhesive films under rapid loading

AbstractThe mechanical properties of optically clear adhesive (OCA) films can be anisotropy and viscoelasticity, and they are distinguished from conventional linear elasticity and hyper‐elasticity. These properties should be considered to analyze the interfacial stress, which plays an important role in evaluating the failure of a structure containing OCA. Based on well‐designed systematical experiments in the material's principal axes, a phenomenological constitutive model of OCA has been proposed in a transversely isotropic and rate‐dependent form. For the application to large deformation cases, the constitutive model was developed by using true stress and true strain. Results show that the well‐known assumption of volume‐incompressibility is not appropriate for OCA, and Poisson's ratio can vary with the loading rate and the current strain. Considering that the mono‐axial mechanical behaviors along the material's principal axes present strong non‐linearity, an incremental three‐dimensional constitutive model has been developed for finite element method (FEM) implementation. By comparing with traditional isotropic elastic and hyperelastic models, numerical examination results show that the proposed constitutive model can give a more accurate description of experimental stress–strain curves.

Topology based modelling of crochet structures

Crocheted textiles receive scarce scientific study and are at present not produced in automatized industrial scale. Computer-aided modelling and simulation offer capabilities for investigating possible technical fields of application. In this context a novel approach for modelling crocheted textiles consisting of chains, slip stitches and single crochets using a topology based and parameterized key point representation at the meso scale is proposed. According to the stitch size, yarn diameter and pattern spline interpolated models, which are free of interpenetrations up to approximately a 1/10 ratio of yarn diameter to stitch size, are generated by a developed Python program and software from the company TexMind. The models are suitable for finite element method (FEM) applications with LS-DYNA with which the mechanical properties of crocheted textiles can be studied. Exemplary simulations show anisotropic properties and homogeneous distribution of stresses in a crocheted textile. Due to the computationally simple and flexible modelling the presented approach may serve as a tool for designing planar crocheted textiles. This allows for estimation of the required yarn length and offers the prediction capabilities of simple and fast FEM simulations based on beam elements.

Determination of constitutive friction laws appropriate for simulation of cutting processes

The influence of friction on machining processes as a function of pressure, velocity and temperature is neither deeply understood nor sufficiently definable for Finite-Element-Method (FEM) simulations. Current simulations therefore often use constant values for the friction coefficients. In this work, friction coefficients for SAE 1045 are determined from different tribometers. An empirical model is subsequently fit to the data and used in different FEM-tools to simulate orthogonal cutting. Results are compared to corresponding experiments. A final evaluation of the model reveals the challenges due to the elasto-plastic contact and thus the derivation and utilisation of such a model.

An advanced Bayesian parameter estimation methodology for concrete dams combining an improved extraction technique of hydrostatic component and hybrid response surface method

It is very important to estimate the mechanical parameters based on monitoring data for investigating the operation behavior of concrete dams. In this paper, an advanced Bayesian parameter estimation method for concrete dams is proposed. The Empirical Mode Decomposition (EMD) is adopted to extract the aging component of the observed deformation sequence, and the hydrostatic component is separated from the remaining periodic term through the statistical regression model (SRM). A hybrid response surface method (HRSM) is proposed as a surrogate model for finite element method (FEM) simulation. The likelihood function, which reflects the error between the observed and simulated deformation, is constructed, then the Bayesian formula for parameter estimation is established. The transitional Markov chain Monte Carlo (TMCMC) algorithm is used to obtain the parameter posterior distribution. The proposed method is applied to estimate the elastic modulus of the GD concrete dam, the parameter posterior distribution is obtained through the fusion of monitoring information and parameter prior information. This method can also avoid the issues of multiple solutions and unreasonable parameter combinations, which may exist in traditional deterministic inversion methods. The case study shows that the proposed method has good applicability in the parameter estimation of concrete dams.

Transmission Loss analysis of a simple expansion chamber muffler with extended inlet and outlet combined with inhomogeneous micro-perforated panel (iMPP)

This paper studies the acoustic performance of a simple expansion chamber muffler combined with an inhomogeneous microperforated panel (iMPP). Three different shaped mufflers, i.e., circular, rectangular, and elliptical, with extended inlet and outlet pipes, have been studied. The thermo-acoustic module of COMSOL Multiphysics 5.5a software is used for finite element method (FEM) simulation. Then the 3D printing (stereolithography) technology is used to manufacture the samples. The transmission loss (TL) of the muffler given by the FEM simulation model is verified and measured by the Two-load method experiment, and the muffler with and without iMPP is tested. Different configurations have been tested to detect the effect of resonator absorbers based on iMPP in the expansion chambers. To observe the effectiveness of using iMPP, it is compared with other homogeneous MPPs. The results show that the TL of the low to medium frequency region increases by 25∼30 dB after adding iMPPs into the expansion chamber. Finally, the air-cavity depth behind the iMPP and the length of the expansion chamber is varied to study its effect on TL performance. The results show that the larger the cavity depth, the lower the TL peak. At the same time, with the decrease of the expansion chamber length, the TL peak gradually decreases and narrows. By carefully controlling and selecting the iMPP and expansion chamber parameters, we can obtain the required TL. Therefore, when the reactive effect of the muffler becomes invalid, iMPP can be used as an alternative further to improve the TL from low frequency to medium frequency.

A geometry-based design approach and structural behaviour for an asymptotic curtain wall system

This paper presents a novel design approach for doubly curved façade structures, based on isothermal networks on minimal surfaces. It combines theories from differential geometry with knowledge in mechanical behaviour and architectural design. By controlling the curvature of surface and network, and allowing the elastic deformations of elements, a curtain wall system is fabricated from straight steel strips, assembled with repetitive 90-degree joints, and covered with planar quadrilateral or developable panels. The goal of this research is to study the complete workflow from digital design through simulation to the physical construction of a 2.4 × 2.4 m steel structure. The article presents the computational and mathematical method to design minimal surfaces, find the path of asymptotic and principal curvature lines, and create isothermal networks. To analyse elastic stress, two methods are compared using analytical beam theory and a novel flatten-reduction approach for Finite Element (FE) shell elements. The novel approach offers benefits in manufacturing, logistics, prefabrication and erection process. The FE method is used to analyse the bent structure, simulate the kinetic behaviour and evaluate the impact of residual stress, lamella slots, joint reinforcement on the structural performance. The study offers a systematic workflow to accurately design for construction and predict kinetic and static behaviour. It provides evidence of the feasibility of this strategy to create low-cost, resilient, smooth doubly curved façade structures.

Apparent permeability of ordered magnetically soft nanowire arrays

Using the equivalent 2D model for finite element method (FEM) we calculated apparent permeability µa and demagnetization factor D for permalloy nanowire and microwire arrays. The simulation results were verified by 3D FEM for arrays up to 3000 wires and experimentally for very large arrays containing up to 40 million wires. We achieved µa = 3 to 33 and coercivities Hc = 1 to 9 kA/m, which are low values for wire arrays. The µa depends mainly on the array geometry; it can be increased by increasing the distance between wires (pitch) and the wire length-to-diameter ratio L/d.

A simple interpolation-based approach towards the development of an accurate phenomenological constitutive relation for isotropic hyperelastic materials

Soft materials such as rubber and hydrogels are commonly used in industry for their excellent hyperelastic behaviour. There are various types of constitutive models for soft materials, and phenomenological models are very popular for finite element method (FEM) simulations. However, it is not easy to construct a model that can precisely predict the complex behaviours of soft materials. In this paper, we suggest that the strain energy density functions should be expressed as functions of ordered principal stretches, which have more flexible expressions and are capable of matching various experimental curves. Moreover, the feasible region is small, and simple experiments, such as uniaxial tension/compression and hydrostatic tests, are on its boundaries. Therefore, strain energy density functions can be easily constructed by the interpolation of experimental curves, which does not need initial guessing in the form of the strain energy density function as most existing phenomenological models do. The proposed strain energy density functions are perfectly consistent with the available experimental curves for interpolation. It is interesting to find that for incompressible materials, a 3D constitutive relation can be obtained from single uniaxial stress–strain experimental curve (from compression to tension) via interpolation, which can predict other experimental curves reasonably well. To further improve the accuracy, additional experiments can be used in the interpolation.

Displacement field measurements in traditional and rotational diamond anvil cells

A digital image correlation-based method has been developed to measure the displacement field during compression in a traditional diamond anvil cell (DAC) and torsion in rotational DAC (RDAC) employing ruby fluorescence microscopy imaging. The optical arrangements for these measurements are adaptable at any commercial or customized micro-confocal system used for in situ high-pressure Raman or ruby fluorescence spectroscopy. In this paper, we describe details of the setup developed at Iowa State University along with a few demonstrative measurements for a zirconium sample. In particular, under compression in DAC, no adhesion zone is found, and relative sliding increases almost linearly along the radius. During torsion in RDAC, actual angular displacement of the material is found to be 5 times smaller than the rotation angle of an anvil, which is routinely used in the definition of the plastic shear for the determination of stress–strain curves and plastic strain-induced kinetics of phase transformations and grain refinement in materials. Obtained displacements can be used as the boundary conditions for finite element method (FEM) simulations of processes in DAC and RDAC instead of hypothetical friction conditions. After iterative fitting of FEM simulations and all measured fields from x-ray diffraction and absorption experiments, this will allow us to more precisely determine contact friction conditions and material parameters in the constitutive equations for elastoplastic flow and strain-induced phase transformations.

Relationship between shear strength and surface roughness of double-layered pipes by cold drawing

Abstract. Pipes applied to marine plants are used in deep-sea environments; therefore, they must be resistant to high pressure and corrosion. Because it is difficult to satisfy both of these factors in a single pipe, studies on a double-layered pipe are continuously being performed. An outer pipe should be made of carbon steel, with high pressure resistance, and an inner pipe should be made of stainless steel, with high corrosion resistance. A pipe formed by combining these two pipes is called a lined pipe. The shear strength of the lined pipe is an important factor because pipe cracking can occur due to stress concentration when two pipes are separated by bending or high pressure. Therefore, various processes have been applied to increase the shear strength. In this paper, we investigate the effect of the surface roughness of the bonding interface on the shear strength. Surface roughness is in units of micrometers, and it cannot be used for finite element method (FEM) analysis. Therefore, surface roughness should be converted into a friction coefficient to perform FEM analysis. The effect of surface roughness on shear strength was studied in the relationship between the results of pressure from FEM analysis and the shear strength test.

A plausible extension of standard penalty, streamline upwind and immersed boundary techniques to the improved element-free Galerkin-based solution of incompressible Navier–Stokes equations

The present work has been conducted in order to propose the extension of standard penalty and stabilization techniques to the improved element-free Galerkin (IEFG) method, for the numerical solution of incompressible fluid flow problems. In principle, the numerical procedures to be implemented in this communication have been conceived for finite element method (FEM)-based solutions, and these include the reduced integration penalty method (RIPM), the streamline upwind Petrov–Galerkin (SUPG) scheme, and a penalty-based immersed boundary method (PBIBM) for the imposition of essential boundary conditions along internal fluid–solid interfaces. The linear momentum balance and mass conservation equations have been coupled via the RIPM, in order to obtain a global weak formulation where the IEFG model is entirely developed in terms of improved moving least squares (IMLS) approximations of the velocity field. A detailed explanation concerning the appropriate extension of both the RIPM and SUPG procedures to the context of IEFG formulations, has also been provided. The resulting formulation has been applied to the solution of two well-known benchmark problems: i) Lid-driven square cavity flow, and ii) Flow past a fixed cylinder. Regarding the flow past a fixed cylinder benchmark problem, the fluid–solid interaction has been imposed as an internal immersed boundary condition via the PBIBM. The feasibility and reliability of implementing the RIPM, SUPG and PBIBM procedures in the IEFG formulation, have been proven by comparison with experimental and mesh-based numerical results reported in the literature. The results obtained in this study have revealed that a proper extension of the aforementioned penalty and stabilization techniques to the IEFG formulation, allows the achievement of accurate and stable numerical results during the solution of incompressible fluid-dynamics problems.

Performance of coir geotextile reinforced subgrade for low volume roads

Reinforcing flexible pavements using different types of geosynthetics is a technique that is widely used to increase the service life, reduce the maintenance costs and, guarantee high performance throughout the service life. This paper presents the insights from combined experimental and numerical analysis conducted on organic soil reinforced with coir geotextiles. A series of small-scale in-box plate load tests were performed to investigate the behavior of coir geotextile reinforced high plastic organic soil under circular loading. Tests were conducted on both homogeneous (sub grade alone) and layered configurations. Two types of commercially available woven coir geotextiles viz. H2M5 and H2M6, were utilized to study the contribution of coir geotextiles when used as reinforcement at the interface of sub-base and subgrade layers in enhancing the strength and stiffness of the low volume road. The primary objective of this exploratory study is to investigate the improvement in the performance of the low volume pavement as a result of the added geotextile reinforcement. The key performance parameters, namely, displacement, stress and strain responses of both reinforced and unreinforced pavement sections are obtained by analyzing the pavement using ABAQUS, which is a software suite for Finite Element Method (FEM) analysis. Test results indicate that the coir geotextile reinforcement substantially improved the performance of high plastic organic subgrade. A maximum reduction of 38% and 24% in vertical strain was observed on top of the subgrade in the case of H2M5 and H2M6 coir geotextile reinforced sections, respectively. Also, a maximum reduction of 30% and 18% in vertical displacement was observed in the case of H2M5 and H2M6 coir reinforced sections, respectively. At an average radial distance of about 1 m from the center of simulated static wheel load, very small displacement and strain value were observed for reinforced sections, relative to the unreinforced sections. Hence, the conclusion is drawn that the H2M5 type of coir geotextile contributes more than the H2M6 type to the structural performance improvement of pavements when used as reinforcement.

GPU-based matrix-free finite element solver exploiting symmetry of elemental matrices

Matrix-free solvers for finite element method (FEM) avoid assembly of elemental matrices and replace sparse matrix-vector multiplication required in iterative solution method by an element level dense matrix-vector product. In this paper, a novel matrix-free strategy for FEM is proposed which computes element level matrix-vector product by using only the symmetric part of the elemental matrices. The proposed strategy is developed to take advantage of the massive parallelism of Graphics Processing Unit (GPU). A unique data structure is also introduced which ensures localized and coalesced memory access suitable for a GPU while storing only the symmetric part of the elemental matrices. In addition, the proposed strategy emphasizes the efficient use of register cache, uniform workload distribution, reducing thread synchronization, and maintaining sufficient granularity to make the best use of GPU resources. The performance of the proposed strategy is evaluated by solving elasticity and heat conduction problems using 4-noded quadrilateral element with two degrees of freedom (DOFs) and one DOF per node, respectively. The performance is compared with the matrix-free solver strategies on GPU from the literature. It is found that a maximum speedup of 4.9 $$\times $$ is obtained for the elasticity problem and a maximum of 3.2 $$\times $$ speedup for the heat conduction problem. Further, the proposed strategy takes the least amount of GPU memory as compared to the existing strategies.