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The prediction of crack propagation is an important engineering problem. In this work, combined with triangular plane stress finite elements, a new remeshing algorithm for crack opening problems was developed. The proposed algorithm extends the crack iteratively until a threshold maximum crack length is achieved. The crack propagation direction is calculated using the maximum tangential stress criterion. In this calculation, in order to smoothen the stress field in the vicinity of the crack tip, a weighted average of the stresses of the integration points around the crack tip is considered. The algorithm also ensures that there are always at least eight elements and nine nodes surrounding the crack tip, unless the crack tip is close to a domain boundary, in which case there can be fewer elements and nodes around the crack tip.
Four benchmark tests were performed showing that this algorithm leads to accurate crack paths when compared to findings from previous research works, as long as the initial mesh is not too coarse. This algorithm also leads to regular meshes during the propagation process, with very few distorted elements, which is generally one of the main problems when calculating crack propagation with the finite element method.
For electronic packaging structure, there are many design parameters that will affect its reliability performance, using experimental way to obtain the reliability result will take a considerable amount of time. Therefore, how to shorten the design time becomes a critical issue for new electronic packaging structure development. This research will combine artificial intelligence (AI) and simulation technology to assess the long-term reliability of wafer level packaging (WLP). A simulation technology using finite element method (FEM) with appropriate mechanics theories has been validated by multiple experiments will replace the experiment to create reliability results for different WLP structures. After a big WLP structure-reliability database created, this study will apply artificial neural network (ANN) theory to analyze this database and obtains a regression model for structure-reliability relationship of WLP. Once the regression model is established and validated, the WLP geometry, such as pad size, die and buffer layer thickness, and solder volume, etc. can be simply entered, and then the WLP reliability results can be immediately obtained through the ANN regression model.
This paper presents a GPU-accelerated implementation of the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) method with an inexact nullspace filtering approach to find eigenvalues in electromagnetics analysis with higher-order FEM. The performance of the proposed approach is verified using the Kepler (Tesla K40c) graphics accelerator, and is compared to the performance of the implementation based on functions from the Intel MKL on the Intel Xeon (E5-2680 v3, 12 threads) central processing unit (CPU) executed in parallel mode. Compared to the CPU reference implementation based on the Intel MKL functions, the proposed GPU-based LOBPCG method with inexact nullspace filtering allowed us to achieve up to 2.9-fold acceleration.
This paper systematically compares the numerical implementation and computational cost between the Fourier spectral iterative perturbation method (FSIPM) and the finite element method (FEM) in solving partial differential equilibrium equations with inhomogeneous material coefficients and eigen-fields (e.g., stress-free strain and spontaneous electric polarization) involved in phase-field models. Four benchmark numerical examples, including inhomogeneous elastic, electrostatic, and steady-state heat conduction problems demonstrate that (1) the FSIPM rigorously requires uniform hexahedral (3D) and quadrilateral (2D) mesh and periodic boundary conditions for numerical implementation while the FEM permits arbitrary mesh and boundary conditions; (2) the FSIPM solutions are comparable to their FEM counterparts, and both of them agree with the analytic solutions, (3) the FSIPM is much faster in solving equilibrium equations than the FEM to achieve the accurate solutions, thus exhibiting a greater potential for large-scale 3D computations.
In this paper, the problem of magnetohydrodynamics (MHD) boundary layer flow of nanofluid with heat and mass transfer through a porous media in the presence of thermal radiation, viscous dissipation and chemical reaction is studied. Three types of nanofluids, namely Copper (Cu)-water, Alumina (Al2O3)-water and Titanium Oxide (TiO2)-water are considered. The governing set of partial differential equations of the problem is reduced into the coupled nonlinear system of ordinary differential equations (ODEs) by means of similarity transformations. Finite element solution of the resulting system of nonlinear differential equations is obtained using continuous Galerkin-Petrov discretization together with the well-known shooting technique. The obtained results are validated using MATLAB “bvp4c” function and with the existing results in the literature. Numerical results for the dimensionless velocity, temperature and concentration profiles are obtained and the impact of various physical parameters such as the magnetic parameter M, solid volume fraction of nanoparticles 𝜙 and type of nanofluid on the flow is discussed. The results obtained in this study confirm the idea that the finite element method (FEM) is a powerful mathematical technique which can be applied to a large class of linear and nonlinear problems arising in different fields of science and engineering.
The purpose of this paper is to propose a critical assessment of Young’s modulus determination of coated materials using Impulse Excitation Technique (IET). In this technique, the coated substrate is excited by an impulse and the acoustic vibrations are recorded. The frequency of the first bending mode is then used in a mechanical model to obtain the Young’s modulus of the coating. The existing models are based on two different theories: the flexural rigidity of a composite beam and the Classical Laminated Beam Theory (CLBT). The aim of the present paper is to assess the accuracy (trueness and precision) of the technique. For this, different models proposed in the literature are compared with a finite element model of the specimen for various conditions. The trueness and precision of models were evaluated and the best model was identified. Then a detailed uncertainty budget is performed to identify and quantify the most influent factors on the global uncertainty.
We develop a two-dimensional thermo-mechanical numerical model in which the formation of oceanic crust and serpentinite due to the hydration of the uprising mantle peridotite has been implemented, with the aim of discussing the behaviour of the lithosphere of the Alps and Northern Apennines during the transition from continental rifting to ocean spreading of the Alpine Tethys. The predictions of the model are compared with natural data related to the Permian–Triassic high-temperature – low-pressure (HT-LP) metamorphism affecting the continental lithosphere and data from the Jurassic P–T evolution of the oceanic lithosphere from the Alps and the Northern Apennines. Our analysis indicates that a thinned continental crust, an ocean–continent transition zone and an oceanic lithosphere characterize the final structure of the system in a poor magma rift pre-Alpine configuration. We also find that mantle serpentinization starts before crustal break-up and that denudation occurs before ocean spreading. The mantle denudation starts several million years before the gabbros/basalt formation, generating an ocean–continent transition zone from the passive continental margin to the oceanic lithosphere of size 160–280 km. The comparative analysis shows that the extension of a hot and weak lithosphere, which promotes the development of hyperextended Alpine margins, better agrees with the natural data. Finally, our comparative analysis supports the hypothesis that the lithospheric extension preceding the opening of the Alpine Tethys did not start in a stable continental lithosphere, but developed by recycling part of the old Variscan collisional suture.
The aerodynamic and structural design of a pitching blade tip with a double-swept planform is presented. The authors demonstrate how high-fidelity finite element (FE) and computational fluid dynamic (CFD) simulations are successfully used in the design phase. Eigenfrequencies, deformation, and stress distributions are evaluated by means of a three-dimensional (3D) FE model. Unsteady Reynolds-averaged Navier-Stokes (RANS) simulations are compared to experimental data for a light dynamic stall case at Ma = 0.5, Re = 1.2 × 106. The results show a very good agreement as long as the flow stays attached. Tendencies for the span-wise location of separation are captured. As soon as separation sets in, discrepancies between experimental and numerical data are observed. The experimental data show that for light dynamic stall cases at Ma = 0.5, a factor of safety of FoS = 2.0 is sufficient if the presented simulation methods are used.
In this paper, a nonconforming mixed finite element method (FEM) is presented to approximate time-dependent Maxwell's equations in a three-dimensional bounded domain with absorbing boundary conditions (ABC). By employing traditional variational formula, instead of adding penalty terms, we show that the discrete scheme is robust. Meanwhile, with the help of the element's typical properties and derivative transfer skills, the convergence analysis and error estimates for semidiscrete and backward Euler fully-discrete schemes are given, respectively. Numerical tests show the validity of the proposed method.
In this paper, numerical study was systematically conducted to analyze the shear banding evolution in bulk metallic glasses (BMGs) with various notches subjected to the uniaxial compression, and the relation between the notched configurations and compressive malleability was therefore elucidated. Free volume was used to be an internal state variable to depict the shear banding nucleation, growth and coalescence in the BMGs with the aid of free volume theory, which was incorporated into ABAQUS finite element method code as a user material subroutine. The present numerical procedure was firstly verified by comparing with the existing experimental data, and then parameter analysis was performed to discuss the impacts of notch shape, notch size, notch orientation, and notch configuration on the plastic deformability of notched samples. The present modeling will shed some light on the failure mechanisms and the toughening design of notched BMG structures in the engineering applications.
This paper proposes a method for determining the mechanical properties (Young's modulus, Poisson's ratio, yield strength, and work hardening factor) of a material at a specific point using an indentation technique that utilizes a specially designed indenter in conjunction with an inverse problem and finite element analyses. The specially designed indenter combines the characteristics of spherical and conical indenters and can be used to produce multiple indentations at a single point. The feasibility of the proposed method for determining the local mechanical properties of a material was confirmed by detailed precision verifications in the ideal case and the worst case.
In this paper, a new algorithm is developed based on the homogenization method integrating with the newly developed Hybrid Treffe FEM (HT-FEM) and Hybrid Fundamental Solution based FEM (HFS-FEM). The algorithm can be used to evaluate effective elastic properties of heterogeneous composites. The representative volume element (RVE) of fiber reinforced composites with periodic boundary conditions is introduced and used in our numerical analysis. The proposed algorithm is assessed through two numerical examples with different mesh density and element geometry and used to investigate the effect of fiber volume fraction, fiber shape and configuration on the effective properties of composites. It is found that the proposed algorithm is insensitive to element geometry and mesh density compared with the traditional FEM (e.g. ABAQUS). The numerical results indicate that the HT-FEM and HFS-FEM are promising in micromechanical modeling of heterogeneous materials containing inclusions of various shapes and distributions. They are potential to be used for future application in multiscale simulation.
This paper concentrates on theoretical and experimental nonlinear stiffness study of milling machine tool spindle angle contact ball bearing. The theoretical study allows us to build an analytical model to define nonlinear stiffness of angle contact ball bearings based on geometrical and physical parameters. Modifications were done on literature's models (e.g. Balls deformations) having positives impacts on conformity of models to experimental results.
FEM model using ANSYS is constructed to analyze the different parameters affecting the nonlinear stiffness of ball bearing. Among those parameters are physical including the geometry, friction coefficient and the boundary conditions of the model and Numerical parameters such as mesh density and penetration.
Experimental tests were done on the spindle ball bearing 7014, to measure the rigidity. Universal tensile testing machine is used to achieve load displacement curves. The developed theoretical model, constructed finite element model and experimental results showed good conformity.
L’objectif principal de cet article est la mise au point d’une méthodologie numérique de
prévision du comportement local d’un procédé de renforcement des poteaux en bois par la
fibre de carbone. En particulier, on s’intéresse à l’étude du comportement
élasto-plastique du matériau bois avec effet du renforcement. Une modélisation basée sur
la thermodynamique des processus irréversibles avec variables d’état est utilisée pour
traduire le couplage entre le comportement plastique à écrouissage isotrope et l’effet du
renforcement. Les aspects théoriques et numériques de cette formulation sont décrits en
détail. La résolution du problème d’équilibre global est assurée par un schéma Dynamique
Explicite. La validation de la procédure de calcul implémentée dans ABAQUS/Explicit est
faite sur la simulation d’un essai de compression des éprouvettes circulaires en bois
renforcées par la fibre de carbone. Les résultats des simulations sont confrontés à ceux
We consider the symmetric FEM-BEM coupling for the numerical solution of a (nonlinear)
interface problem for the 2D Laplacian. We introduce some new a posteriori
error estimators based on the (h − h/2)-error
estimation strategy. In particular, these include the approximation error for the boundary
data, which allows to work with discrete boundary integral operators only. Using the
concept of estimator reduction, we prove that the proposed adaptive algorithm is
convergent in the sense that it drives the underlying error estimator to zero. Numerical
experiments underline the reliability and efficiency of the considered adaptive
Flexible discretization techniques for the approximative solution of coupled wave propagation problems are investigated. In particular, the advantages of using non-matching grids are presented, when one subregion has to be resolved by a substantially finer grid than the other subregion. We present the non-matching grid technique for the case of a mechanical-acoustic coupled as well as for acoustic-acoustic coupled systems. For the first case, the problem formulation remains essentially the same as for the matching situation, while for the acoustic-acoustic coupling, the formulation is enhanced with Lagrange multipliers within the framework of Mortar Finite Element Methods. The applications will clearly demonstrate the superiority of the Mortar Finite Element Method over the standard Finite Element Method both concerning the flexibility for the mesh generation as well as the computational time.
This paper presents a ductile damage-gradient based nonlocal and fully coupled
elastoplastic constitutive equations by adding a Helmholtz equation to regularize the
initial and boundary value problem (IBVP) exhibiting some damage induced softening. First,
a thermodynamically-consistent formulation of gradient-regularized plasticity fully
coupled with isotropic ductile damage and accounting for mixed non linear isotropic and
kinematic hardening is presented. For the sake of simplicity, only a simplified version of
this model based on von Mises isotropic yield function and accounting for the single
nonlinear isotropic hardening is studied and implemented numerically using an in house FE
code. An additional partial differential equation governing the evolution of the nonlocal
isotropic damage is added to the equilibrium equations and the associated weak forms
derived to define the IBVP (initial and boundary value problem). After the time and space
discretization, two algebraic equations: one highly nonlinear associated with the
equilibrium equation and the second purely linear associated with the damage non locality
equation are obtained. Over a typical load increment, the first equation is solved
iteratively thanks to the Newton-Raphson scheme and the second equation is solved directly
to compute the nonlocal damage
D̅ at each node. All the constitutive equations are “strongly” affected by
this nonlocal damage variable transferred to each integration point. Some applications
show the ability of the proposed approach to obtain a mesh independent solution for a
fixed value of the length scale parameter. Comparisons between fully local and nonlocal
solutions are given.
We are concerned with a model of ionic polymer-metal composite (IPMC) materials that consists of a coupled system of the Poisson and Nernst-Planck equations, discretized by means of the finite element method (FEM). We show that due to the transient character of the problem it is efficient to use adaptive algorithms that are capable of changing the mesh dynamically in time. We also show that due to large qualitative and quantitative differences between the two solution components, it is efficient to approximate them on different meshes using a novel adaptive multimesh hp-FEM. The study is accompanied with numerous computations and comparisons of the adaptive multimesh hp-FEM with several other adaptive FEM algorithms.
Transient temperature field of laminated plate which considering radiation is analyzed by laying temperature lines in every layer in this paper. Finite element equations are established by using high-order displacement field which considering shear effect based on the temperature analysis. Then thermally induced vibration of laminated plate is investigated by solving the finite element equation with numerical method. Compared with numerical results of ANSYS by using 3-D coupled element (SOLID5), the methods presented in this paper have a satisfied precision and better efficiency. It can give reference to the thermally induced vibration analysis of thin-large flexible laminated appendages of spacecraft.
As 3D scanners and numerical simulation are now mature, we have made a benchmark by comparing simulation results with real forged parts. We did consider the complete forging process of a cylindrical part using hammer from the billet to the final part. This process has been simulated using a thermo-elasto-viscoplastic constitutive equation including the ductile damage with the implemented with the help of VUMAT subroutine provided by ABAQUS software. Before and after each step, the forged part is scanned and compared with the result of the FEM simulation in order to tune some of the process numerical simulation parameters.