Showing papers on "Finite element method published in 2019"

Numerical Solution of Convection-Diffusion Problems

Abstract: Introduction and overview Selected results from mathematical analysis Difference schemes for steady problems Finite element methods Galerkin schemes Petrov-Galerkin methods Finite volume methods for steady problems Unsteady problems References

Finite Element Methods for Maxwell's Equations

Abstract: We survey finite element methods for approximating the time harmonic Maxwell equations. We concentrate on comparing error estimates for problems with spatially varying coefficients. For the conforming edge finite element methods, such estimates allow, at least, piecewise smooth coefficients. But for Discontinuous Galerkin (DG) methods, the state of the art of error analysis is less advanced (we consider three DG families of methods: Interior Penalty type, Hybridizable DG, and Trefftz type methods). Nevertheless, DG methods offer significant potential advantages compared to conforming methods.

Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions

Abstract: In this research, the nonlinear static, buckling and vibration analysis of viscoelastic micro-composite beam reinforced by various distributions of boron nitrid nanotube (BNNT) with initial geometrical imperfection by modified strain gradient theory (MSGT) using finite element method (FEM) are presented. The various distributions of BNNT are considered as UD, FG-V and FG-X and also, the extended rule of mixture is used to estimate the properties of micro-composite beam. The components of stress are dependent to mechanical, electrical and thermal terms and calculated using piezoelasticity theory. Then, the kinematic equations of micro-composite beam using the displacement fields are obtained. The governing equations of motion are derived using energy method and Hamilton\'s principle based on MSGT. Then, using FEM, these equations are solved. Finally the effects of different parameters such as initial geometrical imperfection, various distributions of nanotube, damping coefficient, piezoelectric constant, slenderness ratio, Winkler spring constant, Pasternak shear constant, various boundary conditions and three material length scale parameters on the behavior of nonlinear static, buckling and vibration of micro-composite beam are investigated. The results indicate that with an increase in the geometrical imperfection parameter, the stiffness of micro-composite beam increases and thus the non-dimensional nonlinear frequency of the micro structure reduces gradually.

Physics-informed neural networks for inverse problems in nano-optics and metamaterials

Abstract: In this paper we employ the emerging paradigm of physics-informed neural networks (PINNs) for the solution of representative inverse scattering problems in photonic metamaterials and nano-optics technologies. In particular, we successfully apply mesh-free PINNs to the difficult task of retrieving the effective permittivity parameters of a number of finite-size scattering systems that involve many interacting nanostructures as well as multi-component nanoparticles. Our methodology is fully validated by numerical simulations based on the Finite Element Method (FEM). The development of physics-informed deep learning techniques for inverse scattering can enable the design of novel functional nanostructures and significantly broaden the design space of metamaterials by naturally accounting for radiation and finite-size effects beyond the limitations of traditional effective medium theories.

A Rotation-Free Wireless Power Transfer System With Stable Output Power and Efficiency for Autonomous Underwater Vehicles

Abstract: This letter proposes a rotation-free wireless power transfer system based on a new coil structure to achieve stable output power and efficiency against rotational misalignments for charging autonomous underwater vehicles. The new coil structure has two decoupled receivers composed of two reversely wound receiver coils and the magnetic flux directions of the two receivers are perpendicular to each other, guaranteeing a relatively constant total mutual inductance and a decoupled characteristic under rotational misalignments. The proposed coil structure is verified via finite element analysis based on ANSYS Maxwell. A rotation-free LCC–LCC compensated WPT prototype is built and the experimental results verify the theoretical analysis and simulations. The system can deliver 664 W with a dc–dc efficiency of 92.26% under the best case and 485 W with a 92.10% dc–dc efficiency under the worst case.

A Geometrically Exact Model for Soft Continuum Robots: The Finite Element Deformation Space Formulation.

Abstract: Mathematical modeling of soft robots is complicated by the description of the continuously deformable three-dimensional shape that they assume when subjected to external loads. In this article we present the deformation space formulation for soft robots dynamics, developed using a finite element approach. Starting from the Cosserat rod theory formulated on a Lie group, we derive a discrete model using a helicoidal shape function for the spatial discretization and a geometric scheme for the time integration of the robot shape configuration. The main motivation behind this work is the derivation of accurate and computational efficient models for soft robots. The model takes into account bending, torsion, shear, and axial deformations due to general external loading conditions. It is validated through analytic and experimental benchmark. The results demonstrate that the model matches experimental positions with errors <1% of the robot length. The computer implementation of the model results in SimSOFT, a dynamic simulation environment for design, analysis, and control of soft robots.

Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensions

Abstract: An initial-boundary value problem with a Caputo time derivative of fractional order $\alpha\in(0,1)$ is considered, solutions of which typically exhibit a singular behaviour at an initial time. For this problem, we give a simple framework for the analysis of the error of L1-type discretizations on graded and uniform temporal meshes in the $L_\infty$ and $L_2$ norms. This framework is employed in the analysis of both finite difference and finite element spatial discretiztions. Our theoretical findings are illustrated by numerical experiments.

Vibration analysis of functionally graded porous cylindrical shell with arbitrary boundary restraints by using a semi analytical method

Abstract: The main purpose of this paper is to provide a new semi analytical method to analyze the free vibration of functionally graded porous (FGP) cylindrical shell with arbitrary boundary restraints. According to the distributions of porous along thickness direction of the structure, two typical types of symmetric and non-symmetric porosity distributions are performed in this paper. The formulations are established on the basis of energy method and first-order shear deformation theory (FSDT). The displacement functions are expressed by unified Jacobi polynomials and Fourier series. The arbitrary boundary restraints are realized by penalty method. The final solutions of FGP cylindrical shell structure are obtained by Rayleigh–Ritz method. To sufficient illustrate the effectiveness of proposed method, some numerical examples about spring stiffness, Jacobi parameters etc. are carried out. In addition, to verify the accuracy of this method, the results are compared with those obtained by FEM, experiment and published literature. The results show that the proposed method has ability to solve the free vibration behaviors of FGP cylindrical shell.

Review of the AC Loss Computation for HTS using the H-formulation.

Abstract: This article presents a review of the finite element method (FEM) model based on the $H$ formulation of Maxwell's equations used to calculate AC losses in high temperature superconductor (HTS) tapes, cables and windings for different applications. This model, which uses the components of the magnetic field as state variables, has been gaining a great popularity and has been in use in tens of research groups around the world. This contribution first reviews the equations on which the model is based and their implementation in finite element method programs for different cases, such 2D longitudinal and axis-symmetric geometries, 3D geometries. Modeling strategies to tackle large number of HTS tapes, such as multi-scale and homogenization methods, are also introduced. Then, the second part of the article reviews the applications for which the $H$ formulations has been used to calculate AC losses, ranging from individual tapes, to complex cables and large magnet windings. Afterwards, a section is dedicated to the discussion of the $H$ formulation in terms of computational efficiency and easiness of implementation. Its pros and cons are listed. Finally, the last section draws the main conclusions.

3D Printing of Ultralight Biomimetic Hierarchical Graphene Materials with Exceptional Stiffness and Resilience.

Abstract: Biological materials with hierarchical architectures (e.g., a macroscopic hollow structure and a microscopic cellular structure) offer unique inspiration for designing and manufacturing advanced biomimetic materials with outstanding mechanical performance and low density. Most conventional biomimetic materials only benefit from bioinspired architecture at a single length scale (e.g., microscopic material structure), which largely limits the mechanical performance of the resulting materials. There exists great potential to maxime the mechanical performance of biomimetic materials by leveraging a bioinspired hierarchical structure. An ink-based three-dimensional (3D) printing strategy to manufacture an ultralight biomimetic hierarchical graphene material (BHGMs) with exceptionally high stiffness and resilience is demonstrated. By simultaneously engineering 3D-printed macroscopic hollow structures and constructing an ice-crystal-induced cellular microstructure, BHGMs can achieve ultrahigh elasticity and stability at compressive strains up to 95%. Multiscale finite element analyses indicate that the hierarchical structures of BHGMs effectively reduce the macroscopic strain and transform the microscopic compressive deformation into the rotation and bending of the interconnected graphene flakes. This 3D printing strategy demonstrates the great potential that exists for the assembly of other functional materials into hierarchical cellular structures for various applications where high stiffness and resilience at low density are simultaneously required.

Experimental and numerical investigation into the behaviour of face-to-face built-up cold-formed steel channel sections under compression

Abstract: Face-to-face built-up cold-formed steel channel sections are becoming increasingly popular for column members in cold-formed steel structures; its applications include cold-formed steel trusses, space frames and portal frames. In such an arrangement, the independent buckling of the members is resisted by intermediate fasteners. In the literature, no research is available for such face-to-face built-up cold-formed steel columns. The issue is addressed herein. This paper presents the results of 36 experimental tests, conducted on face-to-face built-up cold-formed steel channel-sections covering a wide range of slenderness from stub to slender columns. A nonlinear finite element model is then described that shows good agreement with the experimental results. The finite element model includes material non-linearity, initial imperfections and modelling of intermediate fasteners. Both finite element and experimental results are compared against the design strengths calculated in accordance with the American Iron and Steel Institute (AISI), Australian and New Zealand Standards (AS/NZS) and Eurocode (EN 1993-1-3). The verified finite element model is used for the purposes of a parametric study comprising 90 models. The effect of fastener spacing on the axial strength was investigated. From the results of experiments and finite element investigations, it is shown that the design in accordance with the AISI & AS/NZS and Eurocode (EN 1993-1-3) is generally conservative by around 15%, however, AISI & AS/NZS and Eurocode (EN 1993-1-3) can be un-conservative by 8% on average for face-to-face built-up columns failed through local buckling.

Empirical methodology to determine inherent strains in additive manufacturing

Abstract: Part distortion is a critical issue during Additive Manufacturing (AM) of metallic parts since it prevents this technology from being implemented at industrial level. To this regard, distortion prediction even from design stage has become crucial. Actually, numerical modelling methodologies play an important role here. Different modelling approaches have been developed but one of the most computationally efficient methodology to predict distortion is the so called inherent strain method. In this work an empirical methodology to determine inherent strains is presented. This is the input data in simplified Finite Element (FE) models in order to predict distortion and residual stress fields. These inherent strains are calculated considering layer lumping strategies that might be adopted in the numerical model as well. The procedure has been developed and validated using the well-known twin-cantilever beam structure. Ti-6Al-4V beams have been manufactured by LPBF technology following different scanning strategies. Distortion after support removal has been measured in order to be compared against numerical results. The methodology has been applied at coupon level giving accurate results and providing a preliminary validation.

Geometrically Exact Finite Element Formulations for Slender Beams: Kirchhoff–Love Theory Versus Simo–Reissner Theory

Abstract: The present work focuses on geometrically exact finite elements for highly slender beams. It aims at the proposal of novel formulations of Kirchhoff–Love type, a detailed review of existing formulations of Kirchhoff–Love and Simo–Reissner type as well as a careful evaluation and comparison of the proposed and existing formulations. Two different rotation interpolation schemes with strong or weak Kirchhoff constraint enforcement, respectively, as well as two different choices of nodal triad parametrizations in terms of rotation or tangent vectors are proposed. The combination of these schemes leads to four novel finite element variants, all of them based on a $$C^1$$ -continuous Hermite interpolation of the beam centerline. Essential requirements such as representability of general 3D, large deformation, dynamic problems involving slender beams with arbitrary initial curvatures and anisotropic cross-section shapes, preservation of objectivity and path-independence, consistent convergence orders, avoidance of locking effects as well as conservation of energy and momentum by the employed spatial discretization schemes, but also a range of practically relevant secondary aspects will be investigated analytically and verified numerically for the different formulations. It will be shown that the geometrically exact Kirchhoff–Love beam elements proposed in this work are the first ones of this type that fulfill all these essential requirements. On the contrary, Simo–Reissner type formulations fulfilling these requirements can be found in the literature very well. However, it will be argued that the shear-free Kirchhoff–Love formulations can provide considerable numerical advantages such as lower spatial discretization error levels, improved performance of time integration schemes as well as linear and nonlinear solvers and smooth geometry representation as compared to shear-deformable Simo–Reissner formulations when applied to highly slender beams. Concretely, several representative numerical test cases confirm that the proposed Kirchhoff–Love formulations exhibit a lower discretization error level as well as a considerably improved nonlinear solver performance in the range of high beam slenderness ratios as compared to two representative Simo–Reissner element formulations from the literature.

Real-time simulation of large-scale HTS systems: multi-scale and homogeneous models using the T-A formulation

Abstract: The emergence of second-generation high temperature superconducting (HTS) tapes has favored the development of large-scale superconductor systems. The mathematical models capable of estimating electromagnetic quantities in superconductors have evolved from simple analytical models to complex numerical models. The available analytical models are limited to the analysis of single wires or infinite arrays that, in general, do not represent actual devices in real applications. The numerical models based on the finite element method using the H formulation of Maxwell's equations are useful for the analysis of medium-size systems, but their application in large-scale systems is problematic due to the excessive computational cost in terms of memory and computation time. Therefore it is necessary to devise new strategies to make the computation more efficient. The homogenization and the multi-scale methods have successfully simplified the description of the systems allowing the study of large-scale systems. Also, efficient calculations have been recently achieved using the T–A formulation. In the present work, we propose a series of adaptations to the multi-scale and homogenization methods so that they can be efficiently used in conjunction with the T–A formulation to compute the distribution of current density and hysteresis losses in the superconducting layer of superconducting tapes. The computation time and the amount of memory are substantially reduced up to a point that it is possible to achieve real-time simulations of large-scale HTS systems under slow ramping cycles of practical importance on personal computers.

RETRACTED ARTICLE: Analysis of influential factors forpredicting the shear strength of a V-shaped angle shear connector in composite beamsusing an adaptive neuro-fuzzy technique

Abstract: The V-shaped angle shear connector is recognized as to expand certain mechanical properties to the shear connectors, contains adequate ductility, elevate resistance, power degradation resistance under cyclic charging, and high shear transmission, more economical than other shear connectors, for instance, the L-shaped and C-shaped shear connectors. The performance of this shear connector had been investigated by previous researchers (Shariati et al. in Mater Struct 49(9):1–18, 2015), but the strength prediction was not clearly explained. In this investigation, the shear strength prediction of this connector was analyzed based on several factors. The ultimate purpose was to investigate the variations of different factors that were affecting the shear strength of this connector. To achieve this aim, the data (concrete compression strength, thickness, length, height, slope of inclination, and shear strength) were collected from the parametric studies using finite element analysis results for this purpose were input using the ANFIS method (neuro-fuzzy inference system). The finite element analysis results were verified by experimental test results. All variables from the predominant factors that were affected the shear strength of the shear connector (V-shaped angle) were also selected by using the ANFIS process. The results exhibited that the proposed shear connector (V-shaped angle) contained the potentiality to be used practically after several improvements. One option might be the improvement of the testing process for different predictive models with more input variables that will improve the predictive power of the created models.

Structural failure during extrusion-based 3D printing processes

Abstract: This contribution studies failure by elastic buckling and plastic collapse of wall structures during extrusion-based 3D printing processes. Results obtained from the parametric 3D printing model recently developed by Suiker (Int J Mech Sci, 137: 145–170, 2018), among which closed-form expressions useful for engineering practice, are validated against results of dedicated FEM simulations and 3D concrete printing experiments. In the comparison with the FEM simulations, various types of wall structures are considered, which are subjected to linear and exponentially decaying curing processes at different curing rates. For almost all cases considered, the critical wall buckling length computed by the parametric model turns out to be in excellent agreement with the result from the FEM simulations. Some differences may occur for the particular case of a straight wall clamped along its vertical edges and subjected to a relatively high curing rate, which can be ascribed to the approximate form of the horizontal buckling shape used in the parametric model. The buckling responses computed by the two models for a wall structure with imperfections of different wavelengths under increasing deflection correctly approaches the corresponding bifurcation buckling length. Further, under a specific change of the material properties, the parametric model and the FEM model predict a similar transition in failure mechanism, from elastic buckling to plastic collapse. The experimental validation of the parametric model is directed towards walls manufactured by 3D concrete printing, whereby the effect of the material curing rate on the failure behaviour of the wall is explored by studying walls of various widths. At a relatively low curing rate, the experimental buckling load is well described when the parametric model uses a linear curing function. However, the experimental results suggest the extension of the linear curing function with a quadratic term if the curing process under a relatively long printing time is accelerated by thermal heating of the 3D printing facility. In conclusion, the present validation study confirms that the parametric model provides a useful research and design tool for the prediction of structural failure during extrusion-based 3D printing. The model can be applied to quickly and systematically explore the influence of the individual printing process parameters on the failure response of 3D-printed walls, which can be translated to directives regarding the optimisation of material usage and printing time.

Motion equation for a flexible one-dimensional element used in the dynamical analysis of a multibody system

Abstract: In this study, the motion equations of a one-dimensional finite element having a general three-dimensional motion together the body are established, using the Lagrange’s equations. The problem is important in technical applications of the last decades, characterized by high velocities and high applied loads. This leads to qualitative different mechanical phenomena (high deformations, resonance, stability), mainly due to the Coriolis effects and relative motions.