Showing papers on "Finite element method published in 2021"

Enhancement in Thermal Energy and Solute Particles Using Hybrid Nanoparticles by Engaging Activation Energy and Chemical Reaction over a Parabolic Surface via Finite Element Approach

Abstract: Several mechanisms in industrial use have significant applications in thermal transportation. The inclusion of hybrid nanoparticles in different mixtures has been studied extensively by researchers due to their wide applications. This report discusses the flow of Powell–Eyring fluid mixed with hybrid nanoparticles over a melting parabolic stretched surface. Flow rheology expressions have been derived under boundary layer theory. Afterwards, similarity transformation has been applied to convert PDEs into associated ODEs. These transformed ODEs have been solved the using finite element procedure (FEP) in the symbolic computational package MAPLE 18.0. The applicability and effectiveness of FEM are presented by addressing grid independent analysis. The reliability of FEM is presented by computing the surface drag force and heat transportation coefficient. The used methodology is highly effective and it can be easily implemented in MAPLE 18.0 for other highly nonlinear problems. It is observed that the thermal profile varies directly with the magnetic parameter, and the opposite trend is recorded for the Prandtl number.

Multi-Objective Design Optimization of an IPMSM Based on Multilevel Strategy

Abstract: The multiobjective optimization design of interior permanent magnet synchronous motors (IPMSMs) is a challenge due to the high dimension and huge computation cost of finite element analysis. This article presents a new multilevel optimization strategy for efficient multiobjective optimization of an IPMSM. To determine the multilevel optimization strategy, Pearson correlation coefficient analysis and cross-factor variance analysis techniques are employed to evaluate the correlations of design parameters and optimization objectives. A three-level optimization structure is obtained for the investigated IPMSM based on the analysis results, and different optimization parameters and objectives are assigned to different levels. To improve the optimization efficiency, the Kriging model is employed to approximate the finite element analysis for the multiobjective optimization in each level. It is found that the proposed method can provide optimal design schemes with a better performance, such as smaller torque ripple and lower power loss for the investigated IPMSM, while the needed computation cost is reduced significantly. Finally, experimental results based on a prototype are provided to validate the effectiveness of the proposed optimization method. The proposed method can be applied for the efficient multiobjective optimization of other electrical machines with high dimensions.

MFEM: a modular finite element methods library

Abstract: MFEM is an open-source, lightweight, flexible and scalable C++ library for modular finite element methods that features arbitrary high-order finite element meshes and spaces, support for a wide variety of discretization approaches and emphasis on usability, portability, and high-performance computing efficiency. MFEM’s goal is to provide application scientists with access to cutting-edge algorithms for high-order finite element meshing, discretizations and linear solvers, while enabling researchers to quickly and easily develop and test new algorithms in very general, fully unstructured, high-order, parallel and GPU-accelerated settings. In this paper we describe the underlying algorithms and finite element abstractions provided by MFEM, discuss the software implementation, and illustrate various applications of the library.

Computational Engineering - Introduction to Numerical Methods

Abstract: Modeling of Continuum Mechanical Problems.- Discretization of Problem Domain.- Finite-Volume Methods.- Finite-Element Methods.- Time Discretization.- Solution of Algebraic Systems of Equations.- Properties of Numerical Methods.- Finite-Element Methods in Structural Mechanics.- Finite-Volume Methods for Incompressible Flows.- Computation of Turbulent Flows.- Acceleration of Computations.

Optimization of hybrid nanoparticles with mixture fluid flow in an octagonal porous medium by effect of radiation and magnetic field

Abstract: Investigation of fluid behavior in a cavity enclosure has been a significant issue from the past in the field of fluid mechanics. In the present study, hydrothermal evaluation of hybrid nanofluid with a water–ethylene glycol (50–50%) as the base fluid which contains MoS2–TiO2 hybrid nanoparticles, in an octagon with an elliptical cavity in the middle of it, has been performed. In this problem, the effects of the radiation parameter, porosity, and the magnetic parameter have been analyzed on temperature distribution and fluid flow streamlines and also, on the local and average Nusselt numbers. The governing equations have been solved by the finite element method (FEM). As a novelty, the Taguchi method has been utilized for test design. Further, the response surface method (RSM) has been applied to achieving the optimum value of the involved parameters. The obtained results illustrate that with an augment in the Rayleigh number from 10 to 100, the average Nusselt number will improve by about 61.82%. Additionally, regarding the correlation, it is indeed transparent that the Rayleigh number has the most colossal contribution comparing other factors on the achieved equation, by about 61.88%.

Mechanically robust lattices inspired by deep-sea glass sponges.

Abstract: The predominantly deep-sea hexactinellid sponges are known for their ability to construct remarkably complex skeletons from amorphous hydrated silica. The skeletal system of one such species of sponge, Euplectella aspergillum, consists of a square-grid-like architecture overlaid with a double set of diagonal bracings, creating a chequerboard-like pattern of open and closed cells. Here, using a combination of finite element simulations and mechanical tests on 3D-printed specimens of different lattice geometries, we show that the sponge’s diagonal reinforcement strategy achieves the highest buckling resistance for a given amount of material. Furthermore, using an evolutionary optimization algorithm, we show that our sponge-inspired lattice geometry approaches the optimum material distribution for the design space considered. Our results demonstrate that lessons learned from the study of sponge skeletal systems can be exploited for the realization of square lattice geometries that are geometrically optimized to avoid global structural buckling, with implications for improved material use in modern infrastructural applications. Computational analysis and mechanical testing demonstrate that the skeletal system of a marine sponge has, through the course of evolution, achieved a near-optimal resistance to buckling.

Performance Assessment of Concrete and Steel Material Models in LS-DYNA for Enhanced Numerical Simulation, A State of the Art Review

Abstract: One of the biggest challenges associated with modelling the behaviour of reinforced concrete is the difficulty of incorporating realistic material models that can represent the observable behaviour of the physical system. Experiments for relevant loading rates and pressures reveal that steel and concrete exhibits a complicated nonlinear behavior that is difficult to capture in a single constitutive model. LS-DYNA provides several material models to simulate the structural behaviour of reinforced concrete. To provide some guidance in selecting the proper one for users who have limited experience on numerical simulation of steel and concrete, this paper reviews the background theory and evaluates performance of different material models to predicting the response of reinforced concrete structures to dynamic loads as well as advantageous and disadvantageous of models. Comparisons of several widely available concrete constitutive models are presented pertaining to their ability to reproduce basic laboratory data for concrete and steel as well as predict the response of structures subjected to shock and impact loadings. The performance of these models was assessed by comparison of finite element analysis model and experimental results of reinforced concrete structures to insure that the overall behaviour prediction is qualitatively acceptable, even if the exact parameter fit or material characterization is not available. The authors concluded that the accuracy of the finite element results relied on the selection of material model as well as the input parameter values. The material model assessment presented in this study can be used in the numerical simulation to generate appropriate models for concrete and steel.

Dynamics of Continuum and Soft Robots: A Strain Parameterization Based Approach

Abstract: In this article, we propose a new dynamic model of Cosserat beams in view of its application to continuum and soft robotics manipulation and locomotion. In contrast to usual approaches, it is based on the nonlinear parameterization of the beam shape by its strain fields and their reduction on a functional basis of strain modes. While remaining geometrically exact, the approach provides us with a minimal set of ordinary differential equations in the usual Lagrange matrix form that can be exploited for analysis and control design. Inspired from rigid robotics, the calculation of the matrices of this Lagrangian model is performed with a new reduced inverse Newton–Euler algorithm. To assess the approach, this Lagrangian model is compared against a well-validated finite element method through several benches of nonlinear structural statics and dynamics.

BISON: A Flexible Code for Advanced Simulation of the Performance of Multiple Nuclear Fuel Forms

Abstract: BISON is a nuclear fuel performance application built using the Multiphysics Object-Oriented Simulation Environment (MOOSE) finite element library. One of its major goals is to have a great amount ...

On the layerwise finite element formulation for static and free vibration analysis of functionally graded sandwich plates

Abstract: This paper presents a novel C0 higher-order layerwise finite element model for static and free vibration analysis of functionally graded materials (FGM) sandwich plates. The proposed layerwise model, which is developed for multilayer composite plates, supposes higher-order displacement field for the core and first-order displacement field for the face sheets maintaining a continuity of displacement at layer. Unlike the conventional layerwise models, the present one has an important feature that the number of variables is fixed and does not increase when increasing the number of layers. Thus, based on the suggested model, a computationally efficient C0 eight-node quadrilateral element is developed. Indeed, the new element is free of shear locking phenomenon without requiring any shear correction factors. Three common types of FGM plates, namely, (i) isotropic FGM plates; (ii) sandwich plates with FGM face sheets and homogeneous core and (iii) sandwich plates with homogeneous face sheets and FGM core, are considered in the present work. Material properties are assumed graded in the thickness direction according to a simple power law distribution in terms of the volume power laws of the constituents. The equations of motion of the FGM sandwich plate are obtained via the classical Hamilton’s principle. Numerical results of present model are compared with 2D, quasi-3D, and 3D analytical solutions and other predicted by advanced finite element models reported in the literature. The results indicate that the developed finite element model is promising in terms of accuracy and fast rate of convergence for both thin and thick FGM sandwich plates. Finally, it can be concluded that the proposed model is accurate and efficient in predicting the bending and free vibration responses of FGM sandwich plates.

Size-dependent vibration response of porous graded nanostructure with FEM and nonlocal continuum model

Abstract: In the present paper, a refined trigonometric higher-order shear deformation theory has been presented with the conjunction of nonlocal theory for the vibrational response of functionally graded (FG) porous nanoplate. The displacement field is chosen based on assumptions that the out of the plane displacement consists of bending and shear components whereas the transverse shear-strain has nonlinear variation along the thickness direction. The number of unknown variables is four, as against five in other renowned shear deformation theories. The governing equations have been derived using Hamilton's principle. A generalized porosity model has also been developed to accommodate both even and uneven type of distribution of porosity in the FG nanoplates. The closed-form solution of simply-supported FG porous nanoplates is obtained and the results are compared with the available reported results. In finite element solution, a C0 continuous isoparametric quadrilateral element has been used with various conventional and unconventional boundary conditions. The effects of various parameters like small-scale effect, aspect ratio, volume fraction index, porosity volume fraction, and thickness ratio have been investigated. The significant influence of small-scale effects and porosity inclusions have been observed in the reported results. It has been reported that both closed-form and finite element solutions with the present theory can make accurate predictions of the free vibration response.

Physics-Informed Deep Learning for Computational Elastodynamics without Labeled Data

Abstract: Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salie...

Nonlinear dynamic buckling of functionally graded porous beams

Abstract: This article studies nonlinear dynamic buckling of imperfect beams made of functionally graded (FG) metal foams subjected to a constant velocity with various boundary conditions. Four types of FG porosity patterns, including two symmetric porosity distributions, non-symmetric porosity distribution, and uniform porosity distribution, are considered. By introducing the first mode function as a trial function, the Galerkin method is utilized to transform the governing equations into ordinary differential equations, which were then solved by the fourth-order Runge–Kutta method. The proposed methods are validated by using finite element method (FEM) and finally a detailed parametric study is conducted.

NURBS hyper-surfaces for 3D topology optimization problems

Abstract: A general topology optimization strategy is presented in this study for three-dimensional applications. The approach is based on the combination of a well-established density-based method and the N...

Layerwise Theories of Laminated Composite Structures and Their Applications: A Review

Abstract: It is very challenging to accurately analyze the displacement and stress fields in the laminated composite structures due to the transverse anisotropy and higher transverse flexibilities. The equivalent single-layer theory (EST) is first developed to simplify this complex 3D problem to a pure 2D problem based on a displacement assumption in the thickness direction. The EST gives good results for the global responses of the very thin laminates with minimum computation cost, but poor results for the local responses at the interfaces and can not presents the zig-zag distribution of in-plane displacements. The elasticity solutions based on the 3D displacement-based finite element method (FEM) can present the accurate displacement and stress fields, but requires huge computational cost. As a quasi 3D method, the layerwise theories (LWT) is more accurate than most of the ESTs, and its computational cost is less than that of the 3D-based displacement FEMs, so it is attracting more and more attention with the rapid development of computer technology. This paper presents an overall review for the LWTs of the laminated composite structures and their applications. In general, there are two basic schemes employed to establish a LWT according to the construction of the displacements fields in the thickness direction. In the first scheme, the laminated composite structures are described as an assembly of individual layers, and these individual layers are combined by the interlaminar relationships to keep the displacement continuity and stress equilibrium. All of the individual layers are simulated by using the EST. In the second scheme, the displacement and/or stress fields along the thickness direction are constructed by a 1D interpolation functions and the in-plane displacement and/or stress fields are discretized by the 2D finite elements. The review in this paper is organized by the this classification.

The deal.II Library, Version 9.3

Abstract: This paper provides an overview of the new features of the finite element library deal.II, version 9.3.

DiSECt: A Differentiable Simulation Engine for Autonomous Robotic Cutting

Abstract: Robotic cutting of soft materials is critical for applications such as food processing, household automation, and surgical manipulation. As in other areas of robotics, simulators can facilitate controller verification, policy learning, and dataset generation. Moreover, differentiable simulators can enable gradient-based optimization, which is invaluable for calibrating simulation parameters and optimizing controllers. In this work, we present DiSECt: the first differentiable simulator for cutting soft materials. The simulator augments the finite element method (FEM) with a continuous contact model based on signed distance fields (SDF), as well as a continuous damage model that inserts springs on opposite sides of the cutting plane and allows them to weaken until zero stiffness, enabling crack formation. Through various experiments, we evaluate the performance of the simulator. We first show that the simulator can be calibrated to match resultant forces and deformation fields from a state-of-the-art commercial solver and real-world cutting datasets, with generality across cutting velocities and object instances. We then show that Bayesian inference can be performed efficiently by leveraging the differentiability of the simulator, estimating posteriors over hundreds of parameters in a fraction of the time of derivative-free methods. Finally, we illustrate that control parameters in the simulation can be optimized to minimize cutting forces via lateral slicing motions. We publish videos and additional results on our project website at https://diff-cutting-sim.github.io.