scholarly journals On the choice of finite element for applications in geodynamics

2021 ◽  
Author(s):  
Cedric Thieulot ◽  
Wolfgang Bangerth
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Mantle Convection ◽  
Computational Cost ◽  
Great Difficulty ◽  
Convection Flow ◽  
Slow Viscous Flow ◽  
The Past ◽  
Buoyancy Driven Flows ◽  
First Time

Abstract. Geodynamical simulations over the past decades have widely been built on quadrilateral and hexahedral finite elements. For the discretisation of the key Stokes equation describing slow, viscous flow, most codes use either the unstable Q1 × P0 element, a stabilised version of the equal-order Q1 × Q1 element, or more recently the stable Taylor-Hood element with continuous (Q2 × Q1) or discontinuous (Q2 × P−1) pressure. However, it is not clear which of these choices is actually the best at accurately simulating typical geodynamic situations. Herein, we are providing for the first time a systematic comparison of all of these elements. We use a series of benchmarks that illuminate different aspects of the features we consider typical of mantle convection and geodynamical simulations. We will show in particular that the stabilised Q1 × Q1 element has great difficulty producing accurate solutions for buoyancy-driven flows – the dominant forcing for mantle convection flow – and that the Q1 × P0 element is too unstable and inaccurate in practice. As a consequence, we believe that the Q2 × Q1 and Q2 × P−1 elements provide the most robust and reliable choice for geodynamical simulations, despite the greater complexity in their implementation and the substantially higher computational cost when solving linear systems.

scholarly journals Development of Practical Finite Element Models for Collapse of Reinforced Concrete Structures and Experimental Validation

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Mario Bermejo ◽  
Anastasio P. Santos ◽  
José M. Goicolea
Keyword(s):  
Finite Element ◽  
Reinforced Concrete ◽  
Finite Elements ◽  
Finite Element Model ◽  
Computational Cost ◽  
Concrete Structures ◽  
Element Model ◽  
Reinforced Concrete Structures ◽  
Finite Element Models ◽  
Explicit Finite Element

This paper describes two practical methodologies for modeling the collapse of reinforced concrete structures. They are validated with a real scale test of a two-floor structure which loses a bearing column. The objective is to achieve accurate simulations of collapse phenomena with moderate computational cost. Explicit finite element models are used with Lagrangian meshes, modeling concrete, and steel in a segregated manner. The first model uses 3D continuum finite elements for concrete and beams for steel bars, connected for displacement compatibility using a penalty method. The second model uses structural finite elements, shells for concrete, and beams for steel, connected in common nodes with an eccentricity formulation. Both are capable of simulating correctly the global behavior of the structural collapse. The continuum finite element model is more accurate for interpreting local failure but has an excessive computational cost for a complete building. The structural finite element model proposed has a moderate computational cost, yields sufficiently accurate results, and as a result is the recommended methodology.

Nonstationary Random Response Analysis of Spatially Stochastic Structures Without Applying Probabilistic Finite Elements

2000 ◽  
Author(s):  
C. W. S. To
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Response Analysis ◽  
Structural Systems ◽  
Random Response ◽  
Central Difference ◽  
Central Difference Method ◽  
Random Responses ◽  
First Time

Abstract A procedure based on the stochastic central difference method that was presented earlier by the author has been extended to cases involving with spatially and temporally stochastic structural systems that are approximated by the versatile finite element method. It is believed that for the first time nonstationary random responses of this class of systems are considered. The procedure eliminates the limitations associated with those employing the so-called stochastic or probabilistic finite element methods. Owing to its simplicity, the proposed method can easily be incorporated into many commercially available finite element packages.

Large Lateral Deformation Analysis of Angle Steel with Double Bolt Joints

2014 ◽  
Vol 556-562 ◽  
pp. 708-711
Author(s):  
Xing Zhou ◽  
Hai Bo Chen ◽  
Ying Qing Huang ◽  
Peng Wang ◽  
Wei Ling Xiao
Keyword(s):  
Finite Element ◽  
Deformation Analysis ◽  
Finite Element Models ◽  
Lateral Deformation ◽  
3D Finite Element ◽  
The Past ◽  
Different Types ◽  
Finite Element Package ◽  
Angle Steel ◽  
First Time

In the past time, it was neglected that different types of the deformation have an important effect on the Load-Displacement (L-D) relationship in bolt slippage. In this paper, 3D finite element models with double bolt joints are established by the ANSYS finite element package and a series of bolt slippage tests are conducted. The large lateral deformation in the process of bolt slippage is put forward for the first time. Numerical and experimental results show that large lateral deformation makes the stiffness of bolt joint smaller.

Coupling of Finite Element and Meshfree Method for Structure Mechanics Application: A Review

2019 ◽  
Vol 17 (04) ◽  
pp. 1850151 ◽  
Author(s):  
Gaurang R. Rohit ◽  
Jagdish M. Prajapati ◽  
Vikram B. Patel
Keyword(s):  
Finite Element ◽  
Solid Mechanics ◽  
Numerical Solutions ◽  
Computational Cost ◽  
Meshfree Method ◽  
Primary Concern ◽  
Interface Elements ◽  
The Past ◽  
Coupling Techniques ◽  
Element Free

In many engineering problems, the meshfree methods (MMs) have been dynamically projected and increasingly advanced in order to overwhelm some hitches in the predictable numerical methods. Over the past three decades in many different application area, MMs have found their way ranging from solid mechanics analysis, fluid problems, vibration analysis, heat transfer and optimization to numerical solutions of all kinds of (partial) differential equations. As every technique has shortcomings, the meshfree method also has drawbacks like higher computational cost and imposition of boundary condition which can be overruled by coupling it with the finite element method (FEM). In the past two decades, coupled MMs and FEM have appeared into a new session of computational methods with significant achievement. In addition, a noteworthy amount of growth has been made in addressing the major deficiencies that were present in the conventional methods and MMs at the premature phases. The objective of the present work is to provide a comprehensive review of various coupling techniques used for interface elements of MMs and FEM and general discussion on shape function formulation of FE and element free Galerkin method (EFGM). Key contribution of coupling techniques for coupled EFGM and FEM to structure mechanics application as primary concern.

A DIFFERENTIAL QUADRATURE FINITE ELEMENT METHOD

2010 ◽  
Vol 02 (01) ◽  
pp. 207-227 ◽  
Author(s):  
YUFENG XING ◽  
BO LIU ◽  
GUANG LIU
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Differential Quadrature Method ◽  
Computational Cost ◽  
Differential Quadrature ◽  
Weighting Coefficient ◽  
Numerical Comparison ◽  
Dynamic Problems ◽  
Element Method

This paper studies the differential quadrature finite element method (DQFEM) systematically, as a combination of differential quadrature method (DQM) and standard finite element method (FEM), and formulates one- to three-dimensional (1-D to 3-D) element matrices of DQFEM. It is shown that the mass matrices of C 0 finite element in DQFEM are diagonal, which can reduce the computational cost for dynamic problems. The Lagrange polynomials are used as the trial functions for both C 0 and C 1 differential quadrature finite elements (DQFE) with regular and/or irregular shapes, this unifies the selection of trial functions of FEM. The DQFE matrices are simply computed by algebraic operations of the given weighting coefficient matrices of the differential quadrature (DQ) rules and Gauss-Lobatto quadrature rules, which greatly simplifies the constructions of higher order finite elements. The inter-element compatibility requirements for problems with C 1 continuity are implemented through modifying the nodal parameters using DQ rules. The reformulated DQ rules for curvilinear quadrilateral domain and its implementation are also presented due to the requirements of application. Numerical comparison studies of 2-D and 3-D static and dynamic problems demonstrate the high accuracy and rapid convergence of the DQFEM.

scholarly journals Binary Neural Network for Automated Visual Surface Defect Detection

Sensors ◽  
2021 ◽  
Vol 21 (20) ◽  
pp. 6868
Author(s):  
Wenzhe Liu ◽  
Jiehua Zhang ◽  
Zhuo Su ◽  
Zhongzhu Zhou ◽  
Li Liu
Keyword(s):  
Defect Detection ◽  
Surface Defect ◽  
Recognition Accuracy ◽  
Computational Cost ◽  
Real Life ◽  
Great Difficulty ◽  
Binary Neural Network ◽  
Surface Defect Detection ◽  
First Time ◽  
Binary Networks

As is well-known, defects precisely affect the lives and functions of the machines in which they occur, and even cause potentially catastrophic casualties. Therefore, quality assessment before mounting is an indispensable requirement for factories. Apart from the recognition accuracy, current networks suffer from excessive computing complexity, making it of great difficulty to deploy in the manufacturing process. To address these issues, this paper introduces binary networks into the area of surface defect detection for the first time, for the reason that binary networks prohibitively constrain weight and activation to +1 and −1. The proposed Bi-ShuffleNet and U-BiNet utilize binary convolution layers and activations in low bitwidth, in order to reach comparable performances while incurring much less computational cost. Extensive experiments are conducted on real-life NEU and Magnetic Tile datasets, revealing the least OPs required and little accuracy decline. When classifying the defects, Bi-ShuffleNet yields comparable results to counterpart networks, with at least 2× inference complexity reduction. Defect segmentation results indicate similar observations. Some network design rules in defect detection and binary networks are also summarized in this paper.

Uneven Wear of Vehicle Tires

1993 ◽  
Vol 21 (4) ◽  
pp. 202-219 ◽  
Author(s):  
M. H. Walters
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Experimental Techniques ◽  
Lateral Stiffness ◽  
General Increase ◽  
Element Analysis ◽  
The Past ◽  
Uneven Wear

Abstract Advances in tire construction have led to major increases in tire life over the past twenty years, mainly by increasing the lateral stiffness and thus reducing slip during cornering. However, this general increase in tire life has tended to highlight the problem of uneven wear. In the present paper, three new experimental techniques are described which have been developed to study treadwear distributions. These techniques are evaluated and their results compared with a finite element analysis. Taken together, they indicate some of the causes of uneven wear and may be used to identify tire design and service features which contribute to uneven wear.

scholarly journals A New Mixed Functional-probabilistic Approach for Finite Element Accuracy

2020 ◽  
Vol 20 (4) ◽  
pp. 799-813
Author(s):  
Joël Chaskalovic ◽  
Franck Assous
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Asymptotic Relation ◽  
Probabilistic Approach ◽  
Random Variable ◽  
High Order ◽  
Relative Accuracy ◽  
The Difference ◽  
New Perspective

AbstractThe aim of this paper is to provide a new perspective on finite element accuracy. Starting from a geometrical reading of the Bramble–Hilbert lemma, we recall the two probabilistic laws we got in previous works that estimate the relative accuracy, considered as a random variable, between two finite elements {P_{k}} and {P_{m}} ({k<m}). Then we analyze the asymptotic relation between these two probabilistic laws when the difference {m-k} goes to infinity. New insights which qualify the relative accuracy in the case of high order finite elements are also obtained.

scholarly journals Concurrent material and structure optimization of multiphase hierarchical systems within a continuum micromechanics framework

2021 ◽  
Author(s):  
Tarun Gangwar ◽  
Dominik Schillinger
Keyword(s):  
Optimization Problems ◽  
Computational Cost ◽  
Structure Optimization ◽  
Material Behavior ◽  
Hierarchical Systems ◽  
Material Optimization ◽  
Continuum Micromechanics ◽  
Benchmark Tests ◽  
Constraint Optimization Problems ◽  
First Time

AbstractWe present a concurrent material and structure optimization framework for multiphase hierarchical systems that relies on homogenization estimates based on continuum micromechanics to account for material behavior across many different length scales. We show that the analytical nature of these estimates enables material optimization via a series of inexpensive “discretization-free” constraint optimization problems whose computational cost is independent of the number of hierarchical scales involved. To illustrate the strength of this unique property, we define new benchmark tests with several material scales that for the first time become computationally feasible via our framework. We also outline its potential in engineering applications by reproducing self-optimizing mechanisms in the natural hierarchical system of bamboo culm tissue.

scholarly journals Application of Hyperelastic Nodal Force Method to Evaluation of Aortic Valve Cusps Coaptation: Thin Shell vs. Membrane Formulations

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1450
Author(s):  
Yuri Vassilevski ◽  
Alexey Liogky ◽  
Victoria Salamatova
Keyword(s):  
Aortic Valve ◽  
Finite Elements ◽  
Shell Model ◽  
Thin Shell ◽  
Aortic Valves ◽  
Shear Moduli ◽  
Force Method ◽  
Elastic Potentials ◽  
Shell Analysis ◽  
First Time

Coaptation characteristics are crucial in an assessment of the competence of reconstructed aortic valves. Shell or membrane formulations can be used to model the valve cusps coaptation. In this paper we compare both formulations in terms of their coaptation characteristics for the first time. Our numerical thin shell model is based on a combination of the hyperelastic nodal forces method and the rotation-free finite elements. The shell model is verified on several popular benchmarks for thin-shell analysis. The relative error with respect to reference solutions does not exceed 1–2%. We apply our numerical shell and membrane formulations to model the closure of an idealized aortic valve varying hyperelasticity models and their shear moduli. The coaptation characteristics become almost insensitive to elastic potentials and sensitive to bending stiffness, which reduces the coaptation zone.

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