Hybrid Isogeometric-Finite Element Discretization Applied to Stress Concentration Problems

2018 ◽  
Vol 10 (08) ◽  
pp. 1850081 ◽  
Author(s):  
Saeed Maleki-Jebeli ◽  
Mahmoud Mosavi-Mashhadi ◽  
Mostafa Baghani
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Finite Elements ◽  
Field Variable ◽  
Higher Order ◽  
Stable Convergence ◽  
Order Continuity ◽  
Element Discretization ◽  
B Splines ◽  
Computer Methods

Isogeometric analysis (IGA) employs non-uniform rational B-splines (NURBS) or other B-spline-based variants to represent both the geometry and the field variable. Exact geometry representation and higher order global continuity (at least [Formula: see text] even on elements’ boundaries) are two favorable properties that would make IGA an appropriate discretization technique in problems with responses associated with the derivatives of the primary field variable. As a category of these problems, in this paper, 2D elastostatic problems involving stress concentration sites are analyzed with a hybrid isogeometric-finite element (IG-FE) discretization. To exploit higher order continuity of NURBS basis functions, IGA discretization is applied selectively at pre-identified locations of high displacement gradients where the stress concentration occurs. In addition, considering computational efficiency, the rest of problem domain is discretized by means of linear Lagrangian finite elements. The connection of NURBS and Lagrangian domain is carried out through employing specially devised elements [Corbett, C. J. and Sauer, R. A. [2014] “NURBS-enriched contact finite elements”, Computer Methods in Applied Mechanics and Engineering 275, 55–75]. The methodology is applied in some 2D elastostatic examples. Increasing the number of DOFs and comparing convergence of the concentrated stress value using different discretizations, it is shown that the hybrid IG-FE discretizations generally have faster and more stable convergence response compared with pure FE discretizations especially at lower DOFs.

Computational Wear and Contact Modeling for Fretting Analysis with Isogeometric Dual Mortar Methods

2016 ◽  
Vol 681 ◽  
pp. 1-18 ◽  
Author(s):  
Philipp Farah ◽  
Markus Gitterle ◽  
Wolfgang A. Wall ◽  
Alexander Popp
Keyword(s):  
Finite Element ◽  
Three Dimensions ◽  
Fretting Wear ◽  
Additional Contribution ◽  
Shape Functions ◽  
Element Discretization ◽  
B Splines ◽  
Mortar Methods ◽  
Deformation Regime ◽  
Incremental Scheme

A finite element framework based on dual mortar methods is presented for simulating fretting wear effects in the finite deformation regime. The mortar finite element discretization is realized with Lagrangean shape functions as well as isogeometric elements based on non-uniform rational B-splines (NURBS) in two and three dimensions. Fretting wear effects are modeled in an incremental scheme with the help of Archard’s law and the worn material is considered as additional contribution to the gap function. Numerical examples demonstrate the robustness and accuracy of the presented algorithm.

Finite Element Analysis of Stress Concentration Problems Based on Cosserat Continuum Model

2011 ◽  
Vol 99-100 ◽  
pp. 939-943
Author(s):  
Hong Xiang Tang ◽  
Yu Hui Guan
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Finite Elements ◽  
Scale Effects ◽  
Elliptic Hole ◽  
Continuum Theory ◽  
Cosserat Continuum ◽  
Element Analysis ◽  
Concentration Phenomena ◽  
Consistent Solution

In the present work, the Cosserat micro-polar continuum theory is introduced into the FEM numerical model, which is used to simulate the stress concentration problems. The stress concentration phenomena around circular hole, elliptic hole and rhombic hole in plane strain condition, are numerically simulated by two types of Cosserat continuum finite elements of the standard displacement and rotation u4ω4 and u8ω8 based on Dirichlet principle. It is indicated that, compared with the classical continuum finite element, these two Cosserat continuum finite elements can reflect the steep strain gradient and scale effects occurring in the stress concentration problems, and they can weaken the stress concentration and may get consistent solution with actual situation.

On Higher Order Pyramidal Finite Elements

2011 ◽  
Vol 3 (2) ◽  
pp. 131-140 ◽  
Author(s):  
Liping Liu ◽  
Kevin B. Davies ◽  
Michal Křížek ◽  
Li Guan
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Degrees Of Freedom ◽  
Higher Order ◽  
Basis Functions ◽  
Quadratic Functions ◽  
Polynomial Basis

AbstractIn this paper we first prove a theorem on the nonexistence of pyramidal polynomial basis functions. Then we present a new symmetric composite pyramidal finite element which yields a better convergence than the nonsymmetric one. It has fourteen degrees of freedom and its basis functions are incomplete piecewise triquadratic polynomials. The space of ansatz functions contains all quadratic functions on each of four subtetrahedra that form a given pyramidal element.

scholarly journals Shell finite elements, with emphasis on strategies used within Elmer software

2017 ◽  
Vol 50 (3) ◽  
pp. 162-165
Author(s):  
Mika Malinen
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Open Source ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
Finite Element Software ◽  
Structural Shell

The best way to handle finite element discretization of structural shell equationsis still a subject of discussion. This article presents some viewpoints and reviews innovationswhich have recently been taken into use in connection with the implementation of new shell finite elements into the open source finite element software Elmer.

Efficient Residual and Matrix-Free Jacobian Evaluation for Three-Dimensional Tri-Quadratic Hexahedral Finite Elements With Nearly-Incompressible Neo-Hookean Hyperelasticity Applied to Soft Materials on Unstructured Meshes in Parallel, With PETSc and libCEED

2020 ◽  
Author(s):  
Arash Mehraban ◽  
Jed Brown ◽  
Valeria Barra ◽  
Henry Tufo ◽  
Jeremy Thompson ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Optimization Design ◽  
Solid Mechanics ◽  
Soft Materials ◽  
Biological Tissues ◽  
Higher Order ◽  
Mixed Formulation ◽  
Element Formulation ◽  
Matrix Free

Abstract Soft materials such as rubber, elastomers, and soft biological tissues mechanically deform at large strain isochorically for all time, or during their initial transient (when a pore fluid, typically incompressible such as water, does not have time to flow out of the deforming polymer or soft tissue porous skeleton). Simulating these large isochoric deformations computationally, such as with the Finite Element Method (FEM), requires higher order (typically quadratic) interpolation functions and/or enhancements through hybrid/mixed methods to maintain stability. Lower order (linear) finite elements with hybrid/mixed formulation may not perform stably for all mechanical loading scenarios involving large isochoric deformations, whereas quadratic finite elements with or without hybrid/mixed formulation typically perform stably, especially when large bending or folding deformations are being simulated. For topology-optimization design of soft robotics, for instance, the FEM solid mechanics solver must run efficiently and stably. Stability is ensured by the higher order finite element formulation (with possible enhancement), but efficiency for higher order FEM remains a challenge. Thus, this paper addresses efficiency from the perspective of computer science algorithms and programming. The proposed efficient algorithm utilizes the Portable, Extensible Toolkit for Scientific Computation (PETSc), along with the libCEED library for efficient compiler optimized tensor-product-basis computation to demonstrate an efficient nonlinear solution algorithm. For preconditioning, a scalable p-multigrid method is presented whereby a hierarchy of levels is constructed. In contrast to classical geometric multigrid, also known as h-multigrid, each level in p-multigrid is related to a different approximation polynomial order, p, instead of the element size, h. A Chebyshev polynomial smoother is used on each multigrid level. Algebraic MultiGrid (AMG) is then applied to the assembled Q1 (linear) coarse mesh on the nodes of the quadratic Q2 (quadratic) mesh. This allows low storage that can be efficiently used to accelerate the convergence to solution. For a Neo-Hookean hyperelastic problem, we examine a residual and matrix-free Jacobian formulation of a tri-quadratic hexahedral finite element with enhancement. Efficiency estimates on AVX-2 architecture based on CPU time are provided as a comparison to similar simulation (and mesh) of isochoric large deformation hyperelasticity as applied to soft materials conducted with the commercially-available FEM software program ABAQUS. The particular problem in consideration is the simulation of an assistive device in the form of finger-bending in 3D.

A Finite Element Model for Thick-Walled Axisymmetric Shells

1982 ◽  
Vol 104 (3) ◽  
pp. 215-222 ◽  
Author(s):  
D. J. Barrett ◽  
A. Soler
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Finite Element Model ◽  
Thin Shell ◽  
Element Model ◽  
Order Theory ◽  
Higher Order ◽  
Shells Of Revolution ◽  
Geometric Conditions ◽  
Higher Order Theory

The symmetrically loaded moderately thick-walled shell of revolution can be treated by general finite elements, or for certain geometric conditions, by extended thin shell finite elements that have incorporated transverse shear deformation. In this work, we develop a higher order theory finite element model for symmetrically loaded shells of revolution which is useful for configurations which are out of the range of validity of the extended thin shell elements. Legendre polynomial series expansions are key features of the development and lead to nonlinear distributions of both stress and deformation in the thickness variable. Problems are solved to yield some initial data for comparison of the cost and accuracy of the higher order theory finite element model to other shell element models.

Finite Element Modeling of the Contact Geometry and Deformation in Biomechanics Applications1

2013 ◽  
Vol 8 (4) ◽  
Author(s):  
F. Marina Gantoi ◽  
Michael A. Brown ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Contact Surface ◽  
Spline Function ◽  
Geometric Description ◽  
Surface Geometry ◽  
B Splines ◽  
Contact Points ◽  
Contact Formulation ◽  
Parametric Relationship

The main contribution of this paper is to demonstrate the feasibility of using one computational environment for developing accurate geometry as well as performing the analysis of detailed biomechanics models. To this end, the finite element (FE) absolute nodal coordinate formulation (ANCF) and multibody system (MBS) algorithms are used in modeling both the contact geometry and ligaments deformations in biomechanics applications. Two ANCF approaches can be used to model the rigid contact surface geometry. In the first approach, fully parameterized ANCF volume elements are converted to surface geometry using parametric relationship that reduces the number of independent coordinate lines. This parametric relationship can be defined analytically or using a spline function representation. In the second approach, an ANCF surface that defines a gradient deficient thin plate element is used. This second approach does not require the use of parametric relations or spline function representations. These two geometric approaches shed light on the generality of and the flexibility offered by the ANCF geometry as compared to computational geometry (CG) methods such as B-splines and NURBS (Non-Uniform Rational B-Splines). Furthermore, because B-spline and NURBS representations employ a rigid recurrence structure, they are not suited as general analysis tools that capture different types of joint discontinuities. ANCF finite elements, on the other hand, lend themselves easily to geometric description and can additionally be used effectively in the analysis of ligaments, muscles, and soft tissues (LMST), as demonstrated in this paper using the knee joint as an example. In this study, ANCF finite elements are used to define the femur/tibia rigid body contact surface geometry. The same ANCF finite elements are also used to model the MCL and LCL ligament deformations. Two different contact formulations are used in this investigation to predict the femur/tibia contact forces; the elastic contact formulation which allows for penetrations and separations at the contact points, and the constraint contact formulation in which the nonconformal contact conditions are imposed as constraint equations, and as a consequence, no separations or penetrations at the contact points are allowed. For both formulations, the contact surfaces are described in a parametric form using surface parameters that enter into the ANCF finite element geometric description. A set of nonlinear algebraic equations that depend on the surface parameters is developed and used to determine the location of the contact points. These two contact formulations are implemented in a general MBS algorithm that allows for modeling rigid and flexible body dynamics.

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