A novel continuum model for the reduction of numerical errors of finite-element analysis

2011 ◽  
Vol 225 (4) ◽  
pp. 817-825 ◽  
Author(s):  
H Mohammadi ◽  
F Bahramian ◽  
W Herzog
Keyword(s):  
Finite Element ◽  
Continuum Model ◽  
Constitutive Models ◽  
Least Square ◽  
Constitutive Law ◽  
Element Analysis ◽  
Element Mesh ◽  
Numerical Errors ◽  
Proposed Model ◽  
Numerical Formulation

The authors developed a novel numerical formulation that reduces the computational expense of solving linear and non-linear constitutive models. A finite-element constitutive law followed by a novel continuum model is discussed. The proposed approach is employed to reduce numerical errors obtained from the standard finite-element method. The continuum model is based on the Lagrange multipliers strategy along with the finite-difference method and a least-square algorithm. It is crucial to this approach that the components of either the strain or the stress tensor are known at the nodes of the finite-element mesh. The proposed model is independent of element topology which can be strongly and arbitrarily distorted.

Analytical and Numerical Predictions of Thermoelastic Properties of Carbon Single-Walled Nanotubes

Aerospace ◽  
2005 ◽  
Author(s):  
Vinod P. Veedu ◽  
Davood Askari ◽  
Mehrdad N. Ghasemi-Nejhad
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Graphene Sheet ◽  
Effective Properties ◽  
Constitutive Models ◽  
Thermoelastic Properties ◽  
Asymptotic Homogenization ◽  
Element Analysis ◽  
Single Walled Nanotubes ◽  
Numerical Predictions

The objective of this paper is to develop constitutive models to predict thermoelastic properties of carbon single-walled nanotubes using analytical, asymptotic homogenization, and numerical, finite element analysis, methods. In our approach, the graphene sheet is considered as a non-homogeneous network shell layer which has zero material properties in the regions of perforation and whose effective properties are estimated from the solution of the appropriate local problems set on the unit cell of the layer. Our goal is to derive working formulas for the entire complex of the thermoelastic properties of the periodic network. The effective thermoelastic properties of carbon nanotubes were predicted using asymptotic homogenization method. Moreover, in order to verify the results of analytical predictions, a detailed finite element analysis is followed to investigate the thermoelastic response of the unit cells and the entire graphene sheet network.

Elasto-Plastic Coupled Temperature-Displacement Finite Element Analysis of Two-Dimensional Rolling-Sliding Contact With a Translating Heat Source

1991 ◽  
Vol 113 (1) ◽  
pp. 93-101 ◽  
Author(s):  
S. M. Kulkarni ◽  
C. A. Rubin ◽  
G. T. Hahn
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Plastic Material ◽  
Element Model ◽  
Rolling Contact ◽  
Two Dimensional ◽  
Element Analysis ◽  
Element Mesh ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

The present paper, describes a transient translating elasto-plastic thermo-mechanical finite element model to study 2-D frictional rolling contact. Frictional two-dimensional contact is simulated by repeatedly translating a non-uniform thermo-mechanical distribution across the surface of an elasto-plastic half space. The half space is represented by a two dimensional finite element mesh with appropriate boundaries. Calculations are for an elastic-perfectly plastic material and the selected thermo-physical properties are assumed to be temperature independent. The paper presents temperature variations, stress and plastic strain distributions and deformations. Residual tensile stresses are observed. The magnitude and depth of these stresses depends on 1) the temperature gradients and 2) the magnitudes of the normal and tangential tractions.

A Finite Element Analysis for Magnetostrictive Thin Film Structures and Its Experimental Verification

2006 ◽  
Vol 306-308 ◽  
pp. 1151-1156 ◽  
Author(s):  
Chong Du Cho ◽  
Heung Shik Lee ◽  
Chang Boo Kim ◽  
Hyeon Gyu Beom
Keyword(s):  
Thin Film ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Geometric Feature ◽  
Hysteresis Phenomenon ◽  
Finite Element Code ◽  
Element Analysis ◽  
Element Mesh ◽  
Magnetostrictive Actuators ◽  
Large Length

In this paper, a finite element code especially for micro-magnetostrictive actuators was developed. Two significant characteristics of the presented finite element code are: (1) the magnetostrictive hysteresis phenomenon is effectively taken into account; (2) intrinsic geometric feature of typical thin film structures of large length to thickness ratio, which makes it very difficult to construct finite element mesh in the region of the thin film, is considered reasonably in modeling micro-magneostrictive actuators. For verification purpose, magnetostrictive thin films were fabricated and tested in the form of a cantilevered actuator. The Tb-Fe film and Sm-Fe film are sputtered on the Si and Polyimide substrates individually. The magnetic and magnetostrictive properties of the sputtered magnetostrictive films are measured. The measured magnetostrictive coefficients are compared with the numerically calculated ones.

Finite Element Mesh Generator Applying Constraints’ Propagation and Isoparametric Mapping

1991 ◽  
Author(s):  
J. Rodriguez ◽  
M. Him
Keyword(s):  
Finite Element ◽  
Mesh Generation ◽  
Element Model ◽  
Finite Element Mesh ◽  
Fe Model ◽  
Element Analysis ◽  
Element Mesh ◽  
Mesh Generator ◽  
Generation Algorithm ◽  
Essential Input

Abstract This paper presents a finite element mesh generation algorithm (PREPAT) designed to automatically discretize two-dimensional domains. The mesh generation algorithm is a mapping scheme which creates a uniform isoparametric FE model based on a pre-partitioned domain of the component. The proposed algorithm provides a faster and more accurate tool in the pre-processing phase of a Finite Element Analysis (FEA). A primary goal of the developed mesh generator is to create a finite element model requiring only essential input from the analyst. As a result, the generator code utilizes only a sketch, based on geometric primitives, and information relating to loading/boundary conditions. These conditions represents the constraints that are propagated throughout the model and the available finite elements are uniformly mapped in the resulting sub-domains. Relative advantages and limitations of the mesh generator are discussed. Examples are presented to illustrate the accuracy, efficiency and applicability of PREPAT.

J-Integral Analysis of Surface Cracks in Round Bars under Bending Moments

2011 ◽  
Vol 52-54 ◽  
pp. 43-48 ◽  
Author(s):  
Al Emran Ismail ◽  
Ahmad Kamal Ariffin ◽  
Shahrum Abdullah ◽  
Mariyam Jameelah Ghazali ◽  
Ruslizam Daud
Keyword(s):  
Finite Element ◽  
Crack Depth ◽  
Crack Tip ◽  
Bending Moment ◽  
Limit Load ◽  
Fe Model ◽  
Surface Cracks ◽  
Element Analysis ◽  
Reference Stress ◽  
Proposed Model

This paper presents a non-linear numerical investigation of surface cracks in round bars under bending moment by using ANSYS finite element analysis (FEA). Due to the symmetrical analysis, only quarter finite element (FE) model was constructed and special attention was given at the crack tip of the cracks. The surface cracks were characterized by the dimensionless crack aspect ratio, a/b = 0.6, 0.8, 1.0 and 1.2, while the dimensionless relative crack depth, a/D = 0.1, 0.2 and 0.3. The square-root singularity of stresses and strains was modeled by shifting the mid-point nodes to the quarter-point locations close to the crack tip. The proposed model was validated with the existing model before any further analysis. The elastic-plastic analysis under remotely applied bending moment was assumed to follow the Ramberg-Osgood relation with n = 5 and 10. J values were determined for all positions along the crack front and then, the limit load was predicted using the J values obtained from FEA through the reference stress method.

scholarly journals Application of the Generalized Nonlinear Constitutive Law in 2D Shear Flexible Beam Structures

2021 ◽  
Author(s):  
Damian Mrówczyński ◽  
Tomasz Gajewski ◽  
Tomasz Garbowski
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Reference Model ◽  
Constitutive Models ◽  
Constitutive Law ◽  
Flexible Beam ◽  
Beam Model ◽  
Beam Structures ◽  
Nodal Displacements ◽  
Nonlinear Constitutive Law

The paper presents a modified finite element method for nonlinear analysis of 2D beam structures. To take into account the influence of the shear flexibility, a Timoshenko beam element was adopted. The algorithm proposed enables using complex material laws without the need of implementing advanced constitutive models in finite element routines. The method is easy to implement in commonly available CAE software for linear analysis of beam structures. It allows to extend the functionality of these programs with material nonlinearities. By using the structure deformations, computed from the nodal displacements, and the presented here generalized nonlinear constitutive law, it is possible to iteratively reduce the bending, tensile and shear stiffnesses of the structures. By applying a beam model with a multi layered cross-section and generalized stresses and strains to obtain a representative constitutive law, it is easy to model not only the complex multi-material cross-sections, but also the advanced nonlinear constitutive laws (e.g. material softening in tension). The proposed method was implemented in the MATLAB environment, its performance was shown on the several numerical examples. The cross-sections such us a steel I-beam and a steel I-beam with a concrete encasement for different slenderness ratios were considered here. To verify the accuracy of the computations, all results are compared with the ones received from a commercial CAE software. The comparison reveals a good correlation between the reference model and the method proposed.

Finite Element Simulation of the Sachs Boring Method of Measuring Residual Stresses in Thick-Walled Cylinders

2003 ◽  
Vol 125 (3) ◽  
pp. 274-276 ◽  
Author(s):  
R. R. de Swardt
Keyword(s):  
Finite Element ◽  
Residual Stresses ◽  
Data Reduction ◽  
High Speed ◽  
High Strength ◽  
Residual Stress Field ◽  
Element Analysis ◽  
Element Mesh ◽  
Reduction Methods ◽  
Data Reduction Method

During a recent study the residual strain/stress states through the walls of autofrettaged thick-walled high-strength steel cylinders were measured with neutron diffraction, Sachs boring and the compliance methods (Venter et al., 2000, J. Strain Anal. Eng. Des., 35, pp. 459–469). The Sachs boring method was developed prior to the advent of high speed computers. A new method for the data reduction was proposed. In order to verify the proposed procedure, the Sachs boring experimental method was simulated using finite element modeling. A residual stress field was introduced in the finite element method by elasto-plastic finite element analysis. The physical process of material removal by means of boring was simulated by step-by-step removal of elements from the finite element mesh. Both the traditional and newly proposed data reduction methods were used to calculate the residual stresses. The new data reduction method compares favorably with the traditional method.

Finite Element Analysis of Hyperelastic Components

1998 ◽  
Vol 51 (5) ◽  
pp. 303-320 ◽  
Author(s):  
D. W. Nicholson ◽  
N. W. Nelson ◽  
B. Lin ◽  
A. Farinella
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Recent Literature ◽  
Constitutive Models ◽  
Review Article ◽  
Considerable Extent ◽  
Arc Length ◽  
Numerical Techniques ◽  
Element Analysis ◽  
Current Review

Finite element analysis of hyperelastic components poses severe obstacles owing to features such as large deformation and near-incompressibility. In recent years, outstanding issues have, to a considerable extent, been addressed in the form of the hyperelastic element available in commercial finite element codes. The current review article, which updates and expands a 1990 article in Rubber Reviews, is intended to serve as a brief exposition and selective survey of the recent literature. Published simulations are listed. Rubber constitutive models and the measurement of their parameters are addressed. The underlying incremental variational formulation is sketched for thermomechanical response of compressible, incompressible and near-incompressible elastomers. Coupled thermomechanical effects and broad classes of boundary conditions, such as variable contact, are encompassed. Attention is given to advanced numerical techniques such as arc length methods. Remaining needs are assessed. This review article contains 142 references.

scholarly journals An Application of Bi-Directional Evolutionary Structural Optimisation for Optimising Energy Absorbing Structures Using a Material Damage Model

2014 ◽  
Vol 553 ◽  
pp. 836-841 ◽  
Author(s):  
Daniel Stojanov ◽  
Brian G. Falzon ◽  
Xin Hua Wu ◽  
Wen Yi Yan
Keyword(s):  
Finite Element ◽  
Damage Model ◽  
Ductile Material ◽  
Topology Optimisation ◽  
Material Damage ◽  
Structural Optimisation ◽  
Element Analysis ◽  
Element Mesh ◽  
Beso Method ◽  
Energy Absorbing

The Bi-directional Evolutionary Structural Optimisation (BESO) method is a numerical topology optimisation method developed for use in finite element analysis. This paper presents a particular application of the BESO method to optimise the energy absorbing capability of metallic structures. The optimisation objective is to evolve a structural geometry of minimum mass while ensuring that the kinetic energy of an impacting projectile is reduced to a level which prevents perforation. Individual elements in a finite element mesh are deleted when a prescribed damage criterion is exceeded. An energy absorbing structure subjected to projectile impact will fail once the level of damage results in a critical perforation size. It is therefore necessary to constrain an optimisation algorithm from producing such candidate solutions. An algorithm to detect perforation was implemented within a BESO framework which incorporated a ductile material damage model.

Rigid–plastic limit analysis of discontinuous media by a finite element method

1989 ◽  
Vol 26 (3) ◽  
pp. 369-374 ◽  
Author(s):  
T. Tamura ◽  
R. Y. S. Pak
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Bearing Capacity ◽  
Limit Analysis ◽  
Constitutive Law ◽  
Rigid Plastic ◽  
Element Analysis ◽  
Plastic Limit Analysis ◽  
Surface Foundation ◽  
Element Method

This paper describes the formulation of a finite element method by which a limit analysis of a rigid–plastic medium with discontinuities can be performed. The Drucker–Prager criterion is adopted to describe the yielding of the medium, while the Mohr–Coulomb law is used to model the interface of the discontinuous velocity fields. Both associated and nonassociated flow rules are considered in the constitutive characterization. Results are presented to illustrate the influence of discontinuities on the bearing capacity of a surface foundation. Key words: bearing capacity, constitutive law, dilatancy, discontinuity, limit, plasticity, finite element analysis.

Sign in / Sign up

Export Citation Format

Share Document