SMOOTHED FINITE ELEMENT METHODS FOR THERMO-MECHANICAL IMPACT PROBLEMS

2013 ◽  
Vol 10 (01) ◽  
pp. 1340010 ◽  
Author(s):  
V. KUMAR
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Large Deformations ◽  
Physical Domain ◽  
Shape Functions ◽  
Mechanical Impact ◽  
Element Approach ◽  
Impact Problems ◽  
Isoparametric Mapping ◽  
Derivatives Of

We present a Smoothed Finite Element Methods (SFEM) for thermo-mechanical impact problems. The smoothing is applied to the strains and the standard finite element approach is used for the temperature field. The SFEM allows for highly accurate results and large deformations. No isoparametric mapping is needed; the shape functions are computed in the physical domain. Moreover, no derivatives of the shape functions must be computed. We implemented a visco-plastic constitutive model and validate the method by comparing numerical results to experimental data.

Simulation of Deep Spherical Indentation Using Eulerian Finite Element Methods

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
D. Anderson ◽  
A. Warkentin ◽  
R. Bauer
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Large Deformations ◽  
Radial Strain ◽  
Element Model ◽  
Spherical Indentation ◽  
Eulerian Formulation ◽  
Pile Up ◽  
Deep Indentation ◽  
General Material

Simulation of deep indentation, and the associated pile-up effects, requires a robust and accurate finite element model capable of naturally handling the large deformations present. This work successfully demonstrates that the Eulerian formulation is capable of accurately reproducing the forces and general material response of deep indentation. It was found that, in the absence of friction, sink-in dominates at indentation depths less than 1.1% of the indenter radius, there is a transition from sink-in to pile-up from 1.1% to 2.3% of the indenter radius, and pile-up is fully developed at indentation depths larger than 13.2% of the indenter radius for the 4340 steel workpiece and the 0.508 mm radius indenter presented in this work. Friction tended to marginally increase the sink-in and transition depths as well as reduce the material height at the onset of fully developed pile-up due to a reduction in the tensile radial strain directly under the indenter.

Increasing the Solution Accuracy in the Numerical Modeling of Boundary Value Problems Using Finite Element Method Based on Hankel Shape Functions

2019 ◽  
Vol 11 (07) ◽  
pp. 1950062
Author(s):  
S. Farmani ◽  
M. Ghaeini-Hessaroeyeh ◽  
S. Hamzehei-Javaran
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Value Problems ◽  
Numerical Solutions ◽  
Boundary Value ◽  
The Finite Element Method ◽  
Shape Functions ◽  
Element Approach ◽  
Solution Accuracy ◽  
Element Method

A new finite element approach is developed here for the modeling of boundary value problems. In the present model, the finite element method (FEM) is reformulated by new shape functions called spherical Hankel shape functions. The mentioned functions are derived from the first and second kind of Bessel functions that have the properties of both of them. These features provide an improvement in the solution accuracy with number of elements which are equal or lower than the ones used by the classic FEM. The efficiency and accuracy of the suggested model in the potential problems are examined by several numerical examples. Then, the obtained results are compared with the analytical and numerical solutions. The comparisons indicate the high accuracy of the present method.

An Isoparametric Finite Element With Nodal Derivatives

1981 ◽  
Vol 48 (1) ◽  
pp. 64-68
Author(s):  
W. D. Webster
Keyword(s):  
Finite Element ◽  
Cantilever Beam ◽  
Unknown Function ◽  
Nodal Point ◽  
Shape Functions ◽  
Isoparametric Element ◽  
Partial Derivatives ◽  
Isoparametric Finite Element ◽  
Local Coordinates ◽  
Derivatives Of

A finite element using the nodal point values of the first partial derivatives of the unknown function with respect to the coordinates to increase the order of the resulting interpolating polynomial is formulated as an isoparametric element. The shape functions in local coordinates are given and then to satisfy requirements for the transformation of derivatives are modified for use with the global coordinates. Examples of a cantilever beam, a curved cantilever beam, and a flat bar with a hole demonstrate the high-order capabilities of the element. The advantages of the element over other isoparametric elements are discussed.

Analysis of bond-slip and transverse dissipative energies in confined reinforcing bars

2018 ◽  
Vol 45 (9) ◽  
pp. 739-751
Author(s):  
Armin Erfanian ◽  
Alaa E. Elwi
Keyword(s):  
Finite Element ◽  
Large Deformations ◽  
Confined Concrete ◽  
Test Results ◽  
Reinforcing Bars ◽  
Bond Slip ◽  
Finite Element Approach ◽  
Transverse Pressure ◽  
Element Approach ◽  
Plastic Stage

A finite element approach for the analysis of straight and bent reinforcing bars in confined concrete under monotonic loading is presented. This type of anchorage is mostly found in joints. Bond and transverse dissipative energies are included. The proposed approach predicts the capacity, bond, slip, strains, and stresses along the bars in curved and straight configurations. This method can be used to predict bar pullout behavior. Various bond-slip models and test results are available in the literature. Many of the current approaches do not consider the plastic stage bond, transverse pressure, and large deformations. These shortcomings are resolved in this research. A simplified but effective approach is proposed for plastic stage bond. Internal and external transverse pressures are addressed presenting a mathematically sound incremental procedure. These solutions are appended to the existing nonlinear strategies to accommodate large deformations. Comparison with published experimental results demonstrates the accuracy of the proposed method.

Moving Finite Element Methods for a System of Semi-Linear Fractional Diffusion Equations

2016 ◽  
Vol 8 (6) ◽  
pp. 911-931 ◽  
Author(s):  
Jingtang Ma ◽  
Zhiqiang Zhou
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Convergence Rates ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Predator Prey ◽  
Fractional Diffusion Equations ◽  
Predator Prey Models ◽  
Derivatives Of ◽  
Moving Finite Element

AbstractThis paper studies a system of semi-linear fractional diffusion equations which arise in competitive predator-prey models by replacing the second-order derivatives in the spatial variables with fractional derivatives of order less than two. Moving finite element methods are proposed to solve the system of fractional diffusion equations and the convergence rates of the methods are proved. Numerical examples are carried out to confirm the theoretical findings. Some applications in anomalous diffusive Lotka-Volterra and Michaelis-Menten-Holling predator-prey models are studied.

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