scholarly journals Stress evaluation in displacement-based 2D nonlocal finite element method

2018 ◽  
Vol 5 (1) ◽  
pp. 136-145 ◽  
Author(s):  
Aurora Angela Pisano ◽  
Paolo Fuschi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Field ◽  
Nonlocal Elasticity ◽  
Integration Technique ◽  
Stress Evaluation ◽  
Numerical Examples ◽  
Spurious Oscillations ◽  
Displacement Based ◽  
Element Method

Abstract The evaluation of the stress field within a nonlocal version of the displacement-based finite element method is addressed. With the aid of two numerical examples it is shown as some spurious oscillations of the computed nonlocal stresses arise at sections (or zones) of macroscopic inhomogeneity of the examined structures. It is also shown how the above drawback, which renders the stress numerical solution unreliable, can be viewed as the so-called locking in FEM, a subject debated in the early seventies. It is proved that a well known remedy for locking, i.e. the reduced integration technique, can be successfully applied also in the nonlocal elasticity context.

Curvature-Based Finite Element Method for Euler-Bernoulli Beams

2007 ◽  
Author(s):  
Y. L. Kuo ◽  
W. L. Cleghorn
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Transverse Displacement ◽  
Bernoulli Beam ◽  
Numerical Examples ◽  
Displacement Based ◽  
Curvature Distribution ◽  
Euler Bernoulli Beam ◽  
Element Method

This paper presents a new method called the curvature-based finite element method to solve Euler-Bernoulli beam problems. An approximated curvature distribution is selected first, and then the approximated transverse displacement is determined by double integrations. Four numerical examples demonstrate the validity of the method, and the results show that the errors are smaller than those generated by a conventional method, the displacement-based finite element method, for comparison based on the same number of degrees of freedom.

STRESS-BASED FINITE ELEMENT METHOD FOR EULER-BERNOULLI BEAMS

2006 ◽  
Vol 30 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Y.L. Kuo ◽  
W.L. Cleghorn ◽  
K. Behdinan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Degrees Of Freedom ◽  
Transverse Displacement ◽  
Bending Stress ◽  
Numerical Examples ◽  
A New Technique ◽  
Displacement Based ◽  
Element Method

This paper presents a new technique, which can apply the stress-based finite element method to Euler-Bernoulli beams. An approximated bending stress distribution is selected, and then the approximated transverse displacement is determined by twice integration. Due to the satisfaction of compatibility, the integration constants are determined by the boundary conditions related to transverse displacement and rotation. To compare with the displacement-based finite element method, this technique provides the continuities of not only transverse displacement and rotation but also stress at nodes. Besides, the boundary conditions related to stress are satisfied. Two numerical examples demonstrate the validity of this technique. The results show that the errors are smaller than those generated by the displacement-based finite element method for the same number of degrees of freedom.

The Equilibrium Cell-Based Smooth Finite Element Method for Shakedown Analysis of Structures

2019 ◽  
Vol 16 (05) ◽  
pp. 1840013 ◽  
Author(s):  
P. L. H. Ho ◽  
C. V. Le ◽  
T. Q. Chu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Optimization Problem ◽  
Conic Programming ◽  
Equilibrium Equations ◽  
Shakedown Analysis ◽  
Numerical Examples ◽  
Elastic Stresses ◽  
Gauss Points ◽  
Element Method

This paper presents a novel equilibrium formulation, that uses the cell-based smoothed method and conic programming, for limit and shakedown analysis of structures. The virtual strains are computed using straining cell-based smoothing technique based on elements of discretized mesh. Fictitious elastic stresses are also determined within the framework of finite element method (CS-FEM)-based Galerkin procedure, and equilibrium equations for residual stresses are satisfied in an average sense at every cell-based smoothing cell. All constrains are imposed at only one point in the smoothing domains, instead of Gauss points as in a standard FEM-based procedure. The resulting optimization problem is then handled using the highly efficient solvers. Various numerical examples are investigated, and obtained solutions are compared with available results in the literature.

Hot Forging Comparative Analyses by Using a Combined Finite Element Method

2007 ◽  
Vol 340-341 ◽  
pp. 737-742
Author(s):  
Yong Ming Guo
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Hot Forging ◽  
Rigid Plastic ◽  
Numerical Examples ◽  
Comparative Analyses ◽  
Single Action ◽  
Element Method

In this paper, single action die and double action die hot forging problems are analyzed by a combined FEM, which consists of the volumetrically elastic and deviatorically rigid-plastic FEM and the heat transfer FEM. The volumetrically elastic and deviatorically rigid-plastic FEM has some merits in comparison with the conventional rigid-plastic FEMs. Differences of calculated results for the two forging processes can be clearly seen in this paper. It is also verified that these calculated results are similar to those of the conventional rigid-plastic FEM in comparison with analyses of the same numerical examples by the penalty rigid-plastic FEM.

scholarly journals A high order immersed finite element method for parabolic interface problems

2019 ◽  
Vol 29 ◽  
pp. 01007
Author(s):  
Derrick Jones ◽  
Xu Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
High Order ◽  
Interface Problems ◽  
Numerical Schemes ◽  
Numerical Examples ◽  
Immersed Finite Element Method ◽  
Immersed Finite Element ◽  
Time Marching ◽  
Element Method

We present a high order immersed finite element (IFE) method for solving 1D parabolic interface problems. These methods allow the solution mesh to be independent of the interface. Time marching schemes including Backward-Eulerand Crank-Nicolson methods are implemented to fully discretize the system. Numerical examples are provided to test the performance of our numerical schemes.

Modeling and Simulation of High Speed Intermittent Cutting Based on the Finite Element Method

2013 ◽  
Vol 683 ◽  
pp. 556-559
Author(s):  
Bin Bin Jiao ◽  
Fu Sheng Yu ◽  
Yun Jiang Li ◽  
Rong Lu Zhang ◽  
Gui Lin Du ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Field ◽  
Cutting Force ◽  
High Speed ◽  
Element Model ◽  
Periodic Variation ◽  
Element Analysis ◽  
Intermittent Cutting ◽  
Element Method

In order to study the distribution of the stress field in the high-speed intermittent cutting process, finite element model of high-speed intermittent cutting is established. Exponential material model of the constitutive equation and adaptive grid technology are applied in the finite element analysis software AdvantEdge. The material processing is simulated under certain cutting conditions with FEM ( Finite Element Method ) and the distribution of cutting force, stress field, and temperature field are received. A periodic variation to the cutting force and temperature is showed in the simulation of high-speed intermittent cutting. Highest value of the milling temperature appears in front contacting area of the knife -the chip.and maximum stress occurs at the tip of tool or the vicinity of the main cutting edge. The analysis of stress and strain fields in-depth is of great significance to improve tool design and durability of tool.

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