Efficient Updated-Lagrangian Simulations in Forming Processes

2015 ◽  
Vol 651-653 ◽  
pp. 1294-1300
Author(s):  
Diego Canales ◽  
Adrien Leygue ◽  
Francisco Chinesta ◽  
Elias Cueto ◽  
Eric Feulvarch ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Numerical Integration ◽  
General Purpose ◽  
Integration Technique ◽  
Numerical Examples ◽  
Nodal Integration ◽  
Out Of Plane ◽  
Material Forming ◽  
Updated Lagrangian ◽  
Stabilized Conforming Nodal Integration

A new efficient updated-Lagrangian strategy for numerical simulations of material forming processes is presented in this work. The basic ingredients are the in-plane-out-of-plane PGD-based decomposition and the use of a robust numerical integration technique (the Stabilized Conforming Nodal Integration). This strategy is of general purpose, although it is especially well suited for plateshape geometries. This paper is devoted to show the feasibility of the technique through some simple numerical examples.

Comparison of spectral methods for the evaluation of Stokes integral  

2021 ◽  
Author(s):  
Avadh Bihari Narayan ◽  
Ashutosh Tiwari ◽  
Govind Sharma ◽  
Balaji Devaraju ◽  
Onkar Dikshit
Keyword(s):  
Boundary Value Problems ◽  
Numerical Integration ◽  
Spectral Methods ◽  
Boundary Value ◽  
Fundamental Equation ◽  
Computation Time ◽  
Spherical Approximation ◽  
Integration Technique ◽  
Gravity Measurements ◽  
Stokes Integral

<p>The spherical approximation of the fundamental equation of geodesy defines the boundary value problems. Stokes’s integral provides the solution of boundary value problems that enables the computation of geoid from the properly reduced gravity measurements to the geoid. The stokes integral can be evaluated by brute-force numerical integration, spectral methods, and least-squares collocation. There is a trade-off between computation time and accuracy when we chose numerical integration technique or any spectral method. This research will compare time complexity and the accuracy of different spectral methods (1D-FFT, 2D-FFT, Multi-band FFT) and numerical integration technique for the region in the lower Himalaya, around Nainital, Uttarakhand, India. </p>

A GALERKIN MESHFREE METHOD WITH STABILIZED CONFORMING NODAL INTEGRATION FOR GEOMETRICALLY NONLINEAR ANALYSIS OF SHEAR DEFORMABLE PLATES

2011 ◽  
Vol 08 (04) ◽  
pp. 685-703 ◽  
Author(s):  
DONGDONG WANG ◽  
YUE SUN
Keyword(s):  
Nonlinear Analysis ◽  
Large Deflection ◽  
Lagrangian Description ◽  
Geometrically Nonlinear ◽  
Geometrically Nonlinear Analysis ◽  
Nodal Integration ◽  
Galerkin Meshfree ◽  
Shear Deformable ◽  
Shear Deformable Plates ◽  
Stabilized Conforming Nodal Integration

A Galerkin meshfree approach formulated within the framework of stabilized conforming nodal integration (SCNI) is presented for geometrically nonlinear analysis of large deflection shear deformable plates. This method is based upon a Lagrangian curvature smoothing in which the smoothed curvature is constructed within a nodal representative domain on the initial configuration. It is shown that the Lagrangian smoothed nodal gradients of the meshfree shape function is capable of exactly representing arbitrary constant curvature fields in the discrete sense of nodal integration. The consistent linearization is performed on the weak form of large deflection plate in the context of the total Lagrangian description. Subsequently, the discrete incremental equations are obtained by the method of SCNI in which to relieve the locking as well as ensure the stability of the present scheme, the bending contribution is evaluated using the smoothed nodal gradients, while the membrane and shear contributions are computed with the direct nodal gradients. The effectiveness of the present method is thoroughly demonstrated through several numerical examples.

Numerical simulations of non-stationary distributions of electrochemical potentials in SOFC

2017 ◽  
Vol 34 (6) ◽  
pp. 1956-1988 ◽  
Author(s):  
Mayu Muramatsu ◽  
Keiji Yashiro ◽  
Tatsuya Kawada ◽  
Kenjiro Tarada
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Chemical Potential ◽  
Simulation Method ◽  
Open Circuit ◽  
Operating Conditions ◽  
Stationary Distributions ◽  
Experimental Conditions ◽  
Content Type ◽  
Numerical Examples

Purpose The purpose of this study is to develop a simulation method to calculate non-stationary distributions of the chemical potential of oxygen in a solid oxide fuel cell (SOFC) under operation. Design/methodology/approach The initial-boundary value problem was appropriately formulated and the appropriate boundary conditions were implemented so that the problem of non-stationary behavior of SOFC can be solved in accordance with actual operational and typical experimental conditions. The dependencies of the material properties on the temperature and partial pressure of oxygen were also elaborately introduced to realize actual material responses. The capability of the proposed simulation method was demonstrated under arbitrary operating conditions. Findings The steady state calculated with the open circuit voltage condition was conformable with the analytical solution. In addition, the transient states of the spatial distributions of potentials and currents under the voltage- and current-controlled conditions were successfully differentiated, even though they eventually became the same steady state. Furthermore, the effects of dense materials assumed for interconnects and current collectors were found to not be influential. It is thus safe to conclude that the proposed method enables us to simulate any type of transient simulations regardless of controlling conditions. Practical implications Although only uniaxial models were tested in the numerical examples in this paper, the proposed method is applicable for arbitrary shapes of SOFC cells. Originality/value The value of this paper is that adequate numerical simulations by the proposed method properly captured the electrochemical transient transport phenomena in SOFC under various operational conditions, and that the applicability was confirmed by some numerical examples.

Experimental and theoretical investigation of mixed mode I/III brittle fracture of U-notched polystyrene components

2017 ◽  
Vol 53 (1) ◽  
pp. 15-25 ◽  
Author(s):  
A.R. Torabi ◽  
Behnam Saboori
Keyword(s):  
Brittle Fracture ◽  
Mixed Mode ◽  
General Purpose ◽  
Shear Loading ◽  
Mode I ◽  
Mean Stress ◽  
Plane Shear ◽  
Out Of Plane ◽  
Notch Tip ◽  
Stress Criteria

Brittle fracture of components made of the general-purpose polystyrene and weakened by an edge U-notch under combined tension/out-of-plane shear loading conditions (mixed mode I/III) has not been studied yet experimentally or theoretically. In this research, a recently developed loading fixture is employed for experimentally investigating the fracture of U-notched general-purpose polystyrene samples with various notch tip radii of 0.5, 1, 2 and 4 mm when they are subjected to different combinations of tension/out-of-plane shear. The samples are fabricated with four different notch tip radii with the purpose of assessing the influence of this geometrical parameter. The experimental values of fracture load and out-of-plane fracture angle are theoretically predicted by the two stress-based criteria of point stress and mean stress lately extended to general loading case of mixed mode I/II/III. It is shown that both the point stress and mean stress criteria provide acceptable predictions to fracture behavior of U-notched general-purpose polystyrene specimens. The critical distances needed for the point stress and mean stress criteria are determined based on the experimental results of the U-notched samples tested under pure mode I loading. No meaningful difference is found between the fracture loads and fracture initiation angles predicted by the point stress and mean stress criteria. It is also observed that as the mode III contribution in the applied mixed mode I/III loading increases, a larger total external load is needed for the fracture of U-notched general-purpose polystyrene specimens to occur.

CHAOTIC ATTRACTORS OF THE CONJUGATE LORENZ-TYPE SYSTEM

2007 ◽  
Vol 17 (11) ◽  
pp. 3929-3949 ◽  
Author(s):  
QIGUI YANG ◽  
GUANRONG CHEN ◽  
KUIFEI HUANG
Keyword(s):  
Numerical Simulations ◽  
Chaotic Dynamics ◽  
Lorenz System ◽  
Type System ◽  
Chaotic Attractors ◽  
Compound Structure ◽  
Chen System ◽  
Numerical Examples ◽  
Special Cases ◽  
Dynamical Properties

A new conjugate Lorenz-type system is introduced in this paper. The system contains as special cases the conjugate Lorenz system, conjugate Chen system and conjugate Lü system. Chaotic dynamics of the system in the parametric space is numerically and thoroughly investigated. Meanwhile, a set of conditions for possible existence of chaos are derived, which provide some useful guidelines for searching chaos in numerical simulations. Furthermore, some basic dynamical properties such as Lyapunov exponents, bifurcations, routes to chaos, periodic windows, possible chaotic and periodic-window parameter regions and the compound structure of the system are demonstrated with various numerical examples.

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.

Modeling of a Rolling Flexible Circular Ring

2015 ◽  
Vol 82 (11) ◽  
Author(s):  
François Robert Hogan ◽  
James Richard Forbes
Keyword(s):  
Numerical Simulations ◽  
Dynamic Model ◽  
Lagrange Multipliers ◽  
Flat Surface ◽  
Ritz Method ◽  
Free Vibrations ◽  
Circular Ring ◽  
Ring Rolling ◽  
Motion Equations ◽  
Out Of Plane

The motion equations of a rolling flexible circular ring are derived using a Lagrangian formulation. The in-plane flexural and out-of-plane twist-bending free vibrations are modeled using the Rayleigh–Ritz method. The motion equations of a flexible circular ring translating and rotating in space are first developed and then constrained to roll on a flat surface by introducing Lagrange multipliers. The motion equations developed capture the nonholonomic nature of the circular ring rolling without slip on a flat surface. Numerical simulations are performed to validate the dynamic model developed and to investigate the effect of the flexibility of the circular ring on its trajectory. The vibrations of the circular ring are observed to impact the ring's motion.

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