Simulation of Dislocations in Ordered Ni3Al by Atomic Stiffness Matrix Method

1995 ◽  
Vol 408 ◽  
Author(s):  
Y. E. Hsu ◽  
T. K. Chaki
Keyword(s):  
Stiffness Matrix ◽  
Matrix Method ◽  
Linear Equations ◽  
Antiphase Boundary ◽  
Shockley Partial ◽  
Embedded Atom ◽  
Structure And Motion ◽  
Directional Bonding ◽  
Edge Dislocations ◽  
Applied Stresses

AbstractA simulation of structure and motion of edge dislocations in ordered Ni3Al was performed by atomic stiffness matrix method. In this method the equilibrium positions of the atoms were obtained by solving a set of linear equations formed by a stiffness matrix, whose terms consisted of derivatives of the interaction potential of EAM (embedded atom method) type. The superpartial dislocations, separated by an antiphase boundary (APB) on (111), dissociated into Shockley partials with complex stacking faults (CSF) on (111) plane. The core structure, represented by the Burgers vector density distribution and iso-strain contours, changed under applied stresses as well as upon addition of boron. The separation between the superpartials changed with the addition of B and antisite Ni. As one Shockley partial moved out to the surface. a Shockley partial in the interior moved a large distance to join the lone one near the surface, leaving behind a long CSF strip. The decrease in the width of the APB upon addition of B and antisite Ni has been explained by a reduction of the strength of directional bonding between Ni and Al as well as by the dragging of B atmosphere by the superpartials.

Simulation Of Dislocations In Ordered Ni3Al By Atomic Stiffness Matrix Method

1995 ◽  
Vol 409 ◽  
Author(s):  
Y. E. Hsu ◽  
T.K. Chaki
Keyword(s):  
Stiffness Matrix ◽  
Matrix Method ◽  
Linear Equations ◽  
Antiphase Boundary ◽  
Shockley Partial ◽  
Embedded Atom ◽  
Structure And Motion ◽  
Directional Bonding ◽  
Edge Dislocations ◽  
Applied Stresses

AbstractA simulation of structure and motion of edge dislocations in ordered Ni3Al was performed by atomic stiffness matrix method. In this method the equilibrium positions of the atoms were obtained by solving a set of linear equations formed by a stiffness matrix, whose terms consisted of derivatives of the interaction potential of EAM (embedded atom method) type. The superpartial dislocations, separated by an antiphase boundary (APB) on (111), dissociated into Shockley partials with complex stacking faults (CSF) on (111) plane. The core structure, represented by the Burgers vector density distribution and iso-strain contours, changed under applied stresses as well as upon addition of boron. The separation between the superpartials changed with the addition of B and antisite Ni. As one Shockley partial moved out to the surface, a Shockley partial in the interior moved a large distance to join the lone one near the surface, leaving behind a long CSF strip. The decrease in the width of the APB upon addition of B and antisite Ni has been explained by a reduction of the strength of directional bonding between Ni and Al as well as by the dragging of B atmosphere by the superpartials.

The stiffness matrix method

Structures ◽  
2000 ◽  
pp. 239-285
Author(s):  
M. S. Williams ◽  
J. D. Todd
Keyword(s):  
Stiffness Matrix ◽  
Matrix Method

Computer Simulation of Creation and Motion of Edge Dislocations in Face Centered Crystals

1994 ◽  
Vol 356 ◽  
Author(s):  
N. Tajima ◽  
T. Nozaki ◽  
T. Hirade ◽  
Y. Kogure ◽  
Masao Doyama
Keyword(s):  
Molecular Dynamics ◽  
Computer Simulation ◽  
Edge Dislocation ◽  
Embedded Atom ◽  
Small Crystals ◽  
Face Centered ◽  
Edge Dislocations

AbstractComplete and dissociated edge dislocations were created near the center of the surface (101) of aluminum small crystals whose surfaces are (111), (111), (101), (101). (121) and (121). Molecular dynamics with N-body embedded atom potentials were used. Higher stress is needed to create a complete edge dislocation than to create a dissociated dislocation.

A Subspace-Projected Approximate Matrix Method for Systems of Linear Equations

2013 ◽  
Vol 3 (2) ◽  
pp. 120-137 ◽  
Author(s):  
Jan Brandts ◽  
Ricardo R. da Silva
Keyword(s):  
Matrix Method ◽  
Eigenvalue Problems ◽  
Linear Equations ◽  
Computational Cost ◽  
Systems Of Linear Equations ◽  
Definition Of ◽  
Specific Sense ◽  
Low Computational Cost ◽  
Minimal Residual Methods ◽  
Linear Systems Of Equations

AbstractGiven two n × n matrices A and A0 and a sequence of subspaces with dim the k-th subspace-projected approximated matrix Ak is defined as Ak = A + Πk(A0 − A)Πk, where Πk is the orthogonal projection on . Consequently, Akν = Aν and ν*Ak = ν*A for all Thus is a sequence of matrices that gradually changes from A0 into An = A. In principle, the definition of may depend on properties of Ak, which can be exploited to try to force Ak+1 to be closer to A in some specific sense. By choosing A0 as a simple approximation of A, this turns the subspace-approximated matrices into interesting preconditioners for linear algebra problems involving A. In the context of eigenvalue problems, they appeared in this role in Shepard et al. (2001), resulting in their Subspace Projected Approximate Matrix method. In this article, we investigate their use in solving linear systems of equations Ax = b. In particular, we seek conditions under which the solutions xk of the approximate systems Akxk = b are computable at low computational cost, so the efficiency of the corresponding method is competitive with existing methods such as the Conjugate Gradient and the Minimal Residual methods. We also consider how well the sequence (xk)k≥0 approximates x, by performing some illustrative numerical tests.

Static Elastic-Plastic Analysis of a Pipe Structure by the Transfer Matrix Method

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Masayuki Arai ◽  
Shoichi Kuroda ◽  
Kiyohiro Ito
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Stiffness Matrix ◽  
Matrix Method ◽  
Frame Structure ◽  
Pipe System ◽  
Curved Pipe ◽  
Elastic Plastic ◽  
Complex Problems ◽  
Element Method

Abstract Pipe systems have been widely used in industrial plants such as power stations. In these systems, the displacement and stress distributions often need to be predicted. Analytical and numerical methods, such as the finite element method (FEM), boundary element method (BEM), and frame structure method (FSM), are typically adopted to predict these distributions. The analytical methods, which can only be applied to problems with simple geometries and boundary conditions, are based on the Timoshenko beam theory. Both FEM and BEM can be applied to more complex problems, although this usually requires a stiffness matrix with a large number of degrees-of-freedom. In FSM, although the structure is modeled by a beam element, the stiffness matrix still becomes large; furthermore, the matrix size needed in FEM and BEM is also large. In this study, the transfer matrix method, which is simply referred to as TMM, is studied to effectively solve complex problems, such as a pipe structure under a small size stiffness matrix. The fundamental formula is extended to a static elastic-plastic problem. The efficiency and simplicity of this method in solving a space-curved pipe system that involves an elbow are demonstrated. The results are compared with those obtained by FEM to verify the performance of the method.

Effective stiffness matrix method for predicting the dispersion curves in general anisotropic composites

2019 ◽  
Vol 89 (9) ◽  
pp. 1923-1938
Author(s):  
Anvesh R. Nandyala ◽  
Ashish K. Darpe ◽  
Satinder P. Singh
Keyword(s):  
Stiffness Matrix ◽  
Matrix Method ◽  
Dispersion Curves ◽  
Effective Stiffness
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