On classical mechanical systems with non-linear constraints

2004 ◽  
Vol 49 (3-4) ◽  
pp. 385-417 ◽  
Author(s):  
Gláucio Terra ◽  
Marcelo H. Kobayashi
Keyword(s):  
Mechanical Systems ◽  
Linear Constraints ◽  
Non Linear

scholarly journals Automated handling of complex chemical structures in Z-matrix coordinates - the chemcoord library

2021 ◽  
Author(s):  
Oskar Weser ◽  
Björn Hein Hanke ◽  
Ricardo Mata
Keyword(s):  
Structural Changes ◽  
Molecular System ◽  
Linear Constraints ◽  
Analytical Geometry ◽  
Cartesian Coordinates ◽  
Chemical Structures ◽  
Automated Method ◽  
Non Linear ◽  
Linearly Constrained ◽  
Automated Handling

In this work, we present a fully automated method for the construction of chemically meaningful sets of non-redundant internal coordinates (also commonly denoted as Z-matrices) from the cartesian coordinates of a molecular system. Particular focus is placed on avoiding ill-definitions of angles and dihedrals due to linear arrangements of atoms, to consistently guarantee a well-defined transformation to cartesian coordinates, even after structural changes. The representations thus obtained are particularly well suited for pathway construction in double-ended methods for transition state search and optimisations with non-linear constraints. Analytical gradients for the transformation between the coordinate systems were derived for the first time, which allows analytical geometry optimizations purely in Z-matrix coordinates. The geometry optimisation was coupled with a Symbolic Algebra package to support arbitrary non-linear constraints in Z-matrix coordinates, while retaining analytical energy gradient conversion. Sample applications are provided for a number of common chemical reactions and illustrative examples where these new algorithms can be used to automatically produce chemically reasonable structure interpolations, or to perform non-linearly constrained optimisations of molecules.

Algorithms for non-linear constraints

2009 ◽  
pp. 723-747
Author(s):  
Ross Baldick
Keyword(s):  
Linear Constraints ◽  
Non Linear

Non-linear Dynamics of Structures and Mechanical Systems

2006 ◽  
Vol 84 (24-25) ◽  
pp. 1561-1564
Author(s):  
P. Ribeiro ◽  
B.H.V. Topping ◽  
C.A. Mota Soares
Keyword(s):  
Mechanical Systems ◽  
Linear Dynamics ◽  
Non Linear

Combining regression trees and the finite element method to define stress models of highly non-linear mechanical systems

2009 ◽  
Vol 44 (6) ◽  
pp. 491-502 ◽  
Author(s):  
R Lostado ◽  
F J Martínez-De-Pisón ◽  
A Pernía ◽  
F Alba ◽  
J Blanco
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mechanical Systems ◽  
Regression Trees ◽  
Support Vector ◽  
The Finite Element Method ◽  
Multiple Contacts ◽  
Non Linear ◽  
Instance Space ◽  
Element Method

This paper demonstrates that combining regression trees with the finite element method (FEM) may be a good strategy for modelling highly non-linear mechanical systems. Regression trees make it possible to model FEM-based non-linear maps for fields of stresses, velocities, temperatures, etc., more simply and effectively than other techniques more widely used at present, such as artificial neural networks (ANNs), support vector machines (SVMs), regression techniques, etc. These techniques, taken from Machine Learning, divide the instance space and generate trees formed by submodels, each adjusted to one of the data groups obtained from that division. This local adjustment allows good models to be developed when the data are very heterogeneous, the density is very irregular, and the number of examples is limited. As a practical example, the results obtained by applying these techniques to the analysis of a vehicle axle, which includes a preloaded bearing and a wheel, with multiple contacts between components, are shown. Using the data obtained with FEM simulations, a regression model is generated that makes it possible to predict the contact pressures at any point on the axle and for any condition of load on the wheel, preload on the bearing, or coefficient of friction. The final results are compared with other classical linear and non-linear model techniques.

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