Three-dimensional hydrodynamics on finite elements. Part II: Non-linear time-stepping model

1991 ◽  
Vol 12 (6) ◽  
pp. 507-533 ◽  
Author(s):  
Daniel R. Lynch ◽  
Francisco E. Werner
Keyword(s):  
Finite Elements ◽  
Linear Time ◽  
Three Dimensional ◽  
Time Stepping ◽  
Non Linear

Physical nearest-neighbour models and non-linear time-series. II Further discussion of approximate solutions and exact equations

1972 ◽  
Vol 9 (01) ◽  
pp. 76-86
Author(s):  
M. S. Bartlett
Keyword(s):  
Time Series ◽  
Correlation Functions ◽  
Linear Time ◽  
Three Dimensional ◽  
Approximate Solutions ◽  
Nearest Neighbour ◽  
Spatial Correlations ◽  
Orthogonal Expansions ◽  
Non Linear ◽  
Time Series Approach

The approximate two- and three-dimensional solutions for spatial correlations, using the non-linear time-series approach for nearest-neighbour systems developed in my previous paper, are further discussed. Orthogonal expansions for the correlation functions are also developed which determine with this approach, though so far only in principle, the exact solutions.

Free Undamped Vibration of Geometrically Non-Linear Cable Structures

1997 ◽  
Author(s):  
Alan S. K. Kwan
Keyword(s):  
Finite Elements ◽  
Mass Matrix ◽  
Three Dimensional ◽  
Geometrically Nonlinear ◽  
Theoretical Derivation ◽  
Cable Structures ◽  
Non Linear ◽  
Membrane Models ◽  
High Degree ◽  
Axial Element

The stiffness relationship and the distributed mass matrix for a geometrically nonlinear three dimensional straight axial element is derived for use in prestressed cablenet structures. The justification for the use of a linearised stiffness relationship is provided through a theoretical derivation. Results using this simple element have shown a high degree of correlation with results to those available in the literature obtained with more complex curved finite elements, analogous membrane models and other techniques.

A Non-Linear Numerical Method for the Simulation of Parametric Roll Resonance in Regular Waves

2008 ◽  
Author(s):  
T. M. Ahmed ◽  
E. J. Ballard ◽  
D. A. Hudson ◽  
P. Temarel
Keyword(s):  
Numerical Method ◽  
Potential Flow ◽  
Degrees Of Freedom ◽  
Linear Time ◽  
Three Dimensional ◽  
Regular Waves ◽  
Time Step ◽  
Parametric Roll ◽  
Non Linear ◽  
Parametric Roll Resonance

In this paper, a non-linear time-domain method is used for the prediction of parametric roll resonance in regular waves, assuming the ship to be a system with three degrees of freedom in heave, pitch and roll. Coupled heave and pitch motions are obtained using a three-dimensional frequency-domain potential flow method which also provides the requisite hydrodynamic data of the ship in roll i.e. the potential flow based added inertia and damping. Periodic changes in the underwater hull geometry due to heave, pitch and the wave profile are calculated as a function of the instantaneous breadth. This is carried out using a two-dimensional approach i.e. for sections along the ship and at each time step. This formulation leads to a mathematical model that represents the roll equation of motion with third order non-linearities in the parametric excitation terms. Non-linearities in the roll damping and restoring terms are also accounted for. This method has been applied to two different hull forms, a post-Panamax C11 class containership and a transom stern Trawler, both travelling in regular waves. Special attention is focused on the influence of different operational aspects on parametric roll. Obtained results demonstrate that this numerical method succeeds in producing results similar to those available in the literature, both numerical and experimental.

Physical nearest-neighbour models and non-linear time-series

1971 ◽  
Vol 8 (2) ◽  
pp. 222-232 ◽  
Author(s):  
M. S. Bartlett
Keyword(s):  
Equilibrium Distribution ◽  
Linear Models ◽  
Linear Time ◽  
Three Dimensional ◽  
Approximate Solutions ◽  
Nearest Neighbour ◽  
Spatial Equilibrium ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Non Linear

A general class of spatial-temporal Markov processes is defined leading to the standard spatial equilibrium distribution for nearest-neighbour models on a multi-dimensional lattice. Physical properties are obtainable from the marginal spatial spectral function. However, only the simplest one-dimensional case corresponds to a linear model with a readily derived spectrum. Non-linear models corresponding to two- and three-dimensional lattices are presented in their simplest terms, and a preliminary discussion of approximate solutions is included.

Three Dimensional Seismic Response Analyses on the Isolated Spatial Beam String Structure

2011 ◽  
Vol 255-260 ◽  
pp. 2526-2531
Author(s):  
Nan Zhao ◽  
Yang Jiang
Keyword(s):  
Linear Time ◽  
Three Dimensional ◽  
Great Influence ◽  
Time History ◽  
Gravity Load ◽  
Spatial Beam ◽  
Non Linear ◽  
String Structure ◽  
Rare Earthquake ◽  
Filtering Effect

Three dimensional seismic responses of an isolated spatial beam string structure are studied by applying the non-linear finite element theory. The filtering effect of the main structure, which amplifies the ground input, is investigated. The results indicate that the vertical rare earthquake has great influence on the isolated spatial beam string structure, and stresses of cables, frames and slab shells under vertical rare earthquake are all much greater than that under gravity load. Results of non-linear time history analysis show that elements’ stresses are in elastic stage, thus the spatial beam string structure with isolation keeps safe under rare earthquake.

scholarly journals AN EFFICIENT CO-ROTATIONAL FEM FORMULATION USING A PROJECTOR MATRIX

2016 ◽  
Vol 14 (2) ◽  
pp. 227 ◽  
Author(s):  
Viet Anh Nguyen ◽  
Manfred Zehn ◽  
Dragan Marinković
Keyword(s):  
Finite Elements ◽  
Deformation Gradient ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Internal Force ◽  
Linear Analysis ◽  
Efficient Computation ◽  
Tangent Stiffness Matrix ◽  
Non Linear ◽  
Internal Force Vector

Co-rotational finite element (FE) formulations can be seen as a very efficient approach to resolving geometrically nonlinear problems in the field of structural mechanics. A number of co-rotational FE formulations have been well documented for shell and beam structures in the available literature. The purpose of this paper is to present a co-rotational FEM formulation for fast and highly efficient computation of large three-dimensional elastic deformations. On the one hand, the approach aims at a simple way of separating the element rigid-body rotation and the elastic deformational part by means of the polar decomposition of deformation gradient. On the other hand, a consistent linearization is introduced to derive the internal force vector and the tangent stiffness matrix based on the total Lagrangian formulation. It results in a non-linear projector matrix. In this way, it ensures the force equilibrium of each element and enables a relatively straightforward upgrade of the finite elements for linear analysis to the finite elements for geometrically non-linear analysis. In this work, a simple 4-node tetrahedral element is used. To demonstrate the efficiency and accuracy of the proposed formulation, nonlinear results from ABAQUS are used as a reference.

scholarly journals Diverse Novel Stable Traveling Wave Solutions of the Advanced or Voltage Spectrum of Electrified Transmission Through Fractional Non-linear Model

2021 ◽  
Vol 9 ◽  
Author(s):  
Chen Yue ◽  
Li Wu ◽  
A. A. Mousa ◽  
Dianchen Lu ◽  
Mostafa M. A. Khater
Keyword(s):  
Traveling Wave ◽  
Electromagnetic Waves ◽  
Linear Time ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Evolutionary Equations ◽  
Time Space ◽  
Different Types ◽  
Non Linear

This study analyzes the exact solutions of the compliance fractional non-linear time–space telegraph (FNLTST) equation by Oliver Heaviside in 1880 via three non-applied analytical schemes. The solutions obtained to define the advanced or voltage spectrum of electrified transmission with day-to-day distance from electrical communication or the application of electromagnetic waves. Many new solutions are obtained, and three distinct styles of drawings are introduced (two-dimensional, three-dimensional, and density plots). Furthermore, stability characterization of the solutions is addressed using the properties of the Hamiltonian system. The originality of this study is shown by matching the solutions built with solutions produced previously using various analytical methods. Overall, the success of the three systems demonstrates their quality, intensity, and capacity to cope with several different types of non-linear evolutionary equations.

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