scholarly journals Non-linear Superposition Operators on Space C ([0, 1], E)

1994 ◽  
Vol 181 (2) ◽  
pp. 385-391 ◽  
Author(s):  
N.A. Yerzakova
Keyword(s):  
Linear Superposition ◽  
Superposition Operators ◽  
Non Linear

Evaluating Shakedown for Structures Based on the Element Bearing-Ratio

2011 ◽  
Vol 137 ◽  
pp. 16-23 ◽  
Author(s):  
Wei Zhang ◽  
Lu Feng Yang ◽  
Chuan Xiong Fu ◽  
Jian Wang
Keyword(s):  
Yield Criterion ◽  
Solution Procedure ◽  
Superposition Method ◽  
Linear Superposition ◽  
Non Linear Programming ◽  
Elastic Plastic ◽  
Non Linear ◽  
Efficiency And Effectiveness ◽  
Linear Programming Formulation ◽  
Element Bearing

Based on Melan’s theorem, an improved numerical solution procedure for evaluating shakedown loads by non-linear superposition method is presented, and the relationship between the classical non-linear programming formulation of shakedown problem and the numerical method is disclosed. The stress term in classical optimization problem is replaced by the element bearing-ratio (EBR) in the procedure, and series of residual EBR fields can be generated by the D-value of the elastic-plastic EBR fields and the elastic EBR fields at every incremental loading step. The shakedown load is determined by performing the incremental non-linear static analysis when the yield criterion is arrived either by the elastic-plastic EBR fields or residual EBR fields. By introducing the EBR, the proposed procedure can be easily used to those complex structures with multi-material and complicated configuration. The procedure is described in detail and some numerical results, that show the efficiency and effectiveness of the proposed method, are reported and discussed.

Non-linear superposition of monopoles

1981 ◽  
Vol 192 (1) ◽  
pp. 141-158 ◽  
Author(s):  
Peter Forgács ◽  
Zalán Horváth ◽  
László Palla
Keyword(s):  
Linear Superposition ◽  
Non Linear

scholarly journals The dressing method as non linear superposition in sigma models

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Dimitrios Katsinis ◽  
Ioannis Mitsoulas ◽  
Georgios Pastras
Keyword(s):  
Differential Equations ◽  
Sigma Models ◽  
Sigma Model ◽  
Formal Solution ◽  
Superposition Principle ◽  
Auxiliary System ◽  
Linear Sigma Model ◽  
Dressing Method ◽  
Linear Superposition ◽  
Non Linear

Abstract We apply the dressing method on the Non Linear Sigma Model (NLSM), which describes the propagation of strings on ℝ × S2, for an arbitrary seed. We obtain a formal solution of the corresponding auxiliary system, which is expressed in terms of the solutions of the NLSM that have the same Pohlmeyer counterpart as the seed. Accordingly, we show that the dressing method can be applied without solving any differential equations. In this context a superposition principle emerges: the dressed solution is expressed as a non-linear superposition of the seed with solutions of the NLSM with the same Pohlmeyer counterpart as the seed.

scholarly journals Spiral instabilities: linear and non-linear effects

2020 ◽  
Vol 500 (4) ◽  
pp. 5043-5055
Author(s):  
J A Sellwood ◽  
R G Carlberg
Keyword(s):  
Linear Theory ◽  
Normal Mode ◽  
Disc Galaxy ◽  
Linear Superposition ◽  
Non Linear ◽  
Wake Patterns ◽  
Galaxy Model ◽  
Low Mass ◽  
Linear Effects ◽  
The Masses

ABSTRACT We present a study of the spiral responses in a stable disc galaxy model to co-orbiting perturbing masses that are evenly spaced around rings. The amplitudes of the responses, or wakes, are proportional to the masses of the perturbations, and we find that the response to a low-mass ring disperses when it is removed – behaviour that is predicted by linear theory. Higher mass rings cause non-linear changes through scattering at the major resonances, provoking instabilities that were absent before the scattering took place. The separate wake patterns from two rings orbiting at differing frequencies produce a net response that is an apparently shearing spiral. When the rings have low mass, the evolution of the simulation is both qualitatively and quantitatively reproduced by linear superposition of the two separate responses. We argue that apparently shearing transient spirals in simulations result from the superposition of two or more steadily rotating patterns, each of which is best accounted for as a normal mode of the non-smooth disc.

Including Roll in the Evaluation of Bending Loads for the Hull Girder in a Seaway

2004 ◽  
Author(s):  
Enrico Rizzuto
Keyword(s):  
Bending Strength ◽  
Extreme Value ◽  
Roll Angle ◽  
Roll Motion ◽  
Linear Superposition ◽  
Hull Girder ◽  
Bending Load ◽  
Non Linear ◽  
Wave Induced ◽  
Weight Force

The longitudinal strength of the hull girder is traditionally verified by linear superposition of still water (static) loads to wave induced (dynamic) loads. Belonging to the former class, gravitational effects are considered always as directed along the plane of symmetry of the ship, as the static equilibrium position corresponds to the ship floating with a neutral heel angle. This is not the case for a ship in a seaway, as the weight will act in reality along the instantaneous ‘true vertical’, which is not in general contained in the symmetry plane, due to ship motions. The actual direction of the weight force represents one of the non-linear aspects of the seakeeping problem, as the direction of one of the input external forces (weight) depends on the instantaneous roll angle (representing an output of the study). The present paper investigates the above subject, trying to quantify this retro-action effect with reference to the verification of the bending strength of the hull girder. The attention is focussed on the magnitude of the horizontal bending component generated by the inclined direction of the weight force as compared to the bending component induced by waves in the same plane (normal to the plane of symmetry of the ship). The subject is discussed on the basis of a linear seakeeping analysis, which is not able to model properly the non-linear aspects above recalled, but provides anyway as output an estimate of roll motions that can be used to evaluate in a qualitative way how large would be the horizontal load component due to weight, not accounted for in equilibrium equations. The statistical correlation between the wave induced bending load and roll angle is treated with the simplified assumption of a Gaussian joint distribution and a consistent model for the combination of horizontal and vertical bending components is established. The reference situation is chosen as corresponding to the extreme value of the vertical wave induced component, and distribution for the horizontal wave bending component and of roll motion are conditioned to the occurrence of such extreme value. This can be seen as an extension of Turkstra’s rule for the combination of loads to the case of correlated loads. The stochastic model is applied in the evaluation of the hull girder reliability for a test case and the conditioned probability distribution of roll motion at the failure point is derived in order to discuss the influence of a possible inclusion of roll effects in the verification of the hull girder bending strength.

scholarly journals Using singular value decomposition for generalized linear autoregression of signals

2018 ◽  
Vol 4 (1) ◽  
pp. 375-378 ◽  
Author(s):  
Thomas Schanze
Keyword(s):  
Singular Value Decomposition ◽  
Least Squares ◽  
Linear Combination ◽  
Singular Value ◽  
Autoregressive Models ◽  
Current Signal ◽  
Linear Superposition ◽  
Biomedical Signals ◽  
Non Linear ◽  
Value Decomposition

AbstractAutoregressive models (AR) are fundamental for analysis, representation, and prediction of signals. AR modelling uses the premise that past signal values influence current ones. This influence is causal and is modelled as a linear superposition, because a weighted addition of past values is used. The calculation of the required linear superposition parameters or weights can be done by the classical Yule-Walker approach or by least squares procedures. Here we show how to use singular value decomposition (SVD) for generalized linear autoregression (GLAR), i.e. using SVD to compute the weights of a linear combination of functions of given signal values and to check or optimize the GLAR model. The GLAR approach opens the possibility to take directly into account non-linear influences from past to current signal values. T he potential of this approach for analysis and representation is presented and demonstrated for simulated signals, i.e. pure and noisy sequences of non-linear recursions, and biomedical signals.

APPLICABILITY CONDITIONS OF A NON-LINEAR SUPERPOSITION TECHNIQUE

1997 ◽  
Vol 200 (1) ◽  
pp. 3-14 ◽  
Author(s):  
F. Pellicano ◽  
F. Mastroddi
Keyword(s):  
Linear Superposition ◽  
Non Linear ◽  
Superposition Technique
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