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

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

Terahertz CMOS Frequency Generator Using Linear Superposition Technique

2008 ◽  
Vol 43 (12) ◽  
pp. 2730-2738 ◽  
Author(s):  
Daquan Huang ◽  
Tim R. LaRocca ◽  
Mau-Chung Frank Chang ◽  
Lorene Samoska ◽  
Andy Fung ◽  
...  
Keyword(s):  
Linear Superposition ◽  
Frequency Generator ◽  
Superposition Technique

Optimum Synthesis of Plane Mechanisms for the Generation of Paths and Rigid-Body Positions via the Linear Superposition Technique

1975 ◽  
Vol 97 (1) ◽  
pp. 340-346 ◽  
Author(s):  
C. Bagci ◽  
In-Ping Jack Lee
Keyword(s):  
Rigid Body ◽  
System Design ◽  
Linear Superposition ◽  
Loop Closure ◽  
Numerical Examples ◽  
Optimum Synthesis ◽  
Closure Equation ◽  
Superposition Technique

A method of optimum synthesis of plane mechanisms for the generation of paths and rigid-body positions is presented. The method is developed for the four-bar plane mechanism with six and eight unknown dimensions. Dimensions of the optimum mechanism are determined by minimizing the error in the loop-closure equations for N design points on the path, along with the loop-closure equation of the linkage, where N is not limited by the number of the unknown dimensions of the system. Design equations are linearized by the method of linear superposition. Solution of design equations requires no iterations, and it leads to a series of optimum mechanisms of different efficiency of approximation. Numerical examples are given.

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.

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