The Statement of Optimal Design Problem with the Cusp Catastrophe Theory Application

2014 ◽  
Vol 709 ◽  
pp. 530-533 ◽  
Author(s):  
Aleksandr Vasilyevich Pitukhin ◽  
Igor Skobtsov
Keyword(s):  
Optimal Design ◽  
Catastrophe Theory ◽  
Design Problem ◽  
Reliability Function ◽  
Function Evaluation ◽  
Statistical Linearization ◽  
Cusp Catastrophe ◽  
Optimal Design Problem ◽  
Linearization Methods ◽  
Theory Application

The purpose of this paper is to present the catastrophe theory method for the optimal design of machine components. A brief description of the cusp catastrophe is presented in the introduction. The statement of optimal design problem is given in the second part of the paper. A single criterion design is presented; the reliability function is used as the objective function. The last part is devoted to probability approach. Manage variables are viewed as stochastic quantities, analytical and statistical linearization methods are used for the reliability function evaluation.

The Statistical Catastrophe Theory and Optimal Probability Based Design

2015 ◽  
Vol 741 ◽  
pp. 283-286 ◽  
Author(s):  
Aleksandr Vasilyevich Pitukhin ◽  
Igor Skobtsov
Keyword(s):  
Optimal Design ◽  
Catastrophe Theory ◽  
Moment Method ◽  
Reliability Function ◽  
Linearization Method ◽  
Function Evaluation ◽  
Statistical Linearization ◽  
Stationary Processes ◽  
Short Introduction ◽  
Optimal Probability

This paper deals with the statistical catastrophe theory method for the optimal design of machine components. A short introduction to the catastrophe theory is presented, the statement of optimal design problem is given in the first part of the paper. A single criterion design is presented; the reliability function is used as the objective function. The last part is focused on probability approach. Manage variables are viewed as random stationary processes, statistical linearization method and Pearson moment method are used for the reliability function evaluation.

scholarly journals Regularity results for an optimal design problem with a volume constraint

2014 ◽  
Vol 20 (2) ◽  
pp. 460-487 ◽  
Author(s):  
Menita Carozza ◽  
Irene Fonseca ◽  
Antonia Passarelli di Napoli
Keyword(s):  
Optimal Design ◽  
Design Problem ◽  
Volume Constraint ◽  
Optimal Design Problem ◽  
Regularity Results

Existence and regularity for mixtures of micromagnetic materials

2006 ◽  
Vol 462 (2072) ◽  
pp. 2225-2243 ◽  
Author(s):  
Emilio Acerbi ◽  
Irene Fonseca ◽  
Giuseppe Mingione
Keyword(s):  
Optimal Design ◽  
Bounded Variation ◽  
Design Problem ◽  
Optimal Design Problem ◽  
New Model

A new model for the energy of a mixture of micromagnetic materials is introduced within the context of functions with special bounded variation. Existence and regularity for the solution of an optimal design problem in micromagnetics are obtained.

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