Volume 12, Issue 4
Optimization and Identification of the Shape in Elastoplastic Boundary Problems Using Parametric Integral Equation System (PIES)

Adv. Appl. Math. Mech., 12 (2020), pp. 1035-1056.

Published online: 2020-06

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• Abstract

The paper presents optimization and identification of the shape of elastoplastic structures. The optimization process is performed by the particle swarm method (PSO), while direct boundary value problems are solved using the parametric integral equation system (PIES). Modeling the boundary and the plastic zone in PIES is done globally by the small number of control points of parametric curves and surfaces. Such way of defining is very beneficial in comparison to so-called element methods (finite or boundary), because it reduces the number of design variables and does not enforce re-discretization during each shape change. Together with advantages of PSO it is an effective approach to solving optimization problems. There are three examples in the paper: two of identification of the shape and one in which an optimal shape is searched.

65M32, 65M38

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@Article{AAMM-12-1035, author = {Bołtuć , Agnieszka}, title = {Optimization and Identification of the Shape in Elastoplastic Boundary Problems Using Parametric Integral Equation System (PIES)}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {12}, number = {4}, pages = {1035--1056}, abstract = {

The paper presents optimization and identification of the shape of elastoplastic structures. The optimization process is performed by the particle swarm method (PSO), while direct boundary value problems are solved using the parametric integral equation system (PIES). Modeling the boundary and the plastic zone in PIES is done globally by the small number of control points of parametric curves and surfaces. Such way of defining is very beneficial in comparison to so-called element methods (finite or boundary), because it reduces the number of design variables and does not enforce re-discretization during each shape change. Together with advantages of PSO it is an effective approach to solving optimization problems. There are three examples in the paper: two of identification of the shape and one in which an optimal shape is searched.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0100}, url = {http://global-sci.org/intro/article_detail/aamm/16939.html} }
TY - JOUR T1 - Optimization and Identification of the Shape in Elastoplastic Boundary Problems Using Parametric Integral Equation System (PIES) AU - Bołtuć , Agnieszka JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 1035 EP - 1056 PY - 2020 DA - 2020/06 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2019-0100 UR - https://global-sci.org/intro/article_detail/aamm/16939.html KW - Identification, optimization, plasticity, nonlinear, parametric integral equation system (PIES), particle swarm optimization (PSO). AB -

The paper presents optimization and identification of the shape of elastoplastic structures. The optimization process is performed by the particle swarm method (PSO), while direct boundary value problems are solved using the parametric integral equation system (PIES). Modeling the boundary and the plastic zone in PIES is done globally by the small number of control points of parametric curves and surfaces. Such way of defining is very beneficial in comparison to so-called element methods (finite or boundary), because it reduces the number of design variables and does not enforce re-discretization during each shape change. Together with advantages of PSO it is an effective approach to solving optimization problems. There are three examples in the paper: two of identification of the shape and one in which an optimal shape is searched.

Agnieszka Bołtuć. (2020). Optimization and Identification of the Shape in Elastoplastic Boundary Problems Using Parametric Integral Equation System (PIES). Advances in Applied Mathematics and Mechanics. 12 (4). 1035-1056. doi:10.4208/aamm.OA-2019-0100
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