Characterization of AE solution sets of parametric linear systems based on the techniques of convex sets

Rzeżuchowski, Tadeusz; Wa̧sowski, J.

doi:10.1016/j.laa.2017.07.035

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…The The descriptions of united solution set Ξ uni described in the present paper are characterized by the form described above. The descriptions can be found in the papers [23][24][25]. They are presented directly or as special cases of descriptions related to wider class of the families of linear systems.…”

Section: Problem Formulationmentioning

confidence: 99%

Application of the Theory of Convex Sets for Engineering Structures with Uncertain Parameters

Pełczyński

2020

Applied Sciences

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The present paper discusses an innovative approach providing the solution sets of engineering structures with uncertain parameters. The approach is based on the properties of convex sets and can be applied to structures described by the system of algebraic equations. The present paper focuses on trusses and frames applications, but in general it can be applied to various structures made of thin and thick bars and some plate and shell problems. The uncertain parameters are assumed to be independent. In addition, calculations are valid for any level of uncertainty and the obtained solution sets are exact within the assumed theory and are insensitive for perturbed data. Furthermore, solutions obtained by the present approach can be considered as benchmark solutions and can be used as a reference for other algorithms. The presented formulae allow the analysis of the influence of uncertain parameters on the behaviour of the structure. The presented considerations are illustrated by calculation of two truss examples.

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Section: Problem Formulationmentioning

confidence: 99%

Application of the Theory of Convex Sets for Engineering Structures with Uncertain Parameters

Pełczyński

2020

Applied Sciences

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“…The direct algebraic formulation in which the matrix form of the solving system of displacement equations is the product of three matrices with diagonal constitutive matrix [3,4] is a specific mathematical problem within the theory of frames. This form is used, among others, in topological optimization [4,5], analysis of systems with large uncertainties [6], the use of convex sets techniques [7], plastic range of the analysis [8], and shakedown of elastic-plastic structures [9]. Potential applications of the formulation as well as of the present paper can be easily extended for the gridwork and framework methods in plate theories [10], including moderately thick plates.…”

Section: Introductionmentioning

confidence: 99%

Algebraic Formulation for Moderately Thick Elastic Frames, Beams, Trusses, and Grillages within Timoshenko Theory

Pełczyński

Gilewski

2019

Mathematical Problems in Engineering

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The paper is dedicated to the algebraic formulation of elastic frame equations. The obtained set of equations describe deformations of moderately thick frames made of both compressible and incompressible bars, grillages of rigid or pin-joined connections, and trusses. Plane as well as space structures are presented. The paper is an extension of the article of T. Lewiński written in 2001 related to thin bars. Algebraic equations with diagonal constitutive matrix are original and suitable for various engineering applications and for educational purposes.

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Tolerance-localized and control-localized solutions of interval linear equations system and their application to course assignment problem

Leela-apiradee

Gorka

Burimas

et al. 2022

Applied Mathematics and Computation

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Characterization of AE solution sets of parametric linear systems based on the techniques of convex sets

Cited by 3 publications

References 14 publications

Application of the Theory of Convex Sets for Engineering Structures with Uncertain Parameters

Application of the Theory of Convex Sets for Engineering Structures with Uncertain Parameters

Algebraic Formulation for Moderately Thick Elastic Frames, Beams, Trusses, and Grillages within Timoshenko Theory

Tolerance-localized and control-localized solutions of interval linear equations system and their application to course assignment problem

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