Strength optimization of structural elements by means of optimal control

This paper investigates the optimal shaping of the web height of an I-section steel portal frame. The problem is formulated as a control theory task. From a mathematical perspective, the task involves solving the multipoint boundary value problem for the system of forty-three differential equations. The solution is compared to results obtained from the finite element software Abaqus.

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Asymptotic Solution of a Boundary-Value Problem for Linear Singularly-Perturbed Functional Differential Equations Arising in Optimal Control Theory

Journal of Optimization Theory and Applications ◽

10.1023/a:1004651430364 ◽

2000 ◽

Vol 106 (2) ◽

pp. 309-335 ◽

Cited By ~ 21

Author(s):

V. Y. Glizer

Keyword(s):

Optimal Control ◽

Differential Equations ◽

Control Theory ◽

Boundary Value Problem ◽

Asymptotic Solution ◽

Optimal Control Theory ◽

Boundary Value ◽

Functional Differential Equations ◽

Singularly Perturbed ◽

Functional Differential

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Optimal Control Theory Applied to Systems Described by Partial Differential Equations

Advances in Control Systems ◽

10.1016/b978-1-4831-6715-2.50010-7 ◽

1968 ◽

pp. 221-316 ◽

Cited By ~ 27

Author(s):

WILLIAM L. BROGAN

Keyword(s):

Optimal Control ◽

Partial Differential Equations ◽

Differential Equations ◽

Control Theory ◽

Optimal Control Theory ◽

Partial Differential

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On Effective Stochastic Galerkin Finite Element Method for Stochastic Optimal Control Governed by Integral-Differential Equations with Random Coefficients

Journal of Computational Mathematics ◽

10.4208/jcm.1611-m2016-0676 ◽

2018 ◽

Vol 36 (2) ◽

pp. 183-201 ◽

Cited By ~ 1

Author(s):

Wanfang Shen and Liang Ge

Keyword(s):

Finite Element Method ◽

Optimal Control ◽

Finite Element ◽

Differential Equations ◽

Stochastic Optimal Control ◽

Random Coefficients ◽

Galerkin Finite Element Method ◽

Galerkin Finite Element ◽

Stochastic Galerkin ◽

Integral Differential Equations

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Existence of solutions and optimal control for reflecting stochastic differential equations with applications to population control theory*

Stochastic Analysis and Applications ◽

10.1080/07362999208809256 ◽

1992 ◽

Vol 10 (1) ◽

pp. 45-106 ◽

Cited By ~ 2

Author(s):

Situ Rong ◽

W.L. Chan

Keyword(s):

Optimal Control ◽

Differential Equations ◽

Control Theory ◽

Stochastic Differential Equations ◽

Existence Of Solutions ◽

Population Control

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A multipoint boundary-value problem for linear systems of singularly perturbed differential equations

Ukrainian Mathematical Journal ◽

10.1007/bf01092792 ◽

1980 ◽

Vol 32 (2) ◽

pp. 146-150

Author(s):

N. G. Panfilov

Keyword(s):

Differential Equations ◽

Boundary Value Problem ◽

Linear Systems ◽

Boundary Value ◽

Singularly Perturbed ◽

Multipoint Boundary ◽

Multipoint Boundary Value Problem

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A regularization method for the parameter estimation problem in ordinary differential equations via discrete optimal control theory

Journal of Statistical Planning and Inference ◽

10.1016/j.jspi.2020.04.007 ◽

2021 ◽

Vol 210 ◽

pp. 1-19

Author(s):

Quentin Clairon

Keyword(s):

Optimal Control ◽

Parameter Estimation ◽

Differential Equations ◽

Control Theory ◽

Ordinary Differential Equations ◽

Optimal Control Theory ◽

Regularization Method ◽

Estimation Problem ◽

Parameter Estimation Problem ◽

Discrete Optimal Control

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A multipoint boundary value problem for systems of linear generalized differential equations with singularities

Differential Equations ◽

10.1134/s0012266114080011 ◽

2014 ◽

Vol 50 (8) ◽

pp. 987-1002

Author(s):

M. T. Ashordia

Keyword(s):

Differential Equations ◽

Boundary Value Problem ◽

Boundary Value ◽

Multipoint Boundary ◽

Generalized Differential ◽

Multipoint Boundary Value Problem

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Ultimate Bearing Capacity Analysis of Oblique Beam System Supported by Knee Brace

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.578-579.602 ◽

2014 ◽

Vol 578-579 ◽

pp. 602-605

Author(s):

Le Huan Xu ◽

Feng Liu ◽

Shuang Shuang Meng

Keyword(s):

Finite Element ◽

Bearing Capacity ◽

Preliminary Analysis ◽

Ultimate Bearing Capacity ◽

Capacity Analysis ◽

Knee Brace ◽

Finite Element Software ◽

Beam System ◽

Portal Frame

This article established the oblique beam system supported by knee brace in portal frame by using finite element software ANSYS. We analysed the ultimate bearing capacity of the system, and discussed the effects of purlin stiffness and knee brace layout on the bearing capacity of the structure. Preliminary analysis shows that, increasing the number of knee brace or improving purlin stiffness can improve ultimate bearing capacity of the system.

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