Title: Improved gradient projection method for parametric optimisation of bar structures // Magazine of Civil Engineering. – 2020. – № 6 (98). — С. 9812
Creators: Yurchenko V. V.; Peleshko I. D.
Imprint: 2020
Collection: Общая коллекция
Subjects: Строительство; Строительная механика; rod structures; parametric optimization; gradient projection method; nonlinear design; finite element analysis; computer-aided design; mathematical algorithms; стержневые конструкции; параметрическая оптимизация; метод градиентных проекций; нелинейное проектирование; конечно-элементный анализ; автоматизированное проектирование; математические алгоритмы
UDC: 624.04
LBC: 38.112
Document type: Article, report
File type: PDF
Language: English
DOI: 10.18720/MCE.98.12
Rights: Свободный доступ из сети Интернет (чтение, печать, копирование)
Record key: RU\SPSTU\edoc\66104

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Numerical optimization and the finite element method have been developed together to make possible the emergence of structural optimization as a potential design tool. The main research goal of this paper is the development of mathematical support and a numerical algorithm to solve parametric optimization problems of structures with orientation on software implementation in a computer-aided design system. The paper considers parametric optimization problems for bar structures formulated as nonlinear programming ones. The method of the objective function gradient projection onto the active constraints surface with simultaneous correction of the constraints violations has been used to solve the parametric optimization problem. Equivalent Householder transformations of the resolving equations of the method have been proposed. They increase numerical efficiency of the algorithm developed based on the considered method. Additionally, proposed improvement for the gradient projection method also consists of equivalent Givens transformations of the resolving equations. They ensure acceleration of the iterative searching process in the specified cases described by the paper due to decreasing the amount of calculations. The comparison of the optimization results of truss structures presented by the paper confirms the validity of the optimum solutions obtained using proposed improvement of the gradient projection method. The efficiency of the proposed improvement of the gradient projection method has been also confirmed taking into account the number of iterations and absolute value of the maximum violation in the constraints.

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Table of Contents

  • Improved gradient projection method for parametric optimisation of bar structures
    • 1. Introduction
    • 2. Methods
      • 2.1. Parametric optimization problem formulation
      • 2.2. An improved gradient projection method for solving the parametric optimization problem
  • Using Householder’s transformations described above triangular structure of the nonzero elements of matrix is formed step-by-step. Besides, Eq. (2.7) and Eq. (2.9) can be rewritten as follow:
    • 3. Results and Discussion
      • 3.1. Parametric optimization of a three-bar truss
      • 3.2. Optimization of a ten-bar cantilever truss
      • 3.3. Optimization of a 24-bar transmission tower
    • 4. Conclusion
    • 5. Acknowledgement

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