Open AccessOn sensitivity analysis of unsteady responses for FEM models of beams
Author(s) -
M. A. Mironov
Publication year - 2020
Publication title -
trudy krylovskogo gosudarstvennogo naučnogo centra
Language(s) - English
Resource type - Journals
eISSN - 2618-8244
pISSN - 2542-2324
DOI - 10.24937/2542-2324-2020-2-s-i-103-109
Subject(s) - finite element method , sensitivity (control systems) , vibration , boundary value problem , stiffness , harmonic , beam (structure) , parametric statistics , optimal design , structural engineering , computer science , mathematics , mechanics , mathematical analysis , physics , engineering , acoustics , statistics , electronic engineering , machine learning
This paper discusses optimal design of structures in terms of various quality criteria with limitations for the parameters of dynamic stress-strain state (steady, unsteady, spectral). Efficiency of the methods based on the compliance with indirect optimality criteria, in particular, on the Kuhn-Tucker conditions, considerably depends on fast and accurate calculations of derivatives for the parameters of state in terms of design parameters, which is achieved by obtaining the analytical expressions. Introduction of these expressions to the optimization of FEM-based models is only possible if structural design parameters and the parameters of stiffness matrix and element masses are linked explicitly. The purpose of this work is to finalize and verify the methods for obtaining analytical derivatives of design parameters as functions of vibration frequencies, forced harmonic vibration frequencies and natural vibration frequencies of finite-element model with subsequent transition to completely analytical (not subtractive) differentiation of unsteady and spectral responses of design parameters. For an FE model of beam with a large number (one hundred) of finite elements, this study obtained and verified, for various boundary conditions and loading scenarios, the distributions of sensitivity coefficients for steady dynamic parameters in terms of design parameters, i.e. cross-sections of elements.