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Minimum weight design of non‐linear elastic structures with multimodal buckling constraints
Author(s) -
Trentadue Francesco
Publication year - 2002
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.573
Subject(s) - buckling , lagrange multiplier , eigenvalues and eigenvectors , mathematics , bifurcation , minimum weight , differentiable function , context (archaeology) , critical load , mathematical optimization , maxima and minima , sequence (biology) , structural stability , instability , structural engineering , nonlinear system , mathematical analysis , engineering , mechanics , paleontology , statistics , physics , genetics , quantum mechanics , biology
It well known that multimodal instability is an event particularly relevant in structural optimization. Here, in the context of non‐linear stability theory, an exact method is developed for minimum weight design of elastic structures with multimodal buckling constraints. Given an initial design, the method generates a sequence of improved designs by determining a sequence of critical equilibrium points related to decreasing values of the structural weight. Multimodal buckling constraints are imposed without repeatedly solving an eigenvalue problem, and the difficulties related to the non‐differentiability in the common sense of state variables in multimodal critical states, are overcome by means of the Lagrange multiplier method. Further constraints impose that only the first critical equilibrium states (local maxima or bifurcation points) on the initial equilibrium path of the actual designs are taken into account. Copyright © 2002 John Wiley & Sons, Ltd.