Local analytical sensitivity analysis for design of continua with optimized 3D buckling behavior

Abstract

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Buckling load optimization for 2D continuum models, with alternative formulation for buckling load estimation

“…For other dependence than linear proportionality, see Pedersen and Pedersen (2015) and the application to the 3D buckling design in Pedersen and Pedersen (2018). The simple result (18) is also valid for other finite element models, such as axisymmetric ring elements and 3D tetrahedron elements.…”

“…-As seen from the analytical expressions, the coefficient matrix [S σ ] to the eigenvalue λ depends linear on stresses as evaluated from equilibrium corresponding to the load distribution {Ā}. Note, that even for the 3D tetrahedron element the matrix [S σ ] is simple, as listed in Pedersen and Pedersen (2018). -Only geometrical non-linearity is in the present paper included, and the stiffness matrices are based on Green-Lagrange strains in a total Lagrangian formulation.…”

“…where U σ may be normalized to 1 by normalizing the buckling mode {∆}. The modification by non-linear interpolation is described in Pedersen and Pedersen (2018).…”

“…The present paper is a follow up of Pedersen and Pedersen (2018) on 3D continuum design with focus on sensitivity analysis. Here the focus is on alternative formulations of the involved eigenvalue problem, on importance of magnitude of reference load, on dependence of imperfections such as eccentricity and the influence of optimized design to control these dependence's.…”

“…Here the focus is on alternative formulations of the involved eigenvalue problem, on importance of magnitude of reference load, on dependence of imperfections such as eccentricity and the influence of optimized design to control these dependence's. The included references concentrate on these aspects without repeating the references given in Pedersen and Pedersen (2018).…”