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

Buckling load estimation of continua modeled by finite element (FE) should be based on non-linear equilibrium. When suchequilibrium is obtained by incremental solutions and when sensitivity analysis as well as iterative redesigns are included,the computational demands are large especially due to optimization. Therefore, examples presented in the literature relateto few design variables and/or few degrees of freedom. In the present paper a non-incremental analysis is suggested, anda simple sensitivity analysis as well as recursive redesign is proposed. The implicit geometrical non-linear analysis, basedon Green-Lagrange strains, apply the secant stiffness matrix as well as the tangent stiffness matrix, both determined forthe equilibrium corresponding to a given reference load, obtained by the Newton-Raphson method. For the formulatedeigenvalue problem, which solution gives the estimated buckling load, the tangent stiffness matrix is of major importance.In contrast to formulations based on incremental solutions, the tangent stiffness matrix is here divided into two matrices, thestress stiffness matrix that is linear depending on stresses and the remaining part of the tangent stiffness matrix. Examplesverify the effectiveness of the proposed procedure.