A method is presented to determine the critical (most unfavorable) initial inperfection of structures of regular-polygonal symmetry (denoted by dihedral groups). A critical point of such structures is either simple or forced to be double by the symmetry, and the group representation theory is employed to deal with the degeneracy due to symmetry. The method is developed further to incorporate the symmetry of imperfections. In many cases of practical interest, the critical imperfection is given explicitly as the product of 'imperfection sensitivity matrix' and the critical eigenvector. It is shown that the symmetry in the critical eigenvectors of the tangent-stiffness matrix is inherited to the symmetry in the critical imperfection mode.
ASJC Scopus subject areas
- Applied Mathematics