Efficient Adaptive Procedure for Buckling Analysis of Skeletal Structures

Abstract

An efficient numerical technique is proposed for determining the buckling load of two-dimensional skeletal structures. The key formulation is based upon the principle of stationary total potential energy and the solution procedure follows the concept of Rayleigh–Ritz approximation. A crucial aspect of the proposed technique is to supply the adaptivity to the solution space allowing the accurate representation of the buckled shape via a simple iterative scheme. The bases of such solution space are constructed in an elementwise fashion using the exact, closed-form buckled shape. An element axial force contained in the element shape functions is chosen as an adaptive parameter and the exact buckled shape of each element is achieved when such adaptive parameter converges to the element buckling load. In this study, various effects including the lateral restraints, shear deformation, and material nonlinearity are taken into account, and this, as a result, allows plane frames with/without lateral bracings, columns resting on elastic foundations, inelastic columns, and those with shear deformation to be treated. Results from an extensive numerical study have indicated that the proposed technique yields highly accurate buckling loads, comparable to the analytical and reference solutions, without the mesh refinement. In addition, a relatively low number of iterations is required to achieve the converged buckling load.