Computation of lower-bound elastic buckling loads using general-purpose finite element codes

A penalty approach to obtain lower bound buckling loads for imperfection-sensitive shells

“…The procedures for implementation of the Reduced Stiffness Analysis (RSA) and Reduced Energy Analysis (REA) and have been reviewed in [27] and [37], just to cite a couple of references. The necessary background to the energy approach to investigate stability of elastic systems was originally developed by Koiter for continuous systems [2], followed by developments for discrete systems [31,32].…”

Long-term deterioration effects on the buckling strength of metallic bridge girders

“…Buckling is a nonlinear phenomenon whereby a structure cannot any further take up load with its original geometry and so it changes its shape in order to find an alternative equilibrium position (Sosa et al 2006). The way in which buckling occurs depends on how the plate is loaded, its geometrical and material properties as well as the boundary conditions.…”

Challenges in the computation of lower-bound buckling loads for tanks under wind pressures

“…Every part of the shell that forms the whole cylinder (all courses) undergoes simultaneous reductions in the membrane stiffness while the scaled mode is imposed as a prescribed initial displacement. In that configuration, the energy used by the structure to reach that deflected configuration is calculated [15]. With the calculated energy for each reduction factor a eroding the membrane stiffness and having calculated the energy without reduction in its stiffness for the same load conditions, we are able to determine the loss in the buckling capacity to support additional load.…”

“…All these operations were done here to understand the reason for the differences in the results on models under wind loads, but they cannot be implemented as a standard simple procedure to find the knock-down factor for the classical buckling load. This is a limitation of the method described in [15] and it restricts its applicability to those cases in which the classical eigenmode is quite similar to the reduced energy mode.…”

“…This lower-bound theory has been validated extensively for many shell forms [10][11][12][13][14]. Sosa et al [15] investigated the implementation of a lower-bound approach for the buckling of imperfection-sensitive shells using general purpose finite element codes for cylindrical shells with different geometric configurations under uniform pressure. The lower-bound approach can be expressed in terms of reduced stiffness, as well.…”