Adaptive finite element buckling analysis of folded plate structures

Abstract

Publisher Summary This chapter presents the finite element linear buckling analysis of folded plate structures using adaptive h-refinement methods. The variable-node flat shell element used possesses a drilling D.O.F. that, in addition to improvement of the element behavior, permits an easy connection to other elements with six degrees of freedom per node. For the variable-node membrane elements with a drilling D.O.F., the Allman-type interpolations are used for the basic behavior of the element. The variable-node plate bending element is formulated based on Reissner–Mindlin plate theory to account for the shear deformation and has the substitute shear strain fields. The adaptive mesh refinement is normally performed after an initial solution has already been made available, and regions of the solution domain where the accuracy is not satisfactory have been identified according to a prescribed set of criteria. This process can be iterated using the last solution as the new initial solution. Two criteria are essential for adaptive mesh refinement—stopping criterion and refinement criterion. The stopping criterion is used to decide whether the obtained error is within the prescribed maximum error tolerance, and the refinement criterion is used to judge whether an element is to be refined at each iteration step.