Material and Geometric Non-linear Isoparametric Spline Finite Strip Analysis of Perforated Thin-Walled Steel Structures (No. R910)

Abstract

The isoparametric spline finite strip method (ISFSM) is an efficient numerical method which is mostly suitable for analysing prismatic structures. It is able to simulate complex geometries such as holes and can handle arbitrary types of boundary conditions and loadings. The present report extends the application of the ISFSM to the material inelastic and geometric nonlinear analysis of perforated thin-walled steel structures. The general theory of the ISFSM is briefly introduced. The formulations of the kinematics assumptions, the geometric mapping, the strain-displacement relations, and the equilibrium conditions are presented. In particular, the plasticity theory, the constitutive relations and the methods to integrate the ‘rate equations’ are emphasized, and the related ‘backward Euler return method’ and use of a ‘consistent material modulus’ are highlighted. The arc-length method and the line search technique have been successfully integrated to work as the main nonlinear solver, and evidence has shown that the incorporation of the latter is necessary for the efficient implementation of the present analysis. The reliability and efficiency of the method are demonstrated by a number of numerical examples, including analyses of flat plates with different material plasticity models, a classical nonlinear shell problem, perforated flat and stiffened plates, and perforated stiffened channel section storage rack uprights.