Elastic Postbuckling Analysis of Structural Systems- A Unified Computational Framework

Arul Jayachandran, PhD

Department of Civil Engineering

Indian Institute of Technology Madras

Friday, February 14, 2024 | 11:00 a.m. | 140 Ketter Hall 

The talk focuses on computational methods for structural stability assessment based on the total potential energy (TPE) framework. TPE is an effective tool for analyzing the stability of various structural systems, incorporating the "secant matrix technique," also known as the "N1-N2 method". The geometric nonlinear finite element formulations are presented using the total Lagrangian (TL) and co-rotational TL formats. A unified stability assessment formulation has been applied to beams, frames, arches, thin-walled sections, trusses, shells, and plates (both perfect and imperfect), which undergo large displacements and rotations in their postbuckling states.

For structural systems like beams, frames, arches, and thin-walled open sections, conventional quadratic finite element methods have been reported to be inadequate under large deformations. A new Variable order Secant Matrix (VoSM) method is introduced, which offers an accurate postbuckling analysis by employing higher-order strain-displacement relations. This VoSM approach automatically limits the order of the secant matrices based on the nonlinearity encountered in the load-deformation behavior in the postbuckled state.

The VOSM method is extended to analyze frames and thin-walled open sections, while Marguerre's shell theory is employed to model the postbuckling behavior of shallow shells. These nonlinear finite element formulations have been implemented in a custom computer program incorporating the minimum residual displacement (MRD) method and the 'current stiffness parameter' as a stability indicator, which guides the postbuckling path-tracing algorithm.

Arul Jayachandran is a Professor at the Indian Institute of Technology Madras - (IITM), Chennai, India. He obtained his MS and PhD from IITM for his work on the stability design of steel structures. He worked as a Head of the Steel Structures Lab for twenty-one years in the Structural Engineering Research Centre (SERC), CSIR, Chennai, before moving to IITM. He teaches basic and advanced design of steel/steel-concrete composite structures and bridges.

In 2005, he was a visiting Associate Professor at the Georgia Institute of Technology, Atlanta, USA; in 2012 summer, he was a Visiting Senior Fellow at the University of Wollongong, Australia. He is an Editorial board member of the International Journal of Advanced Steel Construction. He has published over a hundred papers in international/national journals and conferences and guided 16 PhDs. He has designed over half a million tonnes of steel structures using Indian code IS:800, EC3, and MBMA codes.

He won two Indian National awards as Outstanding Designer for designing (i) a large phoenix-shaped shell structure and (ii) an all-steel bridge/flyovers. He is a Life Educator member of the American Institute of Steel Construction (AISC), a member of the Institution of Structural Engineers (UK), IABSE, and the Structural Stability Research Council SSRC-AISC: Task Group 3.