Mathematical Discourse by Dr Narravula Harshvardhan Reddy

The Department of Mathematics at SRM University-AP is organising an engaging Guest Lecture on June 14, 2023. Dr Narravula Harshavardhan Reddy will speak on Finite Element Techniques for Thin-shell Deployable Space Structures.

Abstract

Part 1: Rotation-free finite element analysis

While the majority of analytical analyses of plates and shells rely on Kirchhoff-Love (KL) formulations put forth for thin plates and shells, modern finite element formulations draw upon the Reissner-Mindlin (RM) theory for moderately thick shells. The finite element formulations based on RM theory treat translations and rotations as independent variables and are advantageous due to their demand for only C0-continuity of the geometry between elements and the use of relatively simple shape functions. Nonetheless, RM elements suffer from various locking phenomena such as shear locking and are inefficient in analysing very thin shells. With the emergence of stronger materials like carbon fibre-reinforced composites and the realisation of lightweight structures with extremely small thicknesses, KL finite element formulations utilising only translations as the degrees of freedom are gaining prominence. This talk discusses two such rotation-free finite element formulations: Onate’s EBST [1] and NURBS-based isogeometric analysis [2] for thin-shell structures.

Part 2: h-adaptive finite element analysis

Thin-shell deployable structures, including booms and longerons, undergo complex deformations such as localised folding and buckling, and snap-through instabilities. These deformations are often accompanied by moving contact surfaces. Nonlinear Finite element analysis of such behaviours requires highly dense meshes in the regions of interest. Since most of the deployable structures such as booms are very long in one dimension compared to the others, mesh density must be high throughout the domain of the analysis leading to a high computation cost.The computation cost can be reduced by adapting the mesh to the deformation throughout the geometrically nonlinear analysis. This talk focuses on h-adaptive mesh refinement for thin-shell deployable structures.

About the Speaker

Dr Narravula Harshavardhan Reddy is a resourceful Mathematician and researcher, who has made significant contributions to the understanding and application of mathematical principles in various domains. His impressive academic foundations in Mechanical Engineering from IIT, Guwahati and Masters and PhD in Aeronautical Sciences from California Institute of Technology, Pasadena, CA backed with his extensive experience of about a decade in the realm is truly inspiring. He has 10 noteworthy publications and 4 distinguished talks to his credit.

Join the engaging discourse with Dr Reddy and members of the faculty !