Session: 01-04-02: Advances in Aerospace Structures

Paper Number: 122605

122605 - Coupled Field Formulation – a Unified Method for Formulating Structural Mechanics Problems 

Context and Introduction

The paper discusses the need for a unified formulation to model complex 1D and 2D metallic and composite structures in the aerospace and aircraft industries. The use of fiber-reinforced composites has increased in these industries due to their specific strength, stiffness and other favourable properties. However, the analysis of composite structures is more complex due to their heterogeneity, material coupling and the many non-classical effects they exhibit. Current finite element (FE) formulations have limitations in modelling these structures, like shear locking in slender beams, mesh distortion sensitivity, lower convergence rates in composites etc.

Research Aim

The aim of the research is to propose a coupled field formulation (CFF) as a unified method for solving the complex 1D and 2D structural problems in the aerospace industry by addressing the limitations of conventional FE formulations and provide a more accurate and efficient approach.

Methodology

The research develops a framework for the development of exact 1D FE for metallic and composite solid and thin-walled beams by deriving an exact analytical solution using a state space approach for 1D structures. For 2D structures, the methodology uses quadrilateral area coordinates to derive a unified locking-free FE formulation by kinematic coupling of field variables and satisfies the governing equations everywhere in the domain unlike conventional FE formulations.

Findings

The research findings include:

1) The development of a state space method for the exact solution of the governing equations for 1D structures with arbitrary lamination which allow the development of exact FE and provides a method to satisfy natural boundary conditions by expressing them in terms of boundary displacements.

2) The derivation of a 2D membrane FE formulation based on the coupling of field variables using the CFF leads to material dependent interpolation functions ensuring the recovery of all constraints exactly resulting in locking free formulation including volumetric locking (unified formulation for incompressible materials).

3) The 2D formulation satisfied all the quality tests for FE like strong and weak patch test and the Inf-sup test.

3) The findings of the research work offer a hope for addressing a key industry requirement of tolerating showing less sensitivity to mesh distortion.

Theoretical Importance

The research provides a new approach, the coupled field formulation, which addresses the limitations of current FE formulations for modeling complex 1D and 2D structures. The proposed method improves the accuracy and convergence rates for structural analysis, particularly for composite structures.

It also fills the gap in the literature by providing a unified formulation for incompressible materials.

Validation and Benchmarking of Solution Approach

The research involves the collection of data on the behavior of complex 1D and 2D structures, particularly in the aerospace industry. The analysis procedures include the formulation of the exact analytical solution for 1D structures and the derivation of the unified FE formulation for 2D structures using the CFF. Theoretical analyses and numerical simulations are likely conducted to validate the proposed method.

Questions Addressed

The research addresses the following questions:

1) How can the limitations of current FE formulations for 1D structures be overcome, like shear and volumetric locking, mesh distortion sensitivity satisfaction of natural boundary conditions in terms of displacements and lower convergence rates in composites?

2) How can a single unified FE formulation for 2D structures be developed for both compressible and incompressible materials?

3) What are the advantages of the proposed coupled field formulation compared to other conventional methods?

Conclusion

The research proposes a coupled field formulation (CFF) as a unified method to overcome the limitations of current FE formulations for modeling complex 1D and 2D structures. The CFF provides exact analytical solutions for 1D structures with arbitrary lamination, and a locking-free FE formulation for 2D structures by coupling field variables. The unified formulation also addresses the need for a single formulation to model incompressible materials. The proposed method has theoretical importance in improving the accuracy and convergence rates for structural analysis in the aerospace industry.

Presenting Author: Dr. Ramprasad Srinivasan Jain (Deemed to be University)

Presenting Author Biography: Dr. Ramprasad Srinivasan has a Masters in Aeronautical Engineering from IIT Kanpur and MS in Aerospace Engineering from Georgia Institute of Technology Atlanta USA. He completed his Doctoral Degree from Jain University Bangalore. His Thesis Topic is static analysis of Metallic and Composite Structures using Coupled Field Formulation.

He has over 25 years of industry experience having worked for top multinational companies like GE Aircraft Engines, and Honeywell Technologies. He has worked on many technology-intensive projects during his industry career like design of composite filament wound rocket motor cases, Design, Analysis and Manufacturing of Satellite container and Design and justification of Pre-X Launch vehicle, transient rolling analysis of automobiles etc. Prior to Joining Alliance, He worked as a staff scientist and drove the new product development initiatives at Honeywell Technology solutions. He has introduced a new method of structural analysis called as Coupled Field Formulation through his doctoral work which has potential application in many diverse areas of engineering structures. His technology expertise includes many areas of structures like Composites, Structural Dynamics, Finite element Methods, Nonlinear Analysis, Optimization, Structural Health Monitoring, Buckling Analysis, Machine learning, Neural Networks and Genetic Algorithms. His research interest is focused on application of coupled field formulation to novel problems in mechanics like functionally graded material, smart structures, wave propagation, stability problems and development of a family of new 1D, 2D and 3D finite elements devoid of all pathological issues and meets many industry challenges in modelling.

He has a patent filed on Structural Health Monitoring and he is Green Belt Certified on Six Sigma.

He has handled some Key R&D projects like:

1) Development of Enterprise Software Framework for NDE Centric Offline Integrated Aircraft Structural Health Monitoring of Airframe Structures in Collaboration with Indian Institute of Science (IISc) and Indian Institute of Technology (IIT-Chennai).

2) Development of Software Product (.Net Based) for Integration of Non-Destructive Evaluation based Ultrasonic Simulation in collaboration with Indian Institute of Science (IISc), Universitat Des Saarland, Germany and IMA Dresden, Germany (Indo-German Project Sponsored by Department of Science and Technology, India and DLR Germany)

His key publications include the following


Kurt. C. Gramoll, Srinivasan Ramaprasad, “Effects of band weaving on fiber strength in filament wound composite structures”, Composites Engineering, 5, No. 4, 363-373, 1995.

Ramprasad Srinivasan, “Exact Solution of Shear Flexible Laminated Curved Beams Using a Coupled Field Formulation”, International Journal for Computational Methods in Engineering Science and Mechanics, (2014), 15, 54-61.

Ramaprasad Srinivasan, B Dattaguru & Gajbir Singh, “Exact solutions for laminated composite beams using a unified state space formulation”, International Journal for Computational Methods in Engineering Science and Mechanics, (2019), 20, 319-334.

Ramaprasad Srinivasan, B Dattaguru & Gajbir Singh,” Coupled Field Formulation of Exactly Integrated Membrane Finite Elements Insensitive to Distortion”, International Journal for Computational Methods in Engineering Science and Mechanics., Volume 22, 1, (2021) 60-80