Session: 06-04-01: Beam, Plate, and Shell Structures

Paper Number: 173621

Local Buckling of Realistic Shell Structures Using Mechanics of Structure Genome Based Beam Model 

Structural analysis of thin-walled composite structures in the aerospace, space, and wind turbine industries for estimating local 3D stresses and local buckling is computationally expensive in the predesign phase. For complex aeroelastic calculations, engineers prefer beam models without compromising the 3D FEA-based high fidelity. The industry-trusted software, VABS, greatly satisfies the purpose by splitting the three-dimensional elasticity problem into cross-sectional analysis and beam analysis using Mechanics of Structure Genome (MSG) theory. This work discusses the MSG approach extension to extract beam stiffness from a three-dimensional tapered shell segment by replacing the cross-sections. The Timoshenko beam stiffness is computed from the tapered shell segment using MSG based minimization of classical elastic strain energy, having the Reissner-Mindlin shell kinematic model. This numerical implementation of Timoshenko beam stiffness computation is implemented in an open-source multiscale modeling tool, OpenSG, based on the FEniCSx backend. The implementation addresses the challenge of constraining nonperiodic boundaries of tapered shell geometry using separately solved boundary fluctuating functions. This work is an advancement of the existing MSG based Kirchhoff Love shell model implemented in OpenSG for estimating the VABS equivalent Timoshenko beam stiffness of the line element cross-section. However, the choice of the Reissner-Mindlin model for surface shell mesh elements brings a numerical advantage of using standard Lagrange elements following C0 continuity. The work discusses extensive validation of shell segment-based Timoshenko beam stiffness with a corresponding OpenSG implemented solid element-based model, both for prismatic and non-prismatic segments. OpenSG contains immense capability of computing homogenized global models like beam, plate/shell, and 3D model (like conventional RVE) with rigorous benchmarking with VABS and SwiftComp commercial tools. The present work adds a surface element-based beam properties estimation feature using a similar unified approach as MSG solid elements. The validation cases involve analytical calculation of beam stiffnesses for simple geometries using the Variational Asymptotic Method (VAM) approach. The major underlying benefits of this entire work lie in estimating the local buckling computation by the input beam reaction forces. Therefore, the beam reaction forces obtained from the beam analysis (using BeamDyn/GEBT) are directly implemented for the MSG-based local recovered stress field, which in effect predicts the critical eigenvalues and mode shapes corresponding to shell buckling. This unique methodology provides a highly fast and accurate approach for shell buckling without direct numerical simulation of the entire wind turbine blade, which is a breakthrough for design engineers in the predesign phase. The OpenSG implementation would be publicly available in the OpenSG GitHub directory with API-based installation for general usage.  

Presenting Author: Akshat Bagla Purdue University

Presenting Author Biography: Akshat is a PhD student in the Multiscale Structural Mechanics research group at School of Aeronautics and Astronautics, Purdue University. His research focuses on estimating local buckling of solid and shell composite structures using Mechanics of Structure Genome (MSG) theory. He is the developer of MSG based open-source multiscale modeling tool, OpenSG in FEniCSx backend for computing global homogenized models for composite structures like beam, plate or Cauchy continuum model. His local buckling problem would predict the three-dimensional shell buckling of realistic wind turbine blade composite structures. His research interests are composite structures, solid mechanics and multiscale modeling.

Authors:

Akshat Bagla Purdue University
Ernesto Camarena Sandia National Laboratories
Wenbin Yu Purdue University