A Shell-in-Shell FE2 Approach for Internally Resolved Structures

  • Herrmann, Marja-Lisa (RWTH Aachen University)
  • Klarmann, Simon (RWTH Aachen University)
  • Klinkel, Sven (RWTH Aachen University)

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The emergence of innovative materials, such as carbon reinforced components, has sparked a general rethinking of the design of structural concrete buildings. These advancements enable optimized construction, which requires advanced simulation techniques for structural analysis. A high level of accuracy and efficiency is necessary to exploit the full potential of these materials. However, standard finite element methods often result in large models and extended computation times due to intricate geometries. This paper introduces a multiscale approach that uses structure-structure homogenization to simplify complex mesostructures. This method provides a more precise representation while significantly reducing computation time. The method divides the problem into two scales. The macroscopic scale describes the overall geometry and loading conditions, and the mesoscopic scale characterizes the morphology and averaged physical attributes. Building upon existing frameworks for carbon-reinforced concrete shell structures, we discretize the structural element at the macroscopic scale using standard shell elements. Simultaneously, we assign a representative volume element (RVE) to each integration point on the macroscopic level. After applying macroscopic shell strains to the RVE, we solve the mesoscopic boundary value problem, yielding homogenized shell stress resultants and the shell material tangent operator. We further enhance this approach through structure-structure homogenization using Reissner-Mindlin shells within the RVE framework. To connect these scales, we apply the Hill–Mandel condition to ensure energetic equivalence by setting appropriate boundary conditions for the RVE. In this work, we use periodic boundary conditions to prescribe displacements, ensuring proper deformation modes and preventing the length dependency of the shear entries of the material tangent operator by introducing a constraint. Our results are compared with methods that utilize displacement boundary conditions.