2025/09/09 by David Portillo, Portillo, David, Ignacio A. Romero +1
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical Analysis (math.NA) #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.2509.07735
openalex publication_date 2025/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work describes models and numerical approximations that describe the mechanical behavior of deformable continua with embedded structural members, such as rigid bodies, beams, shells, etc. The continuum formulation extends an idea first presented in the context of the Arlequin method and constrains the kinematics of the two types of bodies to be compatible in the energy sense. In the article, we exploit the shared similarities of all structural theories to introduce a general framework for energetically coupling the latter with continua. In addition, we show that the problems, as well as their finite element approximations, are well-posed. Numerical examples of bodies with inclusions, fibers, and embedded surfaces are provided to illustrate the generality and robustness of the approach.