A nonlocal nonlinear stiffened shell theory with stiffeners modeled as geometrically-exact beams - Zhang, Qi (2023)
In the present work, we have developed a nonlocal and nonlinear structure mechanics theory and computational formulations for the nonlinear stiffened shell with its stiffeners modeled by the three-dimensional geometrically exact beam model while the shell part is modeled by three-dimensional geometrically exact shell model. This hybrid beam-shell geometrically exact stiffened shell model is used for solving dynamic problems of stiffened shell structures, including dynamic fracture of the shell. We first formulate the nonlocal equations for geometrically nonlinear beams using the kinematics of geometrically exact beam theory. Then, we develop a stiffened shell model by coupling the nonlocal geometrically exact beam and shell formulations. Several numerical examples are presented to validate and verify both the nonlocal and nonlinear beam formulation and the nonlocal/nonlinear stiffened shell formulation. We have demonstrated that the proposed nonlocal stiffened shell theory can model the crack growth in stiffened shell structures.