Thin membrane structures subjected to compressive or shear loading experience structural wrinkling due to the boundary conditions and the lack of enough bending stiffness to resist these deformations. These wrinkles are out of plane waves which continue to grow in number as the loading is increased until a limit value is reached where their number remains fixed but the size of the wrinkle grows. This phenomena is a known mode of failure in thin structural applications in aerospace applications. These wrinkles affect the functionality of the structural panels. Hence, the numerical simulation of the development of the wrinkles is the first step to study their impact on the overall structural application. The complexity in the numerical simulation arises from the fact that this local buckling producing the wrinkles is highly sensitive to the mesh density. Thus the real behavior of the thin membrane structure can only be captured with a significantly fine mesh, determined by a mesh refinement study. Without the mesh refinement study, one cannot be certain if the local buckling waves represent reality or are filtered by the mesh, in that it is not fine enough to capture them. Since the problem of structural wrinkling is highly nonlinear in nature, therefore, first the performance of various 2-D element technologies in CARAT++ (the finite element analysis tool at the Chair of Structural Analysis) are benchmarked using a set of credible linear and nonlinear problems for which the solutions are available in literature. Currently CARAT++ offers Reissner-Mindlin shell elements, Corotational shell elements and Isogeometric shell elements for the modeling of surface geometries. The convergence characteristics of these elements for each benchmark problem gives insight about their strengths and weaknesses relative to each other. For the linear benchmarks, all the elements converged to the analytical solution fairly well except the corotational element. The corotational element formulation exhibits convergence from a higher deflection to the analytical solution as the mesh is refined. Moreover, for a design problem with a significant initial curvature (cylindrical surface) the solution does not converge to the expected analytical value. It converges to a slightly higher value. In case of nonlinear benchmarks, the appropriate path finding solution methods are employed for the convergence studies. All the element formulations behave normally for relatively less problem nonlinearity. As the nonlinearity increases, the problems with the Corotational elements again show up. For particularly highly nonlinear problems, the Corotational elements fail to solve the problems. In one particular case the solution fails even before the nonlinearity along the load-displacement path is approached. In another, the solution fails right after successfully resolving the nonlinear segment of the load-displacement curve. The Reissner-Mindlin shell and the Isogeometric elements have a fairly smooth convergence for all cases in general. Now for the detailed study of the wrinkling phenomena, a thin shear panel is considered. The problem boundary conditions are based on the previous experimental work by Y. W. Wong at the university of Cambridge. The finite element modeling aspects considered for investigation are the panel thickness, the material stiffness and the mesh density. Moreover, different surface elements are employed to study the development of the wrinkles. The results for the shell elements and the membrane elements are presented in this document. The Isogeometric element could not be solved using the dynamic solution technique. A comparison between the analytically determined wrinkle wavelength and the finite element solution is performed for compressive loading. The numerical analysis results for shear buckling are compared to the experimental findings by Wong as well as the underlying theoretical assumptions for the respective element types and then conclusions are made regarding the influence of the modeling parameters on the results.     «

Thin membrane structures subjected to compressive or shear loading experience structural wrinkling due to the boundary conditions and the lack of enough bending stiffness to resist these deformations. These wrinkles are out of plane waves which continue to grow in number as the loading is increased until a limit value is reached where their number remains fixed but the size of the wrinkle grows. This phenomena is a known mode of failure in thin structural applications in aerospace applications....     »