Dynamic simulation of buckling and wrinkling of thin shells and membranes with smooth discretization methods
The proposed research project aims toward improving dynamic simulation of buckling and wrinkling of thin shells and membranes. When using standard finite elements, correct representation of buckling modes and wrinkling patterns typically require rather fine meshes, particularly in the case of very thin structures. The first working hypothesis is that smooth discretization methods, for instance in the context of isogeometric analysis, are capable of representing the correct modes already for relatively coarse discretizations. The second working hypothesis supposes that the intrinsically locking-free hierarchic shell formulations, developed earlier by the applicant for static problems, offer advantages also in dynamic simulations in comparison to established methods. They avoid transverse shear locking a priori, i.e. independent of the discretization concept, by a smart modification of the kinematic equations via direct parametrization of transverse shear rotations or displacements. Besides, membrane locking is avoided by a novel mixed principle (mixed displacements – MD), which exclusively uses displacement-type degrees of freedom. Apart from avoiding locking, the MD method promises improved convergence properties in the context of iterative methods. Both concepts facilitate to increase efficiency of explicit dynamic analyses via innovative methodological ideas for mass scaling.