Adaptive isogeometric analysis in structural frames using a layer-based discretization to model spread of plasticity. (February 2018) - Liu, Ning; Jeffers, Ann E.
Highlights: Layer discretization leads to the separation of length and thickness integration. Yielding data is collected at layer integration points to guide adaptive analysis. Lobatto quadrature is recommended in lieu of traditional Gaussian quadrature. G 1 constraint only allows for yielding near connections, not the connection itself. Rotation-free discretization represents significant computational saving. Abstract: A distributed plasticity isogeometric frame model utilizing a layer-based discretization is formulated to capture the plasticity growth in large-deformation frames. In our formulation, B-spline basis functions are employed to define the deformation along the length, while a layer-based through-the-thickness discretization is adopted to capture the gradual plastification of the section. This separation of the thickness integration from the length direction enables the full 2D yielding development to be captured while maintaining a 1D data structure. The member-level geometrically nonlinear effects are also included. By introducing a continuity constraint in between two patches, rigid connection between two members is achieved in a multi-patch analysis setting. The formulation includes an adaptive analysis in which knots are inserted based on yield locations. In comparison to conventional layer-based finite elements, fewer degrees of freedom are needed to achieve the same level of accuracy due to the high-order smoothness of B-splines. Compared to existing isogeometric beam elements, the appealing feature is its capability of adaptively capturing the 2D spread of plasticity while maintaining a 1D data structure. The performance of the proposed model is assessed through several numerical examples involving gradual yielding of beams and frames under small and large deformations.