A general curved element for very flexible frames
The objective of this research is to formulate a general curved frame finite element based on a convected material frame approach, and develop a general explicit algorithm for the analysis of flexible structures subjected to large geometrical changes. The algorithm should have the capability of handling nonlinear and inelastic material properties, including fracture.^ In the formulation, each discrete element is associated with a local coordinate system that rotates and translates with the element but does not deform. For each load or time increment, the local coordinate system assumes a new orientation and the element geometry also assumes a new shape. The corresponding strain-displacement and nodal force-stress relationships are defined in the updated local coordinates, and based on the updated geometrical shape. Thus, the rigid body motion and the deformation displacement are decoupled for each increment. More importantly, if the load increment is small, the deformation increment in each element is small. Small strain theory and linear stress-strain relationships can be used in the formulation. The nonlinearities associated with the large geometrical changes are incorporated in the analysis through the continuous updating of the material frame geometry. An advantage of this procedure is that the global stiffness matrices are not developed. By assuming a lumped mass matrix of diagonal form, the finite element analysis involves only vector assemblages and vector storages.^ Standard benchmark problems available in the literature for large deflection finite element analysis were adopted to verify the algorithm. Numerical examples were also performed, which include studies of the post-buckling responses of columns and large deflection transient responses of frames subjected to impact loads.^ The explicit finite element formulation and the convected material frame approach are then extended to develop a fragmentation algorithm. Numerical examples for fixed-fixed frames subjected to a set of impact loads are presented. Trajectories of the fragmented elements due to impact are plotted and verified. ^
Major Professor: Edward C. Ting, Purdue University.
Applied Mechanics|Engineering, Civil