Parallel finite element methods for modeling contact in geometrically nonlinear membrane structures

Date of Completion

January 2002


Engineering, Civil|Engineering, Mechanical




This dissertation involves finite element modeling of geometrically nonlinear membrane structures with emphasis on the development of parallel computational methods for (1) modeling contact phenomena in membrane structures, and (2) mesh updating in fluid structure interaction (FSI) simulations. ^ A parallel contact formulation for large displacement problems is successfully established based on an implicit time integration scheme and the penalty method. The implicit integration is well suited for structural analysis in which contact happens over a long duration. Efficient parallel communication schemes are developed for the implicit contact algorithms. A “lumping” algorithm is developed that overcomes the difficulty in incorporating contact stiffness in large displacement problems, and eliminates the ill-conditioning in structural stiffness matrix caused by the use of a large penalty parameter. Numerical simulations are conducted to verify the accuracy and efficiency of the new contact algorithms. ^ Using the new contact analysis formulation, three large-scale simulations involving contact phenomena in parachute systems are performed. The first involves contact between three parachutes used in a cluster. The second involves contact within a single parachute during inflation from a folded configuration. The third involves contact of an inflated canopy by a foreign object. The new parallel contact algorithms are numerically stable for these problems that involve dynamics of thin fabric structures and sustained contact over a large time period. ^ Several new strategies are developed for updating the fluid mesh in fluid-structure interaction simulations to accommodate large displacements of the structure. These strategies are based on a “pseudo-solid” model, in which the fluid mesh is treated as elastic solid subjected to prescribed motions by the structural model. The methods are applied to a two-dimensional model under different types of motion for verification. Compared to previous work, the approaches developed in this work are able to achieve efficient mesh moving with minimum element shape distortion and volume change. ^