Periodically restarted quasi-newton updates in constant arc-length method

Abstract

In this paper, two types of memory-economized computational strategies on the use of inverse Jacobian matrix updates (rank-one updates: Broyden's and Davidon's, rank-two updates: DFP and BFGS) in constant arc-length method are exploited. The first strategy which employs restarted multicycle updates needs only a limit number of arrays to store the correction vectors for use of displacement updates in iterations. The second one which employs restarted single-cycle updates does not need any extra memory storage for the correction vectors. Both snap-through and snap-through/snap-back problems are used to test the computational strategies. Results from the test examples show that both implementations with rank-one updates are preferable to those with rank-two updates for solving nonlinear finite element equations. Detailed discussions on the computational efficiency and some recommendations on the selection of appropriate algorithm for nonlinear finite element analysis are also given.