AN AUTOMATIC LOAD STEPPING ALGORITHM WITH ERROR CONTROL

This paper presents an algorithm for controlling the error in non-line ar finite element analysis which is caused by the use of finite load s teps. In contrast to most recent schemes, the proposed technique is no n-iterative and treats the governing load-deflection relations as a sy stem of ordinary differential equations. This permits the governing eq uations to be integrated adaptively where the step size is controlled by monitoring the local truncation error. The latter is measured by co mputing the difference between two estimates of the displacement incre ments for each load step, with the initial estimate being found from t he first-order Euler scheme and the improved estimate being found from the second-order modified Euler Scheme. If the local truncation error exceeds a specified tolerance, then the load step is abandoned and th e integration is repeated with a smaller load step whose size is found by local extrapolation. Local extrapolation is also used to predict t he size of the next load step following a successful update. In order to control not only the local load path error, but also the global loa d path error, the proposed scheme incorporates a correction for the un balanced forces. Overall, the cost of the automatic error control is m odest since it requires only one additional equation solution for each successful load step. Because the solution scheme is non-iterative an d founded on successful techniques for integrating systems of ordinary differential equations, it is particularly robust. To illustrate the ability of the scheme to constrain the load path error to lie near a d esired tolerance, detailed results are presented for a variety of elas toplastic boundary value problems.