Incremental sequentially linear analysis of a notched beam

Abstract

Incremental Sequentially Linear Analysis (ISLA) is a new algorithm for non-linear finite element analysis. It is an extension of Sequentially Linear Analysis (SLA) which has been applied since 2001 as an alternative to the Newton-Raphson method when bifurcation, snap-back or divergence problems arise. ISLA is an incremental procedure with an implicit scheme, which starts and ends with an equilibrium state. The solution search path fol-lows damage steps sequentially with secant stiffness. In each iteration only one element is selected for damaging in the next iteration, which is a similar procedure as used in SLA. In this paper, ISLA is explained and demonstrated for a notched beam test. Because of the incremental procedure, ISLA can be extended to non-proportional loading, geometrically non-linear analysis and transient analysis. The searching path of ISLA is based on physical parameters (damage and history) rather than guided by numerical parameters. In addition, the method keeps the same incremental format throughout the entire analysis, circumventing the need to switch intermittently from incremental to total approaches or vice versa.