Mechanical APDL Structural Analysis Guide

The arc-length method causes the Newton-Raphson equilibrium iterations to converge along an arc,
thereby often preventing divergence, even when the slope of the load vs. deflection curve becomes
zero or negative. This iteration method is represented schematically in Figure 8.4:Tr aditional Newton-
Raphson Method vs. Arc-Length Method (p. 196).

Figure 8.4:Traditional Newton-Raphson Method vs. Arc-Length Method

u

Conv ergedsolutions

u

Conv ergedsolutions

Spheric alarc

 F

r 2

r 3

r 1

r
-Thereferencearc -lengthradius

r,r-Subsequentarc -lengthradii

F

F

F

F

To summarize, a nonlinear analysis is organized into three levels of operation:

• The "top" level consists of the load steps that you define explicitly over a "time" span (see the discussion
  of "time" in Loading in the Basic Analysis Guide). Loads are assumed to vary linearly within load steps
  (for static analyses).


• Within each load step, you can direct the program to perform several solutions (substeps or time steps)
  to apply the load gradually.


• At each substep, the program performs a number of equilibrium iterations to obtain a converged
  solution.

Figure 8.5: Load Steps, Substeps, and Time (p. 197) illustrat es a typical load history for a nonlinear ana-
lysis. Also see the discussion of load steps, substeps, and equilibrium iterations in Loading in the Basic
Analysis Guide.

Release 15.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information

Nonlinear Structural Analysis