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Setting Arc-Length Method

The Arc-length method (ALM) is relatively robust method particularly suitable for the solution of problems that require the search for the collapse load of a structure. Stability analysis of earth structures (slopes, embankments) is just one particular example of such a task. Unlike the NRM where the solution is driven purely by prescribing load increments, the ALM introduces an additional parameter representing a certain constraint on the value of load increment in a given load step. The value of the load step thus depends on the course of iteration and is directly related to the selected arc length.

The basic assumption of the method is that the prescribed load varies proportionally during the calculation.  This means that a particular level of the applied load can be expressed as:




current fraction of the total applied load



coefficient of proportionality



overall prescribed load

Note that with ALM the load vector F represents only a certain reference load that is kept constant during the whole response calculation. The actual value of the load at the end of calculation is equal to the λ multiple of F; λ < 1 represents the state when the actual bearing capacity of a structure is less than the prescribed reference load; if λ at the end of response calculation exceeds 1, the program automatically adjusts the arc length in order for the solution to converge to value λ = 1 within a selected tolerance equal to 0.01 (1% the maximum applied load). This value cannot be changed.

The literature offers a number of ALM formulations. The program supports the method suggested by Crisfield and the consistently linearized method proposed by Ramm. The latter one is considerably simple, at least from the formulation point of view, than the Crisfield method. On the other hand it is reportedly less robust. The default setting is the Crisfield method. 

Other important parameters of the method are "Setting arc length" and "Automatic arc length control".

Arc-length - setting the type of Arc-length method