Solution procedure¶

Loads Fa on the structure are applied in increments ΔFa1, ΔFa2, and so on, so that p_66_image002

. The graphical interpretation of the method for a problem with one displacement variable is shown in Figure

For the first computational cycle (i=1) assume Eep =E for all elements. Apply the first load increment ΔF1.
Using the current strains, determine the current Eep or viscoplastic strain increment

in each element. Obtain the self-equilibration body loads for each element. Obtain the current structure (global) self-equilibrating body loads p_66_image006

and solve p_66_image008

,

where Fa is the actual applied external load increment. From p_66_image012

obtain the current strain increment p_66_image014

for each element.

If any element makes the elasto to plastic transition revise Eep return to previous step 2 and repeat the steps 2 and 3 until convergence.
Update the displacement vector

, the strains p_66_image018

and the stress p_66_image020

.

Apply the next load increment and return to step 2.
Stop when sum of incremental loads equals the total load or the structure collapse.

During the iteration process the nodal displacements caused by the actual applied external load increments and the body loads vector at successive iterations are compared. The convergence criterion is based on a dimensionless measure of the amount by which the displacement increment vector changes from one iteration to other. Convergence is said to have occurred, if the absolute change in all components of displacement vector, as a fraction of the maximum absolute component of displacement vector is less than a predefined tolerance.