Solution procedure
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Loads Fa on the structure are applied in increments ΔFa1, ΔFa2, and so on, so that . The graphical interpretation of the method for a problem with one displacement variable is shown in Figure
1. For the first computational cycle (i=1) assume Eep =E for all elements. Apply the first load increment ΔF1.
2. Using the current strains, determine the current Eep or viscoplastic strain increment in each element. Obtain the selfequilibration body loads for each element. Obtain the current structure (global) selfequilibrating body loads and solve , where Fa is the actual applied external load increment. From obtain the current strain increment for each element.
3. 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.
4. Update the displacement vector, the strains and the stress .
5. Apply the next load increment and return to step 2.
6. 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.

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