Solution procedure

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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


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 p_66_image004 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, image010 where Fa is the actual applied external load increment. From p_66_image012obtain the current strain increment p_66_image014for 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 vectorp_66_image016, the strains p_66_image018and the stress p_66_image020.

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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