On the assumed strain formulation for geometrically nonlinear analysis

Abstract

Assumed strain formulation for geometrically nonlinear analysis is reexamined with particular attention to recovery of incremental strain and compatibility mismatch. Two approaches considered for strain recovery lead to alternate expressions for compatibility mismatch but the same incremental load vector due to equilibrium imbalance and compatibility mismatch. However, they result in the differences in the stiffness matrix due to initial stress. Numerical tests conducted on example problems demonstrate that the conventional approach with linearized compatibility condition is superior to the alternate approach when increments in loads or displacements are large. In addition, the results of numerical tests conducted on a geometrically linear problem point out that an assumed strain field that suppresses incompatible spurious kinematic mode could reintroduce element locking, suggesting that it should be undesirable to suppress incompatible modes at element level.