ON THE ASSUMED STRAIN FORMULATION FOR GEOMETRICALLY NONLINEAR-ANALYSIS

Assumed strain formulation for geometrically nonlinear analysis is ree xamined with particular attention to recovery of incremental strain an d compatibility mismatch. Two approaches considered for strain recover y lead to alternate expressions. for compatibility mismatch but the sa me incremental load vector due to equilibrium imbalance and compatibil ity mismatch. However, they result in the differences in the stiffness matrix due to initial stress. Numerical tests conducted on example pr oblems demonstrate that the conventional approach with linearized comp atibility condition is superior to the alternate approach when increme nts in loads or displacements are large. In addition, the results of n umerical tests conducted on a geometrically linear problem point out t hat an assumed strain field that suppresses incompatible spurious kine matic mode could reintroduce element locking, suggesting that it shoul d be undesirable to suppress incompatible modes at element level.