Elastic modulus adjustment procedures—Improved convergence schemes

Elastic modulus reduction method for limit analysis of thin plate and shell structures

“…The SEMAs for existing EMAPs can be illustrated based on stresses as follows [10,[13][14][15][17][18][19]:…”

“…In general, the value of q could be specified as an initial guess since its determination would be dependent on the geometry and loading condition [14,15]. To avoid this guess work, the applications and limitations of four different strategies of elastic modulus adjustment (SEMAs) to determine the parameter q were investigated in this paper.…”

“…The strain energy equilibrium principle (SEEP) assumes that the strain energy of element e before conducting the kth iteration will be equal to the sum of the strain energy remained and dissipated in element e after the kth iteration [14]. Hence, a new point (B) shown in Fig.…”

“…The EMAPs are attractive because they require only minimal conceptual bases for application and moderate computational effort to obtain satisfactory approximations of failure mechanisms and collapse loads for relatively complex structures [13]. Although recent research has improved the understanding of the EMAPs, the numerical examples in literatures reveal that the efficiency and accuracy of the EMAPs rely on the strategies of elastic modulus adjustments (SEMAs) [13][14][15]. That is to say the elastic modulus adjustment parameter q plays an important role in limit analysis utilizing the EMAPs.…”

“…In general, the value of q is specified as an initial guess in literatures. For example, 1 and 2 are proposed for plane strain and plane stress, respectively [13][14][15]. In order to avoid this guess work, it is reasonable to investigate the proper way to define the parameter q in a rational way, which has not been done satisfactorily up to now.…”