Exact solutions for plastic responses of orthotropic strain-hardening rotating hollow cylinders

Shakedown Analysis of Framed Structures: Strong Duality and Primal-dual Analysis

“…Namely maximize =minimize (16) As shown above, we have validated the strong duality between the primal problem (6) and the dual problem (15). Based on the primal formulation (6) or the dual formulation (15), we can acquire the exact solution by equating the greatest lower bound to the least upper bound as done in limit analysis [33][34][35].…”

“…In the previous work on limit analysis [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35], a generalized Hölder inequality [36] was employed to play a key role in establishing the kinematic (dual) formulation from the corresponding static (primal) formulation [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. By using a generalized Hölder inequality [36], we also equate the greatest lower bound to the least upper bound [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Based on the strong duality, exact solutions for certain sequential limit analysis problems have been acquired [33]…”

“…By using a generalized Hölder inequality [36], we also equate the greatest lower bound to the least upper bound [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Based on the strong duality, exact solutions for certain sequential limit analysis problems have been acquired [33][34][35]. On the other hand, Yang [22] stated the primal (lower bound) formulation in the form of l -norm [22,[36][37] on axial forces of truss members while dealing with large deformation of truss structures by limit analysis sequentially.…”

Analytical Solutions for Transversely Isotropic Fiber-Reinforced Composite Cylinders under Internal or External Pressure

“…For functionally graded material cylinders, elastic and/or plastic stress analysis under mechanical [5][6][7][8][9][10] and thermal [11][12][13] loads have been the topic of various articles. When it comes to orthotropic cylinders, studies mainly focus on examining the stresses due to rotation [14][15][16][17][18]. With the developments in material technology, studies have also commenced for cylinders made of fiber reinforced composite materials.…”

A Theory of Autofrettage for Open-Ended, Polar Orthotropic Cylinders

“…In particular, the effect of plastic anisotropy on stress and strain fields in rotating discs has been studied in [34][35][36][37][38][39], using different material models and boundary conditions. Various boundary value problems for orthotropic cylinders have been solved in [40][41][42][43][44]. All of these studies demonstrate that it is important to take into account plastic anisotropy in analysis and the design of structures.…”