Shakedown analysis of truss structures with nonlinear kinematic hardening

• Shakedown analyses of trusses with nonlinear kinematic hardening are conducted.
• An equivalent form of the Koiter׳s kinematic shakedown formulation is derived.
• Static and kinematic shakedown analyses are performed analytically and numerically.
• The shakedown limits are acquired numerically by primal and dual analyses.

The paper aims to perform shakedown analysis of truss structures with nonlinear kinematic hardening. Both the static and kinematic shakedown analyses of truss structures were conducted analytically and numerically to bound the shakedown limit. First, the problem statement leads to the lower bound (primal) formulation accounting for nonlinear kinematic hardening extended from the Melan׳s static shakedown theorem. In particular, the Hölder inequality is then utilized to establish the corresponding upper bound (dual) formulation from the lower bound formulation as well as to confirm the duality relationship between them. The derived upper bound formulation is an equivalent form of the Koiter’s kinematic shakedown formulation for trusses without involving time integrals. Further, both the primal and the dual analyses of truss structures were conducted using the optimization algorithms provided by MATLAB. Accordingly, the primal analysis and the dual analysis are validated by converging to the shakedown limit efficiently. Finally, the step-by-step finite-element analysis by using ABAQUS is also performed to verify the analytical formulation and numerical implementation.