A numerical method of lower bound dynamic shakedown analysis for 3D structures

The safety assessment of engineering structures under repeated variable dynamic loads such as seismic and wind loads can be considered as a dynamic shakedown problem. This paper aims to extend the stress compensation method (SCM) to perform lower bound dynamic shakedown analysis of engineering structures and a double-closed-loop iterative algorithm is proposed to solve the shakedown load.

The construction of the dynamic load vertexes is carried out to represent the loading domain of a structure under both dynamic and quasi-static load. The SCM is extended to perform lower bound dynamic shakedown analysis of engineering structures, which constructs the self-equilibrium stress field by a series of direct iteration computations. The self-equilibrium stress field is not only related to the amplitude of the repeated variable load but also related to its frequency. A novel double-closed-loop iterative algorithm is presented to calculate the dynamic shakedown load multiplier. The inner-loop iteration is to construct the self-equilibrated residual stress field based on the certain shakedown load multiplier. The outer-loop iteration is to update the dynamic shakedown load multiplier. With different combinations of dynamic load vertexes, a dynamic shakedown load domain could be obtained.

Three-dimensional examples are presented to verify the applicability and accuracy of the SCM in dynamic shakedown analysis. The example of cantilever beam under harmonic dynamic load with different frequency shows the validity of the dynamic load vertex construction method. The shakedown domain of the elbow structure varies with the frequency under the dynamic approach. When the frequency is around the resonance frequency of the structure, the area of shakedown domain would be significantly reduced.

In this study, the dynamical response of structure is treated as perfect elastoplastic. The current analysis does not account for effects such as large deformation, stochastic external load and nonlinear vibration conditions which will inevitably be encountered and affect the load capacity.

This study provides a direct method for the dynamical shakedown analysis of engineering structures under repeated variable dynamic load.