Mathematical Modeling for Shakedown Analysis of Offshore Structures

The shakedown analysis process of an offshore structure having elastic-plastic material presented. The finite element model of the structure has been developed first, and then a simple method has been applied for shakedown analysis using matrix tool. Simplifying the relationships together with applying the theory concepts of shakedown analysis is one of the characteristics of the presented method for practical problems. Here, shakedown analysis formulation discussed in four steps. First, the Morison equation adopted for converting the velocity and acceleration terms into resultant forces and it extended to consider arbitrary orientations of the structural members. Then the loads due to the waves have been calculated and they have been converted to specific repeating cyclic loads on the structure nodes. In the second step, the finite element model of the structure has been developed and considered under nodal loads resulted from the specific combined wave loads. Thirdly, the shakedown multiplier has been calculated using shakedown static theorem based upon the stress domain governing the problem. Finally, in the fourth step, a graph has been developed indicating the critical sea waves domain that cause the structure shakedown. The formulation has been applied for two types of offshore structures to verify the concept employed and its analytical capabilities.