# Parallel Analysis of Offshore Wind Turbine Structures under Ultimate Loads
## 3 Optimal Parallel Ultimate Design Procedures for OWT Support Structures  
This section discusses the optimal parallel ultimate design procedures for OWT support structures. In some regions, it is necessary to consider the ultimate loads from earthquakes or tropical cyclones. For seismic loads, we proposed a finite element framework for OWT support structures subjected to seismic, wind, and wave loads, including the soil-structure interaction and a conservative soil liquefaction analysis [35]. For tropical cyclones, this study includes two procedures--one accords to the GL Tropical Cyclone Technical Note (DLCs 11.2 and 11.3) [36] or IEC 61400-3 (DLCs I.1 and I.2) [1], and the other is based on the theory of a tropical cyclone passing the OWT support structure--to obtain the time-history turbulent wind distribution. Figure 2 shows the proposed optimal parallel design procedures for OWT structures under ultimate loads. The procedures are as follows: (1) Only an input file is required to define the structural dimensions, member sizes, loads, and the parallel computer arrangement. (2) A mesh generation program, Windturb, is used to generate a structural mesh with each loading case linked to a directory in a specific computer. (3) The TS, Turbsim, and Fast programs are then performed to find the distribution of the wind load, and the time-history blade forces and moments, where TS, developed in this paper, calculates the wind loads using IEC or DNV-GL codes, and moreover, the non-stationary turbulent wind of tropical cyclones can be generated [19]. Since we assume a rigid support structure to find the blade forces, only a small proportion of the loading cases have to run in the two programs. Moreover, each analysis is executed in a CPU core independently, so this step is fully parallel. (4) After the analyses in Step 3 are finished, the structural analysis and steel design of each loading case are then performed in each directory, using a CPU core, and this step is also fully parallel. (5) An optimal program is executed to find the appropriate thickness of each member from all the structural analysis results, and the total weight of the structure is calculated. (6) If all the member sizes are acceptable, the design procedure is terminated, or the new member sizes are used and, Step 2 is initiated to perform the next design cycle. However, the Turbsim and Fast programs for Step 3 do not have to be run again, since the blade forces are the same. In the above procedures, steps (1), (2), (5), and (6) cannot be parallel, but they only use a very small amount of computer time, since the major computer time is spent on Steps (3) and (4), which are in the fully parallel computation. Figure 3 shows the proposed finite element model and applied loads of the OWT support structures. The 3D two-node beam element is used to model the columns, bracings, piles, and tower, and the four-node plate element is used to model the platform at the bottom of the tower. The p-y, t-z, and Q-z curve springs, according to the API formulations [3], are used to model the soil-structure interaction. The static loads, such as dead and live working loads, are applied and analyzed using a one-step static analysis at the beginning. The dynamic loads, such as the wind, wave, and seismic loads, are analyzed using [PERSON]'s direct integration method with the Raleigh damping scheme. The Turbsim program is used to find the 3D wind distribution, and the Fast program is used to find the time-history of blade forces and moments at the hub center. The wave loads are both regular and irregular; the stream function theory is used to find the regular wave load, and the second-order function theory [37] is used to determine the irregular wave load. The seismic load uses the time and depth dependent displacements applied to one end of each p-y, t-z, and Q-c curve spring, where the Shake91 program [38] is used to find the depth dependent acceleration when the seismic accelerations at a specific depth are known.