### 1. Introduction

### 2. Optimal Design of Fixed Offshore Structure

### 2.1 Design of Fixed Offshore Structure Based on Classification Society Rules

### 2.2 3D Topology Optimization Formulation of the Fixed Offshore Structure

*f*and displacement

*u*for the number of elements (NE) in the entire design domain, as shown in Eq. (1). To compare and verify the high effectiveness of the optimal designs derived by topology optimization, a volume constraint using the relative material density

*ρ*and initial volume

_{i}*V*

_{0}of each element is introduced as Eq. (2). Thereby, an amount of material (

*V*) equal to that in the rule-based scantling design (shown in Fig. 1) could be used in the topology optimization. Based on SIMP, the design variables in the 3D topology optimization problem of the fixed offshore structure can be expressed with

_{c}*ρ*and the initial material property

_{i}*E*

_{0}of each element as shown in Eq. (3). Here, the penalty parameter

*n*was set as 3. The penalty parameter interpolates the relative material density so that it can be close to the extreme values of 0.0 and 1.0 to reduce the proportion of members with intermediate densities in the topology optimization. It generally exhibits stable convergence at values between 2 and 4. Furthermore, a very small value was selected as the lower limit of the relative material density (as shown in Eq. (4)) to prevent singularity in numerical analysis owing to the void elements generated in the topology optimization process.