Based on the discrete-module-beam (DMB) method, this study aims to address the connector stiffness optimization problem of modular box-pontoon-type offshore floating photovoltaic (OFPV) platforms. The floating foundation of such OFPV systems consists of multiple modular units connected by connectors. The connector stiffness design significantly impacts the platform's structural safety and reliability under complex ocean environments.

This research employs comprehensive methods. First, the DMB hydroelastic analysis method is introduced. The connector stiffness matrix form is given, with stiffness values for different degrees of freedom defined, and the numerical modeling method for hydroelastic response briefly outlined. This method allows for efficient calculation of the structure's response to environmental loads. Second, two genetic-algorithm-based approaches are presented. The linear-weighted genetic algorithm converts the multi-objective optimization problem into a single-objective one by assigning weights to different objectives. The NSGA-II (non-dominated sorting genetic algorithm II) is used as a multi-objective optimization algorithm, which can identify a set of Pareto-optimal solutions instead of a single one. Three encoding techniques for stiffness, namely real encoding, exponent encoding, and scientific notation encoding, are elaborated. Each encoding method has its own crossover and mutation operators. For example, real encoding directly operates on stiffness values, while exponent encoding and scientific notation encoding have unique operation mechanisms. The performance of these encoding methods is compared through population initialization and individual distribution analysis across different evolutionary generations. In addition, the concept of equivalent zero stiffness and equivalent infinite stiffness is introduced to reduce the solution space. This enhances the efficiency of the optimization process.

The results show that the NSGA-II algorithm can obtain the Pareto front with the objectives of minimizing the maximum structural shear force and minimizing the maximum structural bending moment. The Pareto front can be regarded as a set of optimal solutions corresponding to different weight settings obtained by the linear-weighted method. Analysis of population initialization and individual distribution reveals that the scientific notation encoding performs better in terms of search efficiency within the solution space. It can explore a wider range of stiffness values, including both low and high magnitudes, compared to the other two encoding methods.

In conclusion, the developed optimization theory model is effective in performing multi-objective optimization on the connector stiffness of modular box-pontoon-type OFPV platforms. The scientific notation encoding provides a more efficient way to search for optimal solutions. However, it should be noted that the OFPV system is complex, and future research can focus on considering additional objectives and combinations to further optimize the design. This research provides a valuable reference for the design and optimization of floating-type photovoltaic platforms in ocean engineering.

This paper integrates the finite element method (FEM) with the discrete-module-beam (DMB) method and improves the derivation of the lumped-mass stiffness matrix in order to efficiently apply the DMB method to complex and compound very large floating structures (VLFS).

First, 3D potential flow theory is introduced to the DMB method to establish the hydroelastic equation. FEM theory is then introduced to discretize each macro-submodule into micro beam elements, and the lumped-mass matrix is then derived on the basis of the sub-structure approach and matrix manipulation. In dealing with complex boundary conditions, the cross-zeros-set-one approach or adding an additional constraint into the total stiffness matrix is adopted. In dealing with complex interconnections, the node numbering is first altered and then an additional constraint stiffness matrix is added to the total stiffness matrix.

When the FEM+DMB method is applied to VLFS with fixed/spring-damped boundary conditions and hinged/rigid/spring-damped interconnections, good agreement is shown with the results from the direct method.

The proposed FEM+DMB method can analyze the hydroelasticity of VLFS in complex engineering scenarios with enhanced speed and accuracy.

The aim of this paper is to proposes new methods for modelling a very large floating structure (VLFS) with complex connections in the framework of the discrete-module-beam (DMB) hydroelasticity theory, and makes a comparison with the existing methods.

First, a brief introduction of the DMB-based hydroelasticity analysis method is given, followed by procedures for calculating the dynamic response of VLFS under regular waves. A structural stiffness matrix is then defined to model connections with complex forms in VLFS. Corrections are made to the relationship between the forces of two lumped masses and their displacements, obtaining a revised structural stiffness matrix and excitation force matrix, and solving the new hydroelastic equations. Finally, the varying trends of the structural dynamic response of VLFS against different bending stiffness by four methods are explored, and the corresponding reasons for their response differences are analyzed.

The results show that all four methods are capable of precisely predicting the hydroelastic response of VLFS with complex forms of interconnection.

The methods in this paper extend the application of the DMB-based method in predicting the dynamic response of non-continuous VLFS, such as multi-hinged VLFS or VLFS with fracture places.