Owen Hughes

A practical method to apply hull girder sectional loads to full-ship 3D finite-element models using quadratic programming

Interest in the seakeeping loads of vessels has increased dramatically in recent years. While many studies focused on predicting seakeeping loads, little attention was given on how loads are transferred to 3D finite-element models. In current design practice, methods for predicting seakeeping motions and loads are mainly based on the potential flow theory, either strip theory methods or 3D-panel methods. Methods based on strip theory provide reasonable motion prediction for ships and are computationally efficient. However, the load outputs of strip theories are only hull girder sectional forces and moments, such as vertical bending moment and vertical shear force, which cannot be directly applied to a 3D finite-element structural model. Methods-based 3D panel methods can be applied to a wide range of structures, but are computationally expensive. The seakeeping load outputs of panel methods include not only the global hull girder loads, but also panel pressures, which are well suited for 3D finite-element analysis. However, because the panel-based methods are computationally expensive, meshes used for hydrodynamic analyses are usually coarser than the mesh used for structural finite-element analyses. When pressure loads are mapped from one mesh to another, a small discrepancy at the element level will occur regardless of what interpolation method is used. The integration of those small pressure discrepancies along the whole ship inevitably causes an imbalanced structural finite-element model. To obtain equilibrium of an imbalanced structural model, a common practice is to use the ‘inertia relief’ approach. However, this type of balancing causes a change in the hull girder load distribution, which in turn could cause inaccuracies in an extreme load analysis (ELA) and a spectral fatigue analysis (SFA). This paper presents a practical method to balance the structural model without using inertia relief. The method uses quadratic programming to calculate equivalent nodal forces such that the resulting hull girder sectional loads match those calculated by seakeeping analyses, either by strip theory methods or 3D-panel methods. To validate the method, a 3D panel linear code, MAESTRO-Wave, was used to generate both panel pressures and sectional loads. A model is first loaded by a 3D-panel pressure distribution with a perfect equilibrium. The model is then loaded with only the accelerations and sectional forces and moments. The sectional forces and moments are converted to finite-element nodal forces using the proposed quadratic programming method. For these two load cases, the paper compares the hull girder loads, the hull deflection and the stresses, and the accuracy proves the validity of this new method.

Permanent Means of Access Structural Design Using Multi-Objective Optimization

Permanent means of access (PMA) of oil tankers and bulk carries consists of a wide platform for walk through inspection. Since PMA structures have a tall web plate, they are vulnerable to elastic tripping. A previous paper [1] proposed a Rayleigh-Ritz method to analyze elastic tripping behavior of PMA structures. The method is parametric formulated, mesh free, computational efficient, and is able to predict both the flange plate critical tripping stress as well as the web plate local buckling stress; therefore the solution process is suitable for design space exploration. In this paper, multi-objective optimization methods are used to determine the Pareto solutions of a PMA structure based on the proposed tripping algorithm. The objective is to solve a design problem aimed at simultaneously minimizing the weight of a PMA structure and maximizing its critical buckling stress. Three multi-objective methods, Pareto Simulated Annealing (PSA), Ulungu Multi-objective Simulated Annealing (UMOSA) and Multi-objective Genetic Algorithm (MOGA) are presented for a case study. The numerical results show that all three methods can efficiently and effectively solve such optimization problems within a short search time. The critical buckling stress of the final optimal designs is validated by the linear and non-linear buckling analysis of NX-NASTRAN [2] .Copyright

Tripping Analysis and Design Consideration of Permanent Means of Access Structure

An efficient Rayleigh-Ritz approach is presented for analyzing the lateral-torsional buckling (“tripping”) behavior of permanent means of access (PMA) structures. Tripping failure is dangerous and often occurs when a stiffener has a tall web plate. For ordinary stiffeners of short web plates, tripping usually occurs after plate local buckling and often happens in plastic range. Since PMA structures have a wide platform for a regular walk-through inspection, they are vulnerable to elastic tripping failure and may take place prior to plate local buckling. Based on an extensive study of finite element linear buckling analysis, a strain distribution is assumed for PMA platforms. The total potential energy functional, with a parametric expression of different supporting members (flat bar, T-stiffener and angle stiffener), is formulated, and the critical tripping stress is obtained using eigenvalue approach. The method offers advantages over commonly used finite element analysis because it is mesh-free and requires only five degrees of freedom; therefore the solution process is rapid and suitable for design space exploration. The numerical results are in agreement with NX NASTRAN [1] linear buckling analysis. Design recommendations are proposed based on extensive parametric studies.Copyright

Ultimate Limit State Based Ship Structural Design Using Multi-Objective Discrete Particle Swarm Optimization

Multi-objective optimization problems consist of several objectives that must be handled simultaneously. These objectives usually conflict with each other, and optimizing a particular solution with respect to a single objective can result in unacceptable results with respect to the other objectives. A reasonable solution to a multi-objective problem is to investigate a set of solutions, each of which satisfies the objectives at an acceptable level without being dominated by any other solution. Genetic or evolution algorithms have been demonstrated to be particularly effective to determine excellent solutions to these problems. Among many algorithms, the particle swarm optimization (PSO) has been found to be faster with less computational overhead. In this paper a multi-objective discrete particle swarm optimization is formulated and used to optimize a large and complex thin-wall structure on the basis of weight, safety and cost. The structure weight and cost are calculated using realistic finite element models. The design process has two stages: (1) the actual stresses are obtained by finite element analysis of the full ship, (2) for a midship segment of the ship (referred to as a “control cluster”) the structural safety is evaluated using the ALPS/ULSAP set of ultimate limit state criteria, and then the segment is optimized using any suitable optimization method (in this paper, the PSO method). Both stages involve iteration, but the process is arranged so as to keep the number of full ship finite element analyses to a minimum. The complete design process is illustrated for a 200,000 ton oil tanker. The numerical results show that the PSO method is very useful to perform ultimate strength based ship structural optimization with multi-objectives, namely minimization of the structural weight and cost and maximization of structural safety. The example also demonstrates that the proper definition of boundary conditions and design load cases is of paramount importance for design optimization.Copyright

Applications of Vector Evaluated Genetic Algorithms (VEGA) in Ultimate Limit State Based Ship Structural Design

Ship structural design often deals with multiple objectives such as weight, safety, and cost. These objectives usually conflict with each other, and optimizing a particular solution with respect to a single objective can result in unacceptable results with respect to the other objectives. A reasonable solution to a multi-objective problem is to investigate a set of solutions, each of which satisfies the objectives at an acceptable level without being dominated by any other solution. Genetic algorithms have been demonstrated to be particularly effective to determine excellent solutions to these problems. In this paper a multi-objective GA, called Vector Evaluated Genetic Algorithm (VEGA) is formulated and used to optimize a large and complex thin-wall structure (a complete cargo hold of a 200,000 ton oil tanker) on the basis of weight, safety and cost. The structure weight and cost and all of the stresses are calculated using a realistic finite element model. The structure adequacy is then evaluated using the ALPS/ULSAP computer program (Paik and Thayamballi, 2003) which can efficiently evaluate all six ultimate limit states for stiffened panels and grillages. This example was chosen because the initial design is severely inadequate. The results show that the proposed method can perform ultimate strength based structural optimization with multi-objectives, namely minimization of the structural weight and cost and maximization of structural safety, and also that the method is very robust.Copyright

APPLYING STRIP THEORY BASED LINEAR SEAKEEPING LOADS TO 3D FULL SHIP FINITE ELEMENT MODELS

Panel based hydrodynamic analyses are well suited for transferring seakeeping loads to 3D FEM structural models. However, 3D panel based hydrodynamic analyses are computationally expensive. For monohull ships, methods based on strip theory have been successfully used in industry for many years. They are computationally efficient, and they provide good prediction for motions and hull girder loads. However, many strip theory methods provide only hull girder sectional forces and moments, such as vertical bending moment and vertical shear force, which are difficult to apply to 3D finite element structural models. For the few codes which do output panel pressure, transferring the pressure map from a hydrodynamic model to the corresponding 3D finite element model often results in an unbalanced structural model because of the pressure interpolation discrepancy. To obtain equilibrium of an imbalanced structural model, a common practice is to use the “inertia relief” approach to rebalance the model. However, this type of balancing causes a change in the hull girder load distribution, which in turn could cause inaccuracies in an extreme load analysis (ELA) and a spectral fatigue analysis (SFA). This paper presents a method of applying strip theory based linear seakeeping pressure loads to balance 3D finite element models without using inertia relief. The velocity potential of strip sections is first calculated based on hydrodynamic strip theories. The velocity potential of a finite element panel is obtained from the interpolation of the velocity potential of the strip sections. The potential derivative along x-direction is computed using the approach proposed by Salvesen, Tuck and Faltinsen (1972). The hydrodynamic forces and moments are computed using direct panel pressure integration from the finite element structural panel. For forces and moments which cannot be directly converted from pressure, such as hydrostatic restoring force and diffraction force, element nodal forces are generated using Quadratic Programing. The equations of motions are then formulated based on the finite element wetted panels. The method results in a perfectly balanced structural model. An example is given to compare the “ordinary strip theory” to the proposed direct pressure integration method. The accuracy proves the validity of this new method.