Resources

Ming Ma Advanced Marine Technology Center DRS Technologies Inc. Stevensville, MD, USA

Owen Hughes Aerospace and Ocean Engineering Virginia Tech Blacksburg, VA, USA

Tobin McNatt Advanced Marine Technology Center DRS Technologies Inc. Stevensville, MD, USA

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.

Chengbi Zhao (V) Naval Architecture and Ocean Engineering, South China University of Technology, Guang Zhou, P.R. China

Ming Ma (AM) Advanced Marine Technology Center, DRS Technologies Inc., Stevensville, MD, USA

As the three-dimensional finite element model has become the de facto standard for ship structural design, interest in accurately transferring seakeeping loads to panel based structural models has increased dramatically in recent years. In today’s design practices, panel based hydrodynamic analyses are often used for mapping seakeeping loads to 3D FEM structural models. However, 3D panel based hydrodynamic analyses are computationally expensive. For monohull ships, methods based on strip theories have been successfully used in the industry for many years. They are computationally efficient, and provide good predictions for motions and hull girder loads. However, many strip theory methods provide only hull girder sectional forces and moments, such as vertical bend ing moment and vertical shear force, which are difficult to apply to 3D finite element structural models. Previously, the authors have proposed a hybrid strip theory method to transfer 2D strip theory based seakeeping loads to 3D finite element models. In the hybrid approach, the velocity potentials of strip sections are first calculated based on the ordinary 2D strip theories. The velocity potentials of a finite element panel are obtained from the interpolation of the velocity potentials of the strip sections. The panel pressures are then computed based on Bernoulli’s equation. Integration of the pressure over the finite element model wetted panels yields the hydrodynamic forces and moments. The equations of motion are then formulated based on the finite element model. The method not only produces excellent ship motion results, but also results in a perfectly balanced structural model. In this paper, the hybrid approach is extended to the 2.5D high speed strip theory. The simple Rankine source function is used to compute velocity potentials. The original linearized free surface condition, where the forward speed term is not ignored, is used to formulate boundary integral equations. A model based on the Series-64 hull form was used for validating the proposed hybrid method. The motion RAOs are in good agreement with VERES’s 2.5D strip theory and with experimental results. Finally, an example is provided for transferring seakeeping loads obtained by the 2.5D hybrid strip theory to a 3D finite element model.

Justin M. Freimuth (AM), Ming Ma (AM) Advanced Marine Technology Center DRS Technologies Inc., Stevensville, MD, USA

This paper presents a method to optimize an oil tanker cargo hold’s structural scantlings based on stiffened panel ultimate limit states. Two different tanker models and their results are presented demonstrating this optimization procedure using models of varying mesh densities. The full ship finite element models are loaded with multiple load cases, design bending moments, external hydrostatic pressure, and internal tank pressure. The working stresses of a stiffened panel, which are used for the panel’s ultimate limit states assessment, are obtained by 3D finite element analysis. Each stiffened panel is then optimized using multi-objective genetic algorithms for its weight and safety. The optimization process is performed on two different versions of the same vessel: one with all stiffeners defined explicitly and one with internal stiffeners (allowing the stiffener layout to be changed during the optimization). The numerical results show that the proposed method is very useful to perform ultimate strength based ship structural optimization with multiple objectives, namely minimizing the structural weight and maximizing structural safety.

Owen Hughes Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University Blacksburg, VA, USA

Ming Ma Advanced Marine Technology Center, DRS Technologies Inc., Stevensville, MD, USA

Jeom Kee Paik Department of Naval Architecture and Ocean Engineering, Pusan National University, Busan, Korea

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 Algorithms (or VEGA), is used to optimize a system of stiffened panels, e.g., ship structures, for their weight, safety and cost. The structure weight and cost are calculated using realistic finite element models. The structure safety is first evaluated through finite element analysis for the permissible stresses, and then revaluated using a set of ultimate limit state criteria, ALPS/ULSAP, which is capable of assessing stiffened panel buckling and stiffener instability efficiently. An example of optimizing a full cargo hold of a 200,000 ton oil tanker is presented. The numerical results show that the proposed 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.

Ming Ma, Justin Freimuth, Bruce Hays DRS Technologies, Stevensville/USA Nick Danese, Design Systems & Technologies, Antibes/France

The paper presents a method to optimize hull girder cross section scantlings based on stiffened panel ultimate limit states. A single frame spacing of the hull girder is modeled using plate and beam elements. A set of stiffened panels is then automatically defined based on the strong supports of the structure. The finite element model is loaded with multiple load cases, including end moments, external hydrostatic pressure, and internal tank pressure. The working stresses of a stiffened panel, which are used for the panel’s ultimate limit states assessment, are obtained by 3D finite element analysis. Each stiffened panel is then optimized using multi-objective genetic algorithms for its weight and safety. An iterative procedure is used to ensure the convergence of the working stresses. The hull girder ultimate strength is then obtained by nonlinear progressive hull girder strength analyses, such as ALPS/HULL. The result shows that the hull girder ultimate strength can be indirectly improved by optimizing local panel scantlings. An example of optimizing a cross section of a 200,000 ton oil tanker is presented. The numerical results show that the proposed 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.

Ming Ma Advanced Marine Technology Center, DRS Technologies Inc., Stevensville, MD, USA

Chengbi Zhao Naval Architecture and Ocean Engineering, South China University of Technology, Guangzhou, China

Owen Hughes Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA

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.

Ming Ma Advanced Marine Technology Center, DRS Technologies Inc., Stevensville, MD, USA

Owen Hughes Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University Blacksburg, VA, USA

Jeom Kee Paik Department of Naval Architecture and Ocean Engineering, Pusan National University, Busan, Korea

An efficient method of predicting the ultimate strength of stiffened panels under combined loads has been implemented in ALPS/ULSAP. The validity of the method was confirmed by various structural collapse tests and nonlinear FEA. The method is parametric formulated, mesh free, computational efficient, and is able to predict six different failure modes for a stiffened panel; therefore the solution process is suitable for design space exploration. In this paper, multi-objective optimization methods are used to determine the Pareto optimal solutions of a stiffened panel based on the ALPS/ULSAP algorithm. The objective is to solve a design problem aiming at simultaneously minimizing the weight and cost of a stiffened panel, and maximizing its buckling and yielding stress. Two multi-objective methods, Pareto Simulated Annealing (PSA) and Ulungu Multi-Objective Simulated Annealing (UMOSA) are presented for a single panel optimization, where the loads applied to the panel are assumed to be constant. To optimize a system of stiffened panels, e.g., ship structures, where the loads applied to an individual panel are functions of the system structural scantlings, an iterative procedure is presented. The numerical results show that the proposed 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.

Chengbi Zhao Naval Architecture and Ocean Engineering, South China University of Technology, Guang Zhou, P.R. China

Ming Ma Advanced Marine Technology Center, DRS Technologies Stevensville, MD, USA

Owen Hughes Aerospace and Ocean Engineering Virginia Polytechnic Institute and State University Blacksburg, VA, USA

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.

Ming Ma Advanced Marine Technology Center, DRS Defense Solutions, LLC, Stevensville, MD, USA

Owen Hughes Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA

Chengbi Zhao Naval Architecture and Ocean Engineering, South China University of Technology, Guang Zhou, P.R. China

Interest in the seakeeping loads of vessels has increased dramatically in recent years. In current design practice, methods for predicting seakeeping motions and loads are mainly in two categories, strip theory methods and 3D- panel methods. Methods based on strip theory provide reasonable motion prediction and are computationally efficient. However, many strip theory methods provide 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. For panel based methods, the outputs 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. Consequently, the panel pressure calculated from a hydrodynamic model mesh has to be transferred to the structural model mesh. The resulting discrepancy of the pressure map, regardless of what interpolation method is used, causes an imbalanced structural model. To obtain equilibrium of an imbalanced structural model, a common practice is to use the “inertia relief” approach [1]. 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 to balance the structural model without using inertia relief. The method uses quadratic programming to calculate corrective 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 [2], 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.

Ming Ma AMTC, DRS Defense Solutions, LLC, USA

Chengbi Zhao South China University of Technology, P.R. China

Nick Danese Design Systems & Technologies, France

Panel based hydrodynamic analysis is well suited for transferring seakeeping loads to 3D FEM structural models. Because panel based hydrodynamic analysis is computationally expensive, and also not very sensitive to the mesh density, it is common to first calculate seakeeping loads from a coarser hydrodynamic mesh, and then to map the panel pressure and inertia loads to the corresponding finer structural model. Various interpolation methods have been proposed to map the loads from one mesh to another. While the pressure integration results in a perfect equilibrium in the hydrodynamic model, it is very difficult to get a balanced structural model through any pressure interpolation methods. To rebalance the structural model, artificial accelerations and/or point loads have to be added. Recently, Malenica et al. (2008) proposed a method which maps the panel source strength instead of the panel pressure from a hydrodynamic mesh to the structural mesh, and then formulated the equations of motion in the structural mesh. The equations of motion also included a gravity term to account for the change in the coordinate system. The method results in a balanced structural model. In this paper, the cause of the unrealistic sway and surge force due to hydrostatic restoring pressure integration is further explained and discussed. A method of applying linear seakeeping pressure loads is presented. The method differs from Bureau Veritas’s approach in the following areas: 1. The corrective hydrostatic restoring force due to pressure integration is distributed to element nodes using quadratic programming; 2. There is no need to create and maintain two different models because the method only uses the structural mesh. A coarser hydrodynamic mesh is automatically generated from the structural mesh when the hydrodynamic analysis is performed; 3. The method is fully integrated within one FEA system, comprising modeling, loading, analysis, and evaluation.

Ming Ma Advanced Marine Technology Center, DRS Defense Solutions, LLC Stevensville, MD, USA

Owen F. Hughes Aerospace and Ocean Engineering Virginia Polytechnic Institute and State University Blacksburg, VA, USA

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].

Ming Ma Advanced Marine Technology Center, DRS Defense Solutions, LLC Stevensville, MD, USA

Beom-Seon Jang Offshore Basic Engineering Team, Samsung Heavy Industries CO. LTD Seoul, Korea

Owen F. Hughes Aerospace and Ocean Engineering Virginia Polytechnic Institute and State University Blacksburg, VA, USA

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.