Optimization of panel forms for improvement in ship structures

This paper presents a model for optimum design of three panel forms, namely tee stiffened, flat-bar stiffened and corrugated panels to be used in ship structures. Scantlings of the three forms have been modelled as free design variables. Limit values against different possible failure modes in conjunction with safety factors and load effects have formed the sets of design constraints. Some production restrictions are also incorporated in the model. An optimization algorithm based on sequential linear programming has been used for optimum design of the three forms. Some special features are incorporated in the optimization algorithm to avoid numerical instability problems and to handle integer variables and more than one design criterion.The capability of the model is demonstrated in a series of practical applications against a wide range of design parameters such as loads, variation of span, price ratio index (labour rate to material price ratio) and design criteria (minimum cost, minimum weight and equal priority). Appropriate presentation and analysis of results have produced a practical guide to strive for improvement in the overall ship structure even satisfying conflicting design demands. Moreover, the designer's capability to reflect his preference level to particular criteria has been demonstrated through the investigation of a wide range of Pareto-optimal designs.     

Integrated layout and topology optimization design of multi-frame and multi-component fuselage structure systems

The purpose of this paper is to present an extended integrated layout and topology optimization method dealing with the multi-frame and multi-component fuselage structure systems design. Considering an aircraft or aerospace fuselage system including main structure, numbers of frames and featured components located on the frames, a simultaneous optimization procedure is proposed here including geometrical design variables of components and frames as well as topological design variables of main structure and frame structures. The multi-point constraints (MPC) scheme is used to simulate the rivets or bolts connecting the components, frames and structures. The finite circle method (FCM) is implemented to avoid the overlaps among different components and frames. Furthermore, to deal with the difficulties of large numbers of non-overlapping constraints, a penalty method is used here to compose the global strain energy and non-overlapping constraints into a single objective function. To guarantee the fuselage system’s balance, the constraint on the system centroid is also introduced into the optimization. Different numerical examples are tested and the optimized solutions have demonstrated the validity and effectiveness of the proposed formulation.     

Optimum configurational and dimensional design of truss structures

The feasibility of simultaneous optimization of member sizing and structural configuration of truss structures is demonstrated. The structural analysis is treated by the finite element displacement method and the optimization accomplished by the steepest descent method. Inequality constraints including limitations on both state variables (stress and displacement) and design variables (element cross sectional areas and nodal point placement) are included.The computational results show that in the presence of displacement constraints, the configuration of the optimum design sometimes differs considerably from the fully stressed design. The techniques can be extended to other structures such as beams, frames, plates, etc. and to include the possibility of Euler buckling.     

The effects of rehabilitation objectives on near optimal trade-off relation between minimum weight and maximum drift of 2D steel X-braced frames considering soil-structure interaction using a cluster-based NSGA II

A cluster-based non-dominated sorting genetic algorithm (NSGA) II has been considered to investigate the effects of rehabilitation objectives on multi-objective design optimization of two-dimensional (2D) steel X-braced frames in the presence of soil-structure interaction. The substructure elasto-perfect plastic model has been adopted for modeling of the soil-structure interaction and the nonlinear pushover analysis is used to evaluate the performance level of the frames for a specified hazard level. Cross-sections of grouped elements of the frames are considered to be discontinuous design variables of the problem. Via implementing some of the constraints, which are independent of doing the time-consuming nonlinear analysis, input population of the optimization technique has been clustered. By using the nonlinear analysis technique in conjunction with the cluster-based NSGA II, near optimal trade-off relation between minimum weight and maximum story drifts of the frames are obtained. The allowable rotations, geometry, and resistance constraints of the structural elements are considered in the optimization design of the frames. The effects of the enhanced basic safety and limited selective rehabilitation objectives on optimum design of the frame are studied. The results show differences between the optimum results of the three mentioned rehabilitation objectives and effects of soil types.

     

A mixed GA-PSO-based approach for performance-based design optimization of 2D reinforced concrete special moment-resisting frames

A mixed genetic algorithm and particle swarm optimization in conjunction with nonlinear static and dynamic analyses as a smart and simple approach is introduced for performance-based design optimization of two-dimensional (2D) reinforced concrete special moment-resisting frames. The objective function of the problem is considered to be total cost of required steel and concrete in design of the frame. Dimensions and longitudinal reinforcement of the structural elements are considered to be design variables and serviceability, special moment-resisting and performance conditions of the frame are constraints of the problem. First, lower feasible bond of the design variables are obtained via analyzing the frame under service gravity loads. Then, the joint shear constraint has been considered to modify the obtained minimum design variables from the previous step. Based on these constraints, the initial population of the genetic algorithm (GA) is generated and by using the nonlinear static analysis, values of each population are calculated. Then, the particle swarm optimization (PSO) technique is employed to improve keeping percent of the badly fitted populations. This procedure is repeated until the optimum result that satisfies all constraints is obtained. Then, the nonlinear static analysis is replaced with the nonlinear dynamic analysis and optimization problem is solved again between obtained lower and upper bounds, which is considered to be optimum result of optimization solution with nonlinear static analysis. It has been found that by mixing the analyses and considering the hybrid GA-PSO method, the optimum result can be achieved with less computational efforts and lower usage of materials.     

Application of topology optimization to design an electric bicycle main frame

Electric bicycle main frame is the most principal structure, connecting and supporting other various components, while bearing a variety of forces and moments. In this paper the topology optimization technology is applied to generate robust electric bicycle main frame by optimizing the material distribution subject to the constraints and dynamic loads. Geometric, mechanical and finite element models, as well as a flexible coupling dynamic model are constructed. Validity and accuracy of these models are investigated through real-life testing. By applying typical road excitation, dynamic loads of all key points are extracted. A set of forces data is extracted every 0.5?s during the whole simulation, including peak values of these forces. In order to obtain appropriate topology optimization results, the values of two crucial parameters, volume fraction and minimum member size, are discussed respectively. Then the topology optimization of multi-load case is implemented with the objective of minimizing the set of weighted compliances resulting from individual load cases. Results illustrate that element density distribution of the model is optimized with manufacturing constraints of minimum member size control and extrusion constraint. Consequently, the better frame form design of the electric bicycle is obtained. Modal analysis for the original and refined models is performed respectively to evaluate the structure stiffness. The results indicate that this optimization program is effective enough to develop a new electric bicycle frame as a reference for manufacturers.     

CAE技术在汽车座椅骨架开发中的应用

为提高汽车座椅骨架的开发质量,在某型汽车座椅骨架开发中应用CAE技术进行骨架静强度和疲劳等模拟.采用壳单元与梁单元相结合建立座椅骨架有限元模型;根据座椅骨架台架耐久试验要求和试验条件,对座椅安装孔进行全约束处理,并在试验加载位置施加相应的载荷;采用Abaqus/Standard分析座椅骨架强度;在静强度分析基础上应用F...     

基于有限元法的客车车架结构分析与研究

在Hypermesh软件中采用板壳单元对车架几何模型进行网格划分,建立车架的有限元模型。根据客车的承载特点和行使工况,对该车车架进行动力学分析。并对车架进行模态计算,得到车架的固有频率和固有振型。配合实验数据,对车架结构的设计提出了合理的改进方案,本文可获得较高的工程应用价值。     

Structural synthesis of frame reinforced,submersible, circular,cylindrical hulls

This paper describes a mathematical programming procedure for the automated optimal structural synthesis of frame stiffened, cylindrical shells. For a specified set of design parameters such as external pressure, shell radius and length and material properties, the method generates those values of the design variables that produce a minimum weight design. The skin, frame web and frame flange thicknesses and the flange width are treated as continuous variables. Frame spacing is considered a discrete variable. Constraint equations control local and general shell and frame instability and yield. Limits may be placed on the variable values, and certain geometric or space constraints can be applied. The mixed (continuous and discrete nonlinear programming problem is solved by a combination of a discrete ‘Golden Search’ for the optimal number of frames and the ‘Direct Search Design Algorithm’ which provides the optimum values of the continuous variables.     

Geometry and topology optimization of plane frames for compliance minimization using force density method for geometry model

A new method is proposed for simultaneous optimization of shape, topology and cross section of plane frames. Compliance against specified loads is minimized under constraint on structural volume. Difficulties caused by the melting nodes can be alleviated to some extent by introducing force density as design variables for defining the geometry, where the side constraints are assigned for force density to indirectly avoid the existence of extremely short members. Force density method is applied to an auxiliary cable-net model with different boundary and loading conditions so that the regularity of force density matrix is ensured by positive force densities. Sensitivity coefficients of the objective and constraint functions with respect to the design variables are also explicitly calculated. After the optimal geometry of the frame is obtained, the topology is further improved by removing the thin members and combining closely spaced nodes. It is demonstrated in the numerical examples of three types of frames that rational geometry and topology can be achieved using the proposed method, and the effect of bending moment on the optimal solution is also discussed.

     

Optimum weight analysis of steel frames with semirigid connections

A fact that should be initially emphasized is that this research work does not mainly aim at development of optimization techniques which have already been well established for some time ago. Our aim here is only to make use of these techniques for another purpose namely; to obtain the optimum weight solution for steel frames using the semirigid connections concept. The purpose of this study was to determine the following: (1) The percent of rigidity of the semirigid connections that would give the optimum steel weight for the common types of steel frame structures. (2) The exact percent of steel saving when using the semirigid connections concept, compared to the classical approach. (3) Which is cheaper, the gable or the portal frame, considering the same condition of loading and geometrical configuration. Also the relative cheapness of the double bay or triple-bay multistory frames having the same number of storys and also same conditions of loading and height of columns and total span. (4) Whether the deflection is a governing parameter which might hinder the benefits of the use of semirigid connections. The problem here is to find the optimum weight of plane semirigid connected steel frames. The objective function is given by the weight of structure in terms of the geometrical properties of the elements and the density of steel. The design variables are the breadth of flange and the height of web for each element. For the portal, the gable, the triple bay three story, and the double bay three story frames the number of design variables are four, four, ten, and ten respectively. The design constraints represent strength and stiffness design code requirements. Side constraints are respected to assure nonviolating of the practical available dimensions. The model is solved using the nonlinear programming techniques. The unconstrained formulation using the interior penalty function technique is selected. Powell's algorithm is chosen for the generation of the search vector, and the quadratic interpolation technique is chosen for the determination of the step size. The conclusions are as follows: (1) The use of semirigid connections will provide a saving in weight equal to 28% in the portal frame for corresponding rigidity ratio (R.R.) of 0.9, and a saving of 19% in the gable frame for a corresponding R.R. of 0.733. (2) The use of semirigid connections will provide a saving in weight of 10.75% in the double bay three story frame for a corresponding R.R = 0.733, and 23% for the triple bay three story frame with a corresponding R.R = 0.75. (3) The variation in the percent of the rigidity of the column to girder connection will not cause a corresponding change in the amount of steel allocated to columns and girders. (4) The saving in weight will occur mainly due to girders rather than columns. (5) The vertical deflections were not regarded as a dominating factor as its value did not exceed the allowable limits.     

Multilevel optimization applied to hull girder design using three panel forms

A multilevel design scheme for ship's hull girders (longitudinal members between two adjacent transverse frames) is presented in this paper. This design scheme handles, very conveniently, the complexity of using an optimization algorithm for such complex design problems having a large number of design variables, nonlinear constraints dealing with different failure modes and interactions among substructures, and nonlinear design objectives. The conventional multilevel design technique is modified by introducing an approach called constraint coordination to increase the probability of achieving the overall optimum very efficiently.The scheme is demonstrated by application to the structural design of hull girders with simple structural modelling to represent inland waterway ships on which there was a special emphasis in the original research project (Rahman 1991). Three possible panel (consisting of one stiffener and its attached plating) forms; tee stiffened, flat-bar stiffened and corrugated, are optimized to synthesize the hull girder in order to achieve the most efficient structure. The effect of price-structure (labour rate to material price ratio) on the design is also investigated.     

Optimization of airplane wing structures under gust loads

A methodology is presented for the optimum design of aircraft wing structures subjected to gust loads. The equations of motion, in the form of coupled integro-differential equations, are solved numerically and the stresses in the aircraft wing structure are found for a discrete gust encounter. The gust is assumed to be one minus cosine type and uniform along the span of the wing. In order to find the behavior of the wing structure under gust loads and also to obtain a physical insight into the nature of the optimum solution, the design of the typical section (symmetric double wedge airfoil) is studied by using a graphical procedure. Then a more realistic wing optimization problem is formulated as a constrained nonlinear programming problem based on finite element modeling and the optimum solution is found by using the interior penalty function method. A sensitivity analysis is conducted to find the effects of changes in design variables about the optimum point on the response quantities of the wing structure.     

Inelastic dynamic response of reinforced concrete infilled frames

An inelastic finite element model to simulate the behaviour of reinforced concrete frames infilled with masonry panels subjected to static load and earthquake excitation has been presented. Under the loads, the mortar may crack causing sliding and separation at the interface between the frame and the infill. Further, the infill may get cracked and/or crushed which changes its structural behaviour and may render the infill ineffective, leaving the bare frame to take all the load which may lead to the failure of the framing system itself. In this study, a mathematical model to incorporate this behaviour has been presented.     

A comparison of simulated annealing and genetic algorithm for optimum design of nonlinear steel space frames

In this article, two algorithms are presented for the optimum design of geometrically nonlinear steel space frames that are based on simulated annealing and genetic algorithm. The design algorithms obtain minimum weight frames by selecting suitable sections from a standard set of steel sections such as the American Institute of Steel Construction (AISC) wide-flange shapes. Stress constraints of AISC Load and Resistance Factor Design (LRFD) and AISC Allowable Stress Design (ASD) specifications, maximum (lateral displacement) and interstorey drift constraints, and also size constraints for columns were imposed on frames. The algorithms were applied to the optimum design of three space frame structures, which have a very small amount of nonlinearity. The unconstrained form of objective function was applied in both optimum design algorithms, and constant penalty factors were used instead of gradually increasing ones. Although genetic algorithm took much less time to converge, the comparisons showed that the simulated annealing algorithm yielded better designs together with AISC-LRFD code specification.     

Optimum design of frames with multiple constraints using an evolutionary method

This paper presents a simple evolutionary method for the optimum design of structures with stress, stiffness and stability constraints. The evolutionary structural optimization method is based on the concept of slowly removing the inefficient material and/or gradually shifting the material from the strongest part of the structure to the weakest part until the structure evolves towards the desired optimum. The iterative method presented here involves two steps. In the first step, the design variables are scaled uniformly to satisfy the most critical constraint. In the second step, a sensitivity number is calculated for each element depending on its influence on the strength, stiffness and buckling load of the structure. Based on the element sensitivity number, material is shifted from the strongest to the weakest part of the structure. These two steps are repeated in cycles until the desired optimum design is obtained. Illustrative examples are given to show the applicability of the method to the optimum design of frames and trusses with a large number of design variables.     

A development of data structure and mesh generation algorithm for whole ship analysis modeling system

In the whole ship structure and vibration analysis, the FEA (finite element analysis) model of whole ship structure is required in the early design stage before the 3D CAD model is defined. Because ship structure has a complex curved surface, and many associated structural members, the whole ship analysis modeling job has become a time consuming job. For the effective support of the whole ship analysis modeling, a method to generate the analysis model using initial design information within the ship design process, hull form offset data and compartment data, is developed. To easily handle initial design information and FE model information, a flexible data structure is proposed. An automatic quadrilateral mesh generation algorithm using initial design information to satisfy the constraints imposed by the ship structure is also proposed. With the proposed data structure and mesh generation algorithm, whole ship analysis modeling job for various ship types can be effectively supported and these results are presented.     

舰船概念设计中振动预报方法

以带有双层隔振装置的舰船模型为对象,利用MSC Nastran的有限元分析方法以及试验手段,对其隔振性能进行研究.将船体与双层隔振装置作为一个系统,建立三维有限元振动分析模型;以降低船体结构振动能量为目标,对发动机激励作用下的双层隔振装置与船体的振动特性进行分析;通过有限元分析方法和试验两方面的研究与对比,为舰船的减振降噪的初期概念设计提供快速预报方法.     

On structural optimization with aeroelasticity constraints

The optimal design of a cantilever wing in incompressible flow is considered. The wing is modelled as a full depth sandwich wing using finite element analysis. A doublet lattice panel method is used for computation of the unsteady aerodynamic loads. The weight of the wing is minimized using the thicknesses of the composite face sheets as design variables subject to constraints on flutter and divergence speed. Imperfection sensitivity of the final design is analysed and general aspects of imperfection sensitivity in optimization subject to aeroelasticity constraints are discussed in some detail.