A hybrid deterministic/stochastic optimization approach for the shape configuration design of structures

Multi-objective optimization design of pile-anchor structures for slopes based on reliability theory considering the spatial variability of soil properties

This paper develops an alternative optimization approach for systematic design of a parametrized engine system and illustrates the procedure through application to a novel conversion device, the patented Stiller-Smith mechanism (1, 2). Using simultaneous interplay between a simulation scheme, presented in detail elsewhere (3), and an optimization scheme, the proposed structural design process integrates the multiple objectives of structural design. Developed here in detail, optimization involves intermediate continuous optimization via a penalty function method, and integer or discrete programming through the branch-and-bound algorithm. The ensuing application illustrates the approach by optimizing a 16-cylinder Stiller-Smith engine for minimum weight-power and dimensions-power ratios under several types of constraints. In the context of a multi-objective constrained non-linear programming problem, the design example proceeds through three stages: (a) preliminary, in which the designer applies the simulation scheme to obtain the system response variables from the design requirements to reflect trade-off relationships among multiple design objectives; (b) secondary, the intermediate continuous optimal design stage, in which a penalty function method is used to specify constraints within a general range to allow variation in the choice of parameters; and (c) final, in which the branch-and-bound algorithm constrains integer variables to take integer values and discrete variables to take discrete values, thereby arriving at an optimal design.

<p>This paper defines basic operations of neutrosophic numbers and neutrosophic number functions for objective functions and constraints in optimization models. Then, we propose a general neutrosophic number optimization model for the optimal design of truss structures. The application and effectiveness of the neutrosophic number optimization method are demonstrated through the design example of a two-bar truss structure under indeterminate environment to achieve the minimum weight objective under stress and stability constraints. The comparison of the neutrosophic number optimal design method with traditional optimal design methods proves the usability and suitability of the presented neutrosophic number optimization design method under an indeterminate / neutrosophic number environment.</p>

An automatic optimization approach for the structural design of turbine blade shroud is presented and applied to the optimal design of a zigzag shroud in this paper. It integrates commercial CAD and CAE softwares into optimization procedure iSIGHT. According to the normal rules of the shroud design and experience, this paper advises a zigzag shroud which is fit for a kind of turbine blade. The parametric model of the shroud is established and the pre-twist angle parameter is taken into consideration. The structural intensity performance of the shroud, which is used to compute the optimal objective and constraints during optimization, is determined by conducting coupled thermal-structural analysis of shrouded turbine blade using the commercial Finite Element code ANSYS. Two application examples of the optimization approach are presented, with optimal objective functions of shrouded blade mass and maximum shroud contact pressure respectively. The latter includes the pre-twist angle as one of design variables. Mechanical and geometry constraints are applied on the design to ensure that the optimized design meets requirements for feasibility of engineering criteria. Simulation results from shroud optimizations by means of the optimization approach prove that the performance of the shroud can be improved significantly through structure optimization. The optimization approach provides an effective method to design and optimize the similar complicated models.

Magnetic-less multilevel dc-dc converters attract much attention in automotive industry due to their small size, high efficiency, and high temperature operation features. A multilevel-modular capacitor-clamped dc-dc converter (MMCCC) is one of the most promising topologies among them with simple control and reduced switch current stress. This paper presents the optimal design considerations for an MMCCC to achieve the highest efficiency and the smallest size. In order to design the converter with the highest efficiency, the analytical power loss equation of an MMCCC should be derived. By considering the stray inductance in the circuit, the optimal design approach should be divided into two cases, overdamped case and underdamped case. The converter can be designed to achieve high efficiency in both cases by varying circuit parameters. If the circuit is designed in overdamped case, huge electrolytic capacitor bank has to be used to achieve high efficiency, which will increase the total converter size. If the circuit is designed in underdamped case, small-size multilayer ceramic capacitor can be utilized due to the low capacitance requirement. Although relatively high switching frequency is required in underdamped case due to practical considerations, zero-current switching (ZCS) can be achieved for all the switching devices which minimize the converter switching loss. Therefore, the optimal design point of an MMCCC with the smallest size and the highest efficiency should be selected at the underdamped case with ZCS for all the switches. Simulation results are provided to validate the design. A prototype of an MMCCC by using the proposed optimal design procedure is built. Experimental results of this optimal designed MMCCC prototype are provided to demonstrate the validity of the proposed method.

Application of endurance time method in performance-based optimum design of structures

Reliability-based optimum distribution of seismic energy dissipation devices in fuzzy structural systems using meta-models

This paper presents the generalized compound scaling algorithm and its application to optimum weight design of plate structures. The optimum designs are reached by simply scaling the design variables to an optimum intersection of multiple constraints. A four-noded isoparametric plate element is used for modeling the structure. Sensitivity computations and the optimization algorithm are discussed. The optimization cost involved (excluding the finite element analyses) is very small using this algorithm. The procedure is demonstrated on three example problems using stress and displacement constraints with side bounds on the design variables.

This chapter introduces the improvement and application of swarm algorithm named Group Search Optimizer (GSO) in civil structure optimization design. GSO is a new and robust stochastic searching optimizer, as it is based on PS (produce and scrounger) model and the animal scanning mechanisms. An improved group search optimizer named IGSO was presented based on harmony search mechanism and GSO. The implementation of IGSO for different optimal purposes is presented in detail, including the application of IGSO to truss structure shape optimal design, to truss structure dynamic optimal design, to truss structure topology optimization design. Different truss structures are used to test the GSO and IGSO in structural shape optimization, dynamic optimization and topology optimization.

Considering uncertainties in engineering optimum design is often a requirement. Here, the use of the deterministic optimum design as the reference point in g-dominance is proposed. The multiobjective optimum robust design in a structural engineering test case where uncertainties in the external loads are taken into account is proposed as application, where the simultaneous minimization of the constrained weight average and the standard deviation of the constraints violation are the objective functions. Results include a comparison between both non-dominated sorting genetic algorithm II (NSGA-II) and strength Pareto evolutionary algorithm (SPEA2), including S-metric (hypervolume) statistical comparisons with and without the g-dominance approach. The methodology is capable to provide robust optimum structural frame designs successfully.

This Chapter describes some of the heuristic methods which have been developed for the optimum design of engineering structures using only components which are available in discrete sizes. As a vehicle for describing the methods the optimum design of trusses using rolled steel sections is used. The combinatorial nature of the problem is first briefly described and the necessity for heuristic methods for finding non-rigorous but very close discrete optimum designs are discussed. An investigation of the practical needs of structural designers rather than the capabilities of numerical algorithms demonstrates that the nature of the discrete design problem in practice is very different from that perceived by many researchers. The standardization problem, which is closely related to discrete optimum design, is described and discussed. The Chapter also examines heuristic methods such as the rounding of continuous optimum designs to a discrete solution and describes the linear segmental approach to discrete optimum design.

Chapter 1 Introduction of swarm intelligent algorithms.- Chapter 2 Application of particle swarm optimization algorithm to engineering structures.- Chapter 3 Optimum design of structures with heuristic particle swarm optimization algorithm .-Chapter 4 Optimum design of structures with group search optimizer algorithm .-Chapter 5 Improvements and applications of group search optimizer in structural optimal design .-Chapter 6 Optimum design of structures with quick group search optimization algorithm .-Chapter 7 Group search optimizer and its applications on multi-objective structural optimal design .-Chapter 8 Prospecting swarm intelligent algorithms.

The optimal and smart design of nonlinear building structures with and without passive dampers subjected to earthquake loading is of great concern in the structural design of building structures. The research started around 1980 and many investigations have been conducted. A comprehensive review on this subject is made in this article. After the description of essential features of the optimal design problem of nonlinear building structures under earthquake ground motions, analysis types of optimization problems are explained and the significance of the dynamic pushover analysis is discussed from the viewpoint of analysis of limit states under earthquake ground motions of magnitude larger than the code-specified level. Then, the categorization by the response of frames and dampers was made. In this categorization, several subjects are discussed first: 1) Optimal design of bare nonlinear building frames under seismic loading, 2) Optimal design of nonlinear dampers for elastic building frames under seismic loading, 3) Optimal design of linear dampers for nonlinear building frames under seismic loading, 4) Optimal design of nonlinear building frames with specified nonlinear dampers under seismic loading, 5) Optimal design of nonlinear dampers for specified nonlinear building frames under seismic loading, 6) Simultaneous optimization of elastic-plastic building structures and passive dampers. Finally, the classification of researches in view of solution strategies is conducted for providing another viewpoint.

A generalized 2-DOF model for optimal design of MDOF structures controlled by Tuned Mass Damper Inerter (TMDI)

To obtain reliable designs, aleatory and epistemic uncertainties are considered recently in the structural analysis and design optimization. The reliability based de-sign optimization (RBDO) method [1] is used when the amount of input data is sufficient enough to create accurate statistical distribution. On the other hand, when the sufficient input data are not available due to limitations in time, human, and facility resources, the optimum design may not be reliable if RBDO method is used. To deal with the situation that input uncertainties have insufficient information, a possibility (or fuzzy set) method can be used for structural analysis and possibility based design optimization (PBDO) [2]. However, in many industry design problems, we may have to deal with design problems that involve with the mixed input statistical random and fuzzy variables simultaneously. For these problems, RBDO may yield unreliable optimum designs because of insufficient data. On the other hand, treating the random variables as fuzzy variables and invoking PBDO to solve the mixed design variable problem may yield too conservative designs with higher optimum costs. This paper proposes a new mixed variable design optimization (MVDO) problem based on the performance measure approach (PMA) [1]. To evaluate the possibilistic constraint in MVDO, a sub-optimization problem for inverse analysis is carried out using a hyper-cylinder domain. To solve this sub-problem efficiently and effectively, a new numerical algorithm, maximum failure search (MFS) method, is proposed in this paper by combining the enhanced hybrid mean value (HMV+) method [3] for the inverse reliability analysis in RBDO and the maximal possibility search (MPS) method [2] for the inverse possibility analysis in PBDO. Some mathematical examples are used to demonstrate the efficiency and effectiveness of the proposed numerical MFS method. Some physical design examples are used to compare the proposed MVDO results with RBDO and PBDO results.