Topology optimization of continuum structures subjected to pressure loading

This paper presents a generalization of topology optimization of linearly elastic continuum structures to problems involving loadings that depend on the design. Minimum compliance is chosen as the design objective, assuming the boundary conditions and the total volume within the admissible design domain to be given. The topology optimization is based on the usage of a SIMP material model. The type of loading considered in this paper occurs if free structural surface domains are subjected to static pressure, in which case both the direction and location of the loading change with the structural design. The presentation of the material is given in a 2D context, but an extension to 3D is straightforward. The robustness of the optimization method is illustrated by some numerical examples in the end of the paper. Received August 3, 1999     

A hierarchical approach to dynamic optimization of power systems

The power production system in The Netherlands is characterized by a relatively large number of thermal power-generating units, the presence of autonomous power stations, a strong national grid and a fluctuating daily load. The calculation of the most economic production policy for one or two days ahead, given all cost functions and the predicted demand for electricity, leads to a nonlinear mixed-integer optimization problem. A real solution can only be found at the expense of rather unrealistic values for computing time and memory. To cope with this problem, a hierarchical approach is described that is able to solve problems with up to 100 units and 24 periods.     

Optimal synthesis method for transmission tower truss structures subjected to static and seismic loads

In this study, an efficient optimal synthesis method for determining the optimum solutions for the structural shape, cross-sectional dimensions, and material type of all member elements of large-scale transmission tower truss structures subjected to static and seismic loads is presented. The method is developed by using the dual method, the response spectrum method, suboptimization techniques, and a two-stage optimization process. The example of a cost-minimization problem for a 218-bar transmission tower truss that considers not only the material costs but also the cost of land as objective functions is presented to demonstrate the rigorousness, efficiency, and reliability of the proposed method.     

A new boundary search scheme for topology optimization of continuum structures with design-dependent loads

The identification of the load surface is a key problem in solving topology optimization of continuum structures with design-dependent loads. In this paper, an element-based search scheme is introduced to identify the load surface. The load surfaces are formed by the connection of the real boundary of elements and the pressures are transferred directly to corresponding element nodes. The search scheme is very convenient to apply and is found to be efficient and effective in identifying the load surfaces. Only slight modifications to the load codes in the routine procedure are required and there is no need to calculate the sensitivities of the load with respect to the material density changes. Numerical examples are presented to demonstrate the efficiency of the boundary search scheme.     

The use of finite element techniques for calculating the dynamic response of structures to moving loads

This paper presents a technique for using standard finite element packages for analysing the dynamic response of structures to time-variant moving loads. To illustrate the method and for validation purposes, the technique is first applied to a simply supported beam subject to a single load moving along the beam. Finally, it is applied to the problem that initiated the work: calculation of the effects of two-dimensional motion of the trolley on the response of the base structure of a mobile gantry crane model.     

A multi-point reduced-order modeling approach of transient structural dynamics with application to robust design optimization

Predicting the transient response of structures by high-fidelity simulation models within design optimization and uncertainty quantification often leads to unacceptable computational cost. This paper presents a reduced-order modeling (ROM) framework for approximating the transient response of linear elastic structures over a range of design and random parameters. The full-order response is projected onto a lower-dimensional basis spanned by modes computed from a proper orthogonal decomposition (POD) of full-order model simulation results at multiple calibration points. The basis is further enriched by gradients of the POD modes with respect to the design/random parameters. A truncation strategy is proposed to compensate for the increase in basis vectors due to the proposed enrichment strategies. The accuracy, efficiency and robustness of the proposed framework are studied with a two-dimensional model problem. The numerical results suggest that the proposed ROM approach is well suited for large parameter changes and that the number of basis vectors needs to be increased only linearly with the number of design and random parameters to maintain a particular ROM performance. The application of the proposed ROM approach to robust shape optimization demonstrates significant savings in computational cost over using full-order models. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000.     

Buckling design optimization of complex built-up structures with shape and size variables

The design optimization of buckling behaviour is studied for complex built-up structures composed of various kinds of elements and implemented within JIFEX95, a general-purpose software for finite element analysis and design optimization. The direct and adjoint methods of sensitivity analysis for critical buckling loads are presented with detailed computational procedures. Particularly, the variations of prebuckling stresses and external loads have been accounted for. The design model and solution methods presented in this paper are available for both shape and size optimization, and buckling optimization can also be combined with static, frequency and dynamic response optimization. The numerical examples show the applications of the buckling optimization method and the effectiveness of the methods and the program of this paper. Received February 23, 1999     

Interval optimization of dynamic response for structures with interval parameters

This paper presents an interval optimization method for the dynamic response of structures with interval parameters. The matrices of structures with interval parameters are given. Combining the interval extension of function with the perturbation theory of dynamic response, the method for interval dynamic response analysis is derived. The interval optimization problem is transformed into a corresponding deterministic one. Because the mean values and the uncertainties of the interval parameters can be elected as the design variables, more information of the optimization results can be obtained by the present method than that obtained by the deterministic one. The present method is implemented for a truss structure and a frame structure. The numerical results show that the method is effective.     

水下爆炸载荷作用下加筋板的动态响应分析

利用Abaqus计算不同水下爆炸载荷作用下加筋板的动态响应,并与RAMAJEYATHILAGAM得出的试验值进行对比,以保证计算分析过程的正确性.计算得到的位移-时间历程曲线可以为加筋板的优化设计提供参考,从而提高其水下爆炸的抗爆能力.     

Nonlinear dynamic system identification for automotive crash using optimization: A review

Literature on linear and nonlinear dynamic system identification is reviewed. The main motivation is to document the state-of-the-art, allowing one to propose further advancements in this field. The main problem is to identify system properties when experimental/numerical input and output data are specified. Parametric as well as nonparametric approaches for system identification are reviewed. For linear systems, both the first order and second order forms of the equations of motion are discussed. The use of first order form is more general as it can treat nonproportional structural damping as well. For nonlinear systems, the second order form of the equations of motion is used. A conclusion from the study is that more work is needed to develop identification formulations for nonlinear dissipative dynamic systems, especially for multi-degree of freedom systems. Received September 11, 2001     

On the use of optimization models for portfolio selection: A review and some computational results

Portfolio theory deals with the question of how to allocate resources among several competing alternatives (stocks, bonds), many of which have an unknown outcome. In this paper we provide an overview of different portfolio models with emphasis on the corresponding optimization problems. For the classical Markowitz mean-variance model we present computational results, applying a dual algorithm for constrained optimization.     

Evaluation of multiple muscle loads through multi-objective optimization with prediction of subjective satisfaction level: Illustration by an application to handrail position for standing

Proposed here is an evaluation of multiple muscle loads and a procedure for determining optimum solutions to ergonomic design problems. The simultaneous muscle load evaluation is formulated as a multi-objective optimization problem, and optimum solutions are obtained for each participant. In addition, one optimum solution for all participants, which is defined as the compromise solution, is also obtained. Moreover, the proposed method provides both objective and subjective information to support the decision making of designers. The proposed method was applied to the problem of designing the handrail position for the sit-to-stand movement. The height and distance of the handrails were the design variables, and surface electromyograms of four muscles were measured. The optimization results suggest that the proposed evaluation represents the impressions of participants more completely than an independent use of muscle loads. In addition, the compromise solution is determined, and the benefits of the proposed method are examined.     

Parallel Evolutionary Optimization of Multibody Systems with Application to Railway Dynamics

The optimization of multibody systems usually requires many costlycriteria computations since the equations of motion must be evaluated bynumerical time integration for each considered design. For activelycontrolled or flexible multibody systems additional difficulties ariseas the criteria may contain non-differentiable points or many localminima.Therefore, in this paper a stochastic evolution strategy is used incombination with parallel computing in order to reduce the computationtimes whilst keeping the inherent robustness. For the parallelization amaster-slave approach is used in a heterogeneous workstation/PCcluster. The pool-of-tasks concept is applied in order to deal withthe frequently changing workloads of different machines in the cluster.In order to analyze the performance of the parallel optimizationmethod, the suspension of an ICE passenger coach, modelled as an elasticmultibody system, is optimized simultaneously with regard to severalcriteria including vibration damping and a criterion related to safetyagainst derailment. The iterative and interactive nature of a typicaloptimization process for technical systems is emphasized.     

A review on the design and optimization of interval type-2 fuzzy controllers

A review of the methods used in the design of interval type-2 fuzzy controllers has been considered in this work. The fundamental focus of the work is based on the basic reasons for optimizing type-2 fuzzy controllers for different areas of application. Recently, bio-inspired methods have emerged as powerful optimization algorithms for solving complex problems. In the case of designing type-2 fuzzy controllers for particular applications, the use of bio-inspired optimization methods have helped in the complex task of finding the appropriate parameter values and structure of the fuzzy systems. In this review, we consider the application of genetic algorithms, particle swarm optimization and ant colony optimization as three different paradigms that help in the design of optimal type-2 fuzzy controllers. We also mention alternative approaches to designing type-2 fuzzy controllers without optimization techniques. We also provide a comparison of the different optimization methods for the case of designing type-2 fuzzy controllers.     

Global optimization of linear hybrid systems with explicit transitions

The global optimization of hybrid systems described by linear time-varying ordinary differential equations is examined. A method to construct convex relaxations of general, nonlinear Bolza-type objective functions or constraints subject to an embedded hybrid system with explicit transitions is presented. The optimization problem can be solved using gradient-based algorithms in a branch and bound framework that is shown to be infinitely convergent when the implied state bounds are employed.     

Examining the benefits and challenges of using audience response systems: A review of the literature

Audience response systems (ARSs) permit students to answer electronically displayed multiple choice questions using a remote control device. All responses are instantly presented, in chart form, then reviewed and discussed by the instructor and the class. A brief history of ARSs is offered including a discussion of the 26 labels used to identify this technology. Next a detailed review of 67 peer-reviewed papers from 2000 to 2007 is offered presenting the benefits and challenges associated with the use of an ARS. Key benefits for using ARSs include improvements to the classroom environment (increases in attendance, attention levels, participation and engagement), learning (interaction, discussion, contingent teaching, quality of learning, learning performance), and assessment (feedback, formative, normative). The biggest challenges for teachers in using ARSs are time needed to learn and set up the ARS technology, creating effective ARS questions, adequate coverage of course material, and ability to respond to instantaneous student feedback. Student challenges include adjusting to a new method of learning, increased confusion when multiple perspectives are discussed, and negative reactions to being monitored. It is concluded that more systematic, detailed research is needed in a broader range of contexts.     

A random set approach to the optimization of uncertain structures

The single-objective optimization of structures, whose parameters are assigned as fuzzy numbers or fuzzy relations, is presented in this paper as a particular case of the random set theory and evidence theory approach to uncertainty. Some basic concepts concerning these theories are reviewed and the relationships among interval analysis, convex modeling, possibility theory and probability theory are pointed out. In this context a frequentistic view of fuzzy sets makes sense and it is possible to calculate bounds on the probability that the solution satisfies the constraints. Some special but useful cases illustrate in detail the meaning of the approach proposed and its links with a recent formulation conceived within the context of convex modeling. Some theorems allow a very efficient computational procedure to be set up in many real design situations. Two numerical examples illustrate the model presented.     

A computational procedure for response statistics-based optimization of stochastic non-linear FE-models

An approach for an efficient solution of response statistics-based optimization problems of non-linear FE systems under stochastic loading is presented. A sequential approximate optimization approach, where approximate stochastic analyses are used during portions of the optimization process, is implemented in the proposed formulation. In this approach, analytical approximations of the performance functions in terms of the design variables are considered during the optimization process. The analytical approximations are constructed by combining a mixed linearization approach with a stochastic response sensitivity analysis. The state of the system is defined in terms of the statistical second-moment characteristics of the structural response. The stochastic loading and the response of the system are represented by an orthogonal series expansion of the corresponding covariance matrices. In particular, a truncated Karhunen-Loève (K-L) expansion is applied. The system of non-linear equations is replaced by a statistical equivalent linear system. The evaluation of the K-L vectors is carried out by an efficient procedure that combines local linearization, modal analysis and static response of higher structural modes. An illustrative example is presented that shows the efficiency of the proposed methodology: it considers a building finite element model enforced with non-linear hysteretic devices and subject to a stochastic ground acceleration. Two types of problems are considered: a minimum structural weight design problem and an optimal non-linear device design problem.     

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.