Computational Mechanics in Structural Engineering

Recent Developments

F.Y. Cheng, Yuanxian Gu

• Publisher: Elsevier Science
• Year: 1999
• Print ISBN: 9780080430089
• eBook ISBN: 9780080529493
• Topic: Mathematics
• Subtopic: Computer Science General
• Index: Mathematics

The Second Sino-US Symposium Workshop on Recent Advancement of Computational Mechanics in Structural Engineering was held between May 25-28, 1998, in Dalian, China. The objectives were: to share the insights and experiences gained from recent developments in theory and practice; to assess the current state of knowledge in various topic areas of mechanics and computational methods and to identify joint research opportunities; to stimulate future cooperative research and to develop joint efforts in subjects of common needs and interests; to build and to strengthen the long-term bilateral scientific relationship between academic and professional practicing communities.Topics discussed covered the entire field of computational structural mechanics. These topics have advanced broad applications in the engineering practice of modern structural analysis, design and construction of buildings and other structures, and in natural hazard mitigation.

MULTIOBJECTIVE OPTIMUM DESIGN OF STRUCTURES WITH GENETIC ALGORITHM AND GAME THEORY: APPLICATION TO LIFE-CYCLE COST DESIGN

Franklin Y. Cheng, Curators’ Professor, Department of Civil Engineering, Senior Investigator, Intelligent Systems Center, University of Missouri-Rolla, Rolla, MO 65409-0030 USA

ABSTRACT

Loss of life and property from possible future earthquakes as well as the expense and difficulty of post-earthquake rehabilitation and reconstruction strongly suggest the need for proper structural design with damage control. Design criteria should balance initial cost of the structure with expected losses from potential earthquake-induced structural damage. Life-cycle cost design addresses these issues. Such a design methodology can be developed using multiobjective and multilevel optimization techniques. Presentation here focuses on genetic algorithm and game theory as well as a life-cycle cost model for this innovative design methodology.Genetic algorithms (GAs) have the characteristic of maintaining a population of solutions, and can search in a parallel manner for many nondominated solutions. These features coincide with the requirement of seeking a Pareto optimal set in a multiobjective optimization problem. The rationale for multiobjective optimization via GAs is that at each generation, the fitness of each individual is defined according to its nondominated property. Since nondominated individuals are assigned the highest fitness values, the convergence of a population will go to the nondominated zone – the Pareto optimal set. Based on this concept, a Pareto GA whose goal is to locate the Pareto optimal set of a multiobjective optimization problem is developed. In this GA, to avoid missing Pareto optimal points during evolutionary processes, a new concept called Pareto-set filter is adopted. At each generation, the points of rank 1 are put into the filter and undergo a nondominated check. In addition, a niche technique is provided to prevent genetic drift in population evolution. This technique sets a replacement rule for reproduction procedures. For a constrained optimization problem, a revised penalty function method is introduced to transfer a constrained problem into a nonconstrained one. The transferred function of a point contains information on a point’s status (feasible or infeasible), position in a search region, and distance to the Pareto optimal set. Three numerical examples are provided: 1) optimum design of a seismic-resistant structure with/without control, 2) optimum design for a final structural system selected from steel frame, reinforced concrete, or composite system, and 3) sensitivity analysis of the effect of cost function on structural probability failure. It is concluded that multiobjective and multilevel optimization is essential to determine target reliability and seismic building code performance.

KEYWORDS

Genetic algorithm

game theory

life-cycle cost

multiobjective and multilevel optimization

earthquake

probability failure

fuzzy logic

Pareto set filter

niche technique

control.

INTRODUCTION

In the current engineering design community, major design efforts are based on a conventional trial and error approach for which the relative stiffness of a structure’s constituent members must be assumed. If preliminary stiffness is misjudged, then repeat analysis, even with a sophisticated computer program, will usually not yield an improved design. The optimum design concept is recognized as being more rational and reliable than the conventional design approach. Considerable literature has been published on the subject of optimal structural design for single-objective function (Cheng and Truman, 1985; Cheng [ed.], 1986; Cheng and Juang, 1988; Frangopol and Cheng [eds.], 1996)

Most real-world design optimization problems in structures are multimodal. There often exist several objectives to be considered by the designer. Usually these objectives are conflicting rather than complementary. A single-objective optimization formulation does well with respect to an optimal objective, but the design may not always be a “good” design. Consider a hypothetical example. If a structure is optimized for minimum weight subject to constraints such as stress, displacement, buckling and vibration period, a structure is then obtained with minimum constructed materials. However, the structure may have a poor performance of dynamic response under the action of seismic loadings. If the minimum earthquake input energy is also included as objective, a more rational, compromise design will be produced (Cheng and Li, 1996; Cheng and Li, X.S., 1998)). This combined formulation is a multiobjective optimization problem (MOP). Multiobjective optimization offers the possibility to consider effectively all the different, mutually conflicting requirements inherent in a design problem.

In game theory, if players agree to cooperate, a Pareto optimum will be an ideal solution because it has the property that if any other solution is used, at least one player’s performance index is worse, or all the players do the same. This study demonstrates how game theory as a design tool applies to an MOP, and describes the relationship between cooperative game theory and Pareto optimal solution. Three genetic algorithms for multiobjective optimization are proposed based on game theory. In the Pareto GA, whose goal is to find a representative sampling of solutions along with the Pareto optimal set, two new techniques are investigated: a new operator called Pareto-set filter is introduced to prevent the loss of Pareto optimum points in evolutionary progress; and niche technique is created by putting limitations on reproduction operators. Pareto GA for a constrained MOP is further studied to include fuzzy-logic scheme. Life-cycle cost model is introduced along with multilevel optimization concept. The proposed multiobjective optimization techniques are applied to the optimum design of a seismic structure with/without control and applied to evaluate a structural system as wether it should be steel frame, reinforced concrete frame, or composite steel-and-reinforced-concrete frame. Numerical results show that multiobjective optimization is essential to produce a good seismic structural design.

MULTIOBJECTIVE OPTIMIZATION AND PARETO OPTIMUM

Multiobjective optimization can be defined as determining a vector of design variables that are within the feasible region to minimize (maximize) a vector of objective functions and can be mathematically expressed as follows

(1)

where x is the vector of design variables, f_i(x) is the ith objective function, and g(x) is the constraint vec...

Table of contents

• Cover image
• Title page
• Table of Contents
• Elsevier Science Internet Homepage
• Copyright
• PREFACE
• ACKNOWLEDGMENTS
• Symposium Activities
• RESOLUTIONS OF SECOND SINO-US JOINT SYMPOSIUM / WORKSHOP ON RECENT ADVANCEMENT OF COMPUTATIONAL MECHANICS IN STRURCTURAL ENGINEERING
• Chapter 1: MULTIOBJECTIVE OPTIMUM DESIGN OF STRUCTURES WITH GENETIC ALGORITHM AND GAME THEORY: APPLICATION TO LIFE-CYCLE COST DESIGN
• Chapter 2: NEW SOLUTION SYSTEM FOR PLATE BENDING
• Chapter 3: FINITE ELEMENT ALGORITHM BASED ON TWO-SCALE ANALYSIS METHOD
• Chapter 4: Control of Lateral-Torsional Motion of Nanjing TV Transmission Tower
• Chapter 5: FAST COMPUTATION OF STATIONARY/NON-STATIONARY RANDOM RESPONSES OF COMPLEX STRUCTURES
• Chapter 6: RESPONSE OF DYNAMICAL SYSTEMS DRIVEN BY ADDITIVE GAUSSIAN AND POISSON WHITE NOISES
• Chapter 7: SOLVING LARGE SYSTEMS OF EQUATIONS ON INTEL-PARAGON
• Chapter 8: DYNAMIC BEHAVIOR OF RAILWAY BRIDGES UNDER RANDOM LOADING AND ASSESSMENT OF VEHICLE-RUNNING SAFETY
• Chapter 9: A REVIEW ON THE NUMERICAL SOLUTION SCHEMES FOR LOCALIZATION PROBLEMS
• Chapter 10: ɛ-CONTINUATION APPROACH FOR TRUSS TOPOLOGY OPTIMIZATION
• Chapter 11: RECENT DEVELOPMENTS IN BASIC FINITE ELEMENT TECHNOLOGIES
• Chapter 12: STRUCTURAL OPTIMIZATION FOR PRACTICAL ENGINEERING: SOFTWARE DEVELOPMENT AND APPLICATIONS
• Chapter 13: PARALLEL INTEGRATION ALGORITHMS FOR DYNAMIC ANALYSIS OF STRUCTURES IN THE CLUSTERED NETWORK SYSTEM
• Chapter 14: MAXIMUM ENTROPY PRINCIPLE AND TOPOLOGICAL OPTIMIZATION OF TRUSS STRUCTURES
• Chapter 15: PRACTICAL ISSUES IN THE APPLICATION OF STRUCTURAL IDENTIFICATION
• Chapter 16: ER DEVICES FOR CONTROL OF SEISMICALLY EXCITED STRUCTURES
• Chapter 17: PARALLEL PCG ALGORITHM ON DISTRIBUTED NETWORK BY PVM
• Chapter 18: COMPUTER AIDED DESIGN FOR VIBRATION ISOLATION SYSTEMS WITH DAMPED ELASTIC STOPS
• Chapter 19: CALCULATION OF THIN PLATES ON STATISTICAL NON—UNIFORM FOUNDATIONS
• Chapter 20: COMPUTER SIMULATION OF STRUCTURAL ANALYSIS IN CIVIL ENGINEERING
• Chapter 21: A MIXED FINITE ELEMENT FOR LOCAL AND NONLOCAL PLASTICITY
• Chapter 22: BEHAVIOR OF IN-FILLED STEEL PLATE PANELS SUBJECTED TO CYCLIC SHEAR
• Chapter 23: A FINITE ELEMENT MODEL FOR GEOMETRICALLY NONLINEAR ANALYSIS OF MULTI-LAYERED COMPOSITE SHELLS
• Chapter 24: NONLINEAR AND BUCKLING ANALYSIS OF COMPLEX BRANCHED SHELLS OF REVOLUTION
• Chapter 25: Structural Optimization for Seismic Loads: Pseudo-Static, Response Spectra and Time History
• Chapter 26: MONITORING OF CABLE FORCES USING MAGNETO-ELASTIC SENSORS
• Chapter 27: FRACTURE ESTIMATION: BOUND THEOREM AND NUMERICAL STRATEGY
• Chapter 28: FINITE ELEMENT-BASED BUFFETING ANALYSIS OF LONG SPAN BRIDGES
• Chapter 29: ODE-ORIENTED SEMI-ANALYTICAL METHODS
• INDEX OF CONTRIBUTORS
• KEYWORD INDEX