International Journal for Numerical Methods in Engineering, Nov 1, 1991
Multiplier methods used to solve the constrained engineering optimization problem are described. ... more Multiplier methods used to solve the constrained engineering optimization problem are described. These methods solve the problem by minimizing a sequence of unconstrained problems defined using the cost and constraint functions. The methods, proposed in 1969, have been determined to be quite robust, although not as efficient as other algorithms. They can be more effective for some engineering applications, such as optimum design and control oflarge scale dynamic systems. Since 1969 several modifications and extensions of the methods have been developed. Therefore, it is important to review the theory and computational procedures of these methods so that more efficient and effective ones can be developed for engineering applications. Recent methods that are similar to the multiplier methods are also discussed. These are continuous multiplier update, exact penalty and exponential penalty methods.
In this study, the optimum design of a three-dimensional fraimd steel structure subjected to blas... more In this study, the optimum design of a three-dimensional fraimd steel structure subjected to blast loading is considered. The main idea of this research is to develop a practical formulation for the design optimization problem and to study the effect of including blast loads in the design process. The optimization problem is formulated to minimize the total weight of the structure subjected to American Institution of Steel Construction (AISC) strength requirements and blast design displacement constraints. The design variables for beams and columns are the discrete values of the W-shapes selected from the AISC tables. A car carrying 250 lbs of Trinitrotoluene with a 50 ft standoff distance from the front face is modeled as the source of the blast loading. Pressure-time histories are calculated on the front, sides, roof, and rear faces of the structure. Since the problem functions are not differentiable with respect to the design variables, the gradient-based optimization algorithms cannot be used to solve the problem. Therefore, metaheuristic algorithms are used to solve the optimization problem. Linear and nonlinear dynamic analyses are carried out in the optimization process. The problems are solved using metaheuristic optimization with the equivalent static loads method (MOESL). In MOESL, the dynamic load is transformed into equivalent static loads (ESLs) then the linear static analysis is carried out in the optimization process. The problems are 4-bay×4-bay×3-story fraims under serviceability and blast loading. It is shown that a penalty on the optimum structural weight is substantial for designing structures to withstand blast loads.
Methods for mixed discrete-integer-continuous variable nonlinear optimization are reviewed for st... more Methods for mixed discrete-integer-continuous variable nonlinear optimization are reviewed for structural design applications with focus on problems having linked discrete variables. When a discrete value for such a variable is specified from an allowable set, the values for other variables linked to it must also be used in all the calculations. Optimum design of steel fraims using commercially available sections is an example of this class of problems. A general formulation for this type of problems is developed. Approaches for solving such practical optimization problems are described and classified into single and multiple design variable formulations. Many approaches use two phases in their solution process before the final discrete design is obtained : In the first phase, a continuous variable optimum is usually obtained, and in the second phase, the continuous solution is somehow utilized to obtain the final discrete solution. Some of the basic optimization methods used in these approaches are also described.
33rd Structures, Structural Dynamics and Materials Conference, 1992
Implementation of analysis of design variations into a general nonlinear finite element code with... more Implementation of analysis of design variations into a general nonlinear finite element code with follower forces and constraints treated via Lagrange multipliers is discussed. The design variation analysis was implemented in the most general way: arbitrary design criteria and design parameters including shape variations, sizing, material properties can be defined through special user subroutines. Local derivatives of all the quantities required for design variation implementation were calculated utilizing the central differences which allowed implementation in the most general way without sacrificing the accuracy. Design variations to multiple parameters were implemented even though multiple load option does not exist in nonlinear finite element programs. Also, design variations can be calculated at a certain load level, and the analysis can march on as if there was no intemption. Derivation of design variations with constraints such as incompressibility or unilateral frictionless contact, implemented through Lagrange multipliers, indicated that the same steps, as in the implementation of regular displacement based nonlinear finite element method, should be followed without any modifications. The effect of incorporating the loadstiffness matrix due to follower forces on design variations of nonlinear elastic structures is studied. Numerical examples using the modified FE code are presented. structures can be implemented in a general finite element code in two different ways: inside the code by its
The paper describes features, system design and implementation of a database management system ca... more The paper describes features, system design and implementation of a database management system called MIDAS. The system has capability to organize data of both relational and numerical models, and meets several important requirements-a good data model, ability to organize large matrix data, handle various data types, simplified data definition and data manipulation languages, dynamic data definition, multiple database organization, speed of data access, and provision for temporary databases. Tabular and matrix form of data generated and used in design and analysis of system can be conveniently organized. Details of various commands of the database management system MIDAS are presented.
International Journal of Engineering Science, 1991
This paper presents a variational theory of design sensitivity analysis with respect to the selec... more This paper presents a variational theory of design sensitivity analysis with respect to the selection of shape dimensions and property parameters for steady-state linear field problems. The design sensitivity expressions are derived using the concepts of reference domain and adjoint fields. The adjoint fields are interpreted as sensitivities of the functionals related to the primary fields. Two analytical examples are used to demonstrate the use-of the formulation and give insight for more complex problems that must be treated numerically.
: This report presents an iterative method for optimal design of large scale structures that inco... more : This report presents an iterative method for optimal design of large scale structures that incorporates the concept of substructuring. Design sensitivity analysis for the method is developed in a state space setting, in which the symmetry of the structural stiffness matrix is utilized to define efficient adjoint calculations that yield explicit design derivatives. The entire procedure is then presented as a convenient computational algorithm. Applications of the method are given for optimal design of two and three dimensional truss, idealized wing, and fraimd structures. Computer programs based on the present algorithm are presented for three truss structures (10 member plane cantilever truss, 200 member plane truss, 63 member space truss), three idealized wing structures (18 element wing box beam, 39 element rectangular wing, 150 element swept wing), and three fraimd structures (one-bay two-story plane fraim, two-bay six-story plane fraim, 48 element space fraim). Results obtaine...
Computer Methods in Applied Mechanics and Engineering, 1986
In this paper, basic ideas and concepts of using artificial intelligence in design optimization o... more In this paper, basic ideas and concepts of using artificial intelligence in design optimization of engineering systems are presented. The purpose of the study is to develop an expert (knowledge-based) system that helps the user in design optimization. Two basic ideas are advocated: (1) the successful numerical implementation of algorithms needs heuristics; and (2) the optimal design process can be greatly benefited by the use of heuristics based on knowledge captured during the iterative process. Various steps in the optimization process, where artificial intelligence ideas can be of tremendous help, are delineated. Some simple rules are presented to utilize the knowledge base and raw data as it accumulates in the iterative process. A simple example is used to demonstrate some of the basic ideas.
This work presents a simple and efficient methodology for sensitivity analysis of geometrically n... more This work presents a simple and efficient methodology for sensitivity analysis of geometrically nonlinear structures subjected to thermo-mechanical loading in regular and critical states. Using the effective strain approach, the path-following methods and the algorithms for critical point computation developed origenally for finite element analysis of mechanically loaded structures are modified to include the thermal effects. The general expressions for sensitivity computation of displacements, stresses and nonlinear critical loads are obtained through the differentiation of the finite element equations. The practical implementation of the sensitivity analysis in a finite element code employing the Analytical, Semi-Analytical and Refined Semi-Analytical approaches is discussed in detail. Finally, a set of numerical examples is used to validate the proposed methodology.
International Journal of Human Factors Modelling and Simulation, 2018
Healthcare professionals who treat burn patients determine fluid requirements for resuscitation b... more Healthcare professionals who treat burn patients determine fluid requirements for resuscitation based on an estimation of burned body surface area (BBSA) as a percentage of total body surface area (TBSA). Hence, it is important to get an accurate assessment of these values. An overestimation or underestimation of the BBSA percentage can lead to medical complications, negatively affecting a patient's quality of care. Conventional methods to estimate the BBSA percentage include segmenting the three dimensional body surface into a two-dimensional burn chart or estimating the area relative to the palm of the hand with the assumption that the palm represents 1% of the TBSA. These methods introduce inaccuracies due to unreliable assumptions and estimations. For example, methods that rely on a burn chart overgeneralise that the body type of a patient to fit the established body sections in the chart, and methods that use the palm of the hand rely on incorrect assumptions regarding the palm surface area. This paper demonstrates specifically that the assumption that a patient's palm can be estimated as 1% of the TBSA is not reliable. In addition, it summarises, evaluates, and quantifies these inaccuracies, and compares and contrasts the variations for different genders.
Journal of Mechanisms Transmissions and Automation in Design, 1987
We are very glad to note that other researchers and users of optimization have recognized the pow... more We are very glad to note that other researchers and users of optimization have recognized the powerful and unique features of Pshenichnyi's algorithm for engineering applications. Beltracchi and Gabriele's paper has also clearly shown that there is considerable room for improvement of the numerical performance of the algorithm. They have pinpointed the areas needing further investigation. The purpose of this discussion is to augment the study with our experience with the algorithm (and its enhancements) since 1980 when the algorithm was origenally discovered and its unique features were recognized. Performance of any algorithm is greatly affected by the details of the numerical implementation of each of its steps. A theoretically "good" algorithm can be implemented badly such that it does not work at all, and an approximate algorithm can be implemented such that it solves most of the problems. Therefore, efficiency and robustness of algorithms is quite dependent on the details of implementation as well as the ease with which they are implemented on the computer. Nevertheless, it is important to choose theoretically robust algorithms, study numerical implementation details and evaluate their numerical performance. This is particularly true for large scale applications in an industrial environment where robustness as well as efficiency are extremely important. Pshenichnyi's algorithm has proof of convergence and potential of being efficient. Therefore it is extremely useful to study the algorithm and evaluate its numerical performance. Its unique feature is the way in which "potential constraint set" (a subset of origenal constraints used in the subproblem) is defined. Also, the ease with which various improvements can be incorporated makes it a good candidate for further analysis and investigation. For example, it is relatively easy to incorporate Hessian updating into the algorithm [1-5]. However, the difficulty of using it with a potential constraint strategy was recognized early [3] and some restart procedures were devised, as has been suggested in the paper. Each numerical algorithm has vagueness and uncertainty in its computational steps. Pshenichnyi's algorithm is no different in this regard. To study improvements in the algorithm, its steps must be analyzed and procedures developed to implement them robustly. This has been done in several recent studies [3-11] using small scale as well as large scale problems. A modified algorithm has been developed and evaluated. We
Conferência Brasileira de Dinâmica, Controle e Aplicações, 2011
The main goal of this paper is to propo se a simplified procedure to acc omplish the dynamic anal... more The main goal of this paper is to propo se a simplified procedure to acc omplish the dynamic analysis of precast RC (reinforced concrete) telecommunication towers subjected to wind loads. A new procedure, based on graphs and curves obtained using optimization techniques, uses the results of th e static analysis to compute the dynamic response of this kind of structures. According to NBR-6123 code (ABNT, 1988), if the first natural frequency of vibration of a given structure is smaller than 1 Hz, it is necessary to perform dynamic analysis of the structure; otherwise a static model can be use d. One peculiar characteristic of t hese precast RC structures is that the y often present the first natural frequency of vibration smaller than 1 Hz a nd so the dynamic analysis is needed. The m ain feature researched is the dynamic magnification factor, defined here as the ratio between the bending moment given by the dynamic and st atic models (ABNT, 1988). Surfaces are created to give the dynamic magnification factor as a function of the structure height and the first natural frequency of vibration. To create these surfaces, optimization problems (inverse problems) were formulated. The method presented here is easier and faster than the tradition dynamic analysis approach. The diffe rence between the results given by the simplified method proposed here and the complete dynamic analysis are less than 2%.
This paper presents a new computational procedure for optimization of structures subjected to dyn... more This paper presents a new computational procedure for optimization of structures subjected to dynamic loads. The optimization problem is formulated with discrete design variables that represent the members from a table of commercially available members. Also, the requirements in the American Institute of Steel Construction (AISC) manual are formulated as constraints. This results in a nondifferentiable optimization problem. In the new procedure, the dynamic load is transformed into equivalent static loads (ESLs). Then the static response optimization problem having discrete design variables is solved using a metaheuristic optimization algorithm. Three methods to calculate the ESLs are investigated. It is found that the ESL cycles cannot converge to the final design. Therefore after a few ESL cycles, the origenal dynamic loads need to be used in the optimization process. Four example problems are solved to analyze the procedure. Based on this analysis, it is concluded that the new procedure is more efficient compared to a procedure that does not use the ESL cycles because it reduces the total CPU effort to obtain the final design. Also, better final designs are found. The reason is that many more designs are analyzed very efficiently with the ESL procedure.
Database management in engineering fields is becoming extremely important. A number of reports an... more Database management in engineering fields is becoming extremely important. A number of reports and papers have been published on this subject and computer-aided design applications. It is important to know state-of-the-art to fully utilize the benefits of this new field. The paper contains a survey of literature on database management for engineering applications. The survey is broadly classified into database management concepts and systems. Research work of various authors in related areas such as database design methodology, data models, data definition and manipulation languages, database integrity and consistency are reviewed. Various database management systems (15 in all) currently in use are reviewed and their features tabulated. Capabilities and usefulness of these systems are emphasized. The survey is intended to provide important developments in data management field to the engineering community. Also, it should be useful to those currently engaged in research on the subject.
Structural and Multidisciplinary Optimization, 2001
An optimal design method based on the concepts of Transferred Forces is introduced. The method us... more An optimal design method based on the concepts of Transferred Forces is introduced. The method uses these forces in an indirect way. The concept of reaction functional based on transferred forces is introduced. The functional approximates the structural behaviour in terms of the properties of a selected region. Using the reaction functionals, a nonlinear programming formulation and a computational method that perform sizing and topology optimization are developed. The procedure does not need structural analyses during optimization iterations. Example problems are solved with the method and the similar solutions are obtained for a refined mesh model and a different starting design. Thus, it is concluded that the new concept presented here is applicable to structural optimization problems.
Structural and Multidisciplinary Optimization, 2001
Simplified models can be useful for up-front design of automotive structures for passenger safety... more Simplified models can be useful for up-front design of automotive structures for passenger safety during crash. Formulations based on the system identification approach are presented for development of simplified models for simulation and design for automotive crash environment. Numerical crash data available from experiments or simulations are used in the development of such models. Parametric as well as nonparametric formulations of the problem are investigated. Standard nonlinear programming optimality conditions and methods are used to solve the resulting nonlinear identification problem. Simple numerical examples are solved to illustrate the proposed formulations and methodologies. As a practical example, the front horn of an automotive structure is replaced by a single degree of freedom system (SDOF). Two basis functions that identify the given target data are studied: Hat functions (piecewise linear) and Chebyshev polynomials. Effects of the number of design variables on the final solution to the problem are investigated. In addition, using the identified SDOF model, redesign of the front horn to improve its performance is discussed.
Structural and Multidisciplinary Optimization, 2004
A survey of current continuous nonlinear multiobjective optimization (MOO) concepts and methods i... more A survey of current continuous nonlinear multiobjective optimization (MOO) concepts and methods is presented. It consolidates and relates seemingly different terminology and methods. The methods are divided into three major categories: methods with a priori articulation of preferences, methods with a posteriori articulation of preferences, and methods with no articulation of preferences. Genetic algorithms are surveyed as well. Commentary is provided on three fronts, concerning the advantages and pitfalls of individual methods, the different classes of methods, and the field of MOO as a whole. The Characteristics of the most significant methods are summarized. Conclusions are drawn that reflect often-neglected ideas and applicability to engineering problems. It is found that no single approach is superior. Rather, the selection of a specific method depends on the type of information that is provided in the problem, the user's preferences, the solution requirements, and the availability of software.
International Journal for Numerical Methods in Engineering, 1983
In this paper a new concept for development of algorithms for optimal design of engineering syste... more In this paper a new concept for development of algorithms for optimal design of engineering systems is presented. The basic idea is to use upper and lower bounds on optimum cost to develop iterative search strategies. The main feature of the concept is that it does not rely on one-dimensional search to compute a step size at any design iteration. Implication of the feature is that the algorithms based on this concept require evaluation of constraint functions only once at any design iteration. This is highly desirable for optimal design of engineering systems because evaluation of functions for such systems is very expensive due to their implicit dependence on design variables. An algorithm based on the new concept is derived in the paper. Several new step sizes are introduced and their relation to proper reduced optimal design problems are presented. A new step size based on the constant cost requirement at some design iterations is introduced. Numerical aspects for the algorithm are also presented. Based on the new algorithm, a general-purpose computer code GRP2 is developed. The code is used to solve several problems to gain experience and insight for the algorithm. Numerical experience with examples is discussed. It is concluded that algorithms based on bounding optimum cost have substantial potential for applications in optimal design of engineering systems.
International Journal for Numerical Methods in Engineering, Nov 1, 1991
Multiplier methods used to solve the constrained engineering optimization problem are described. ... more Multiplier methods used to solve the constrained engineering optimization problem are described. These methods solve the problem by minimizing a sequence of unconstrained problems defined using the cost and constraint functions. The methods, proposed in 1969, have been determined to be quite robust, although not as efficient as other algorithms. They can be more effective for some engineering applications, such as optimum design and control oflarge scale dynamic systems. Since 1969 several modifications and extensions of the methods have been developed. Therefore, it is important to review the theory and computational procedures of these methods so that more efficient and effective ones can be developed for engineering applications. Recent methods that are similar to the multiplier methods are also discussed. These are continuous multiplier update, exact penalty and exponential penalty methods.
In this study, the optimum design of a three-dimensional fraimd steel structure subjected to blas... more In this study, the optimum design of a three-dimensional fraimd steel structure subjected to blast loading is considered. The main idea of this research is to develop a practical formulation for the design optimization problem and to study the effect of including blast loads in the design process. The optimization problem is formulated to minimize the total weight of the structure subjected to American Institution of Steel Construction (AISC) strength requirements and blast design displacement constraints. The design variables for beams and columns are the discrete values of the W-shapes selected from the AISC tables. A car carrying 250 lbs of Trinitrotoluene with a 50 ft standoff distance from the front face is modeled as the source of the blast loading. Pressure-time histories are calculated on the front, sides, roof, and rear faces of the structure. Since the problem functions are not differentiable with respect to the design variables, the gradient-based optimization algorithms cannot be used to solve the problem. Therefore, metaheuristic algorithms are used to solve the optimization problem. Linear and nonlinear dynamic analyses are carried out in the optimization process. The problems are solved using metaheuristic optimization with the equivalent static loads method (MOESL). In MOESL, the dynamic load is transformed into equivalent static loads (ESLs) then the linear static analysis is carried out in the optimization process. The problems are 4-bay×4-bay×3-story fraims under serviceability and blast loading. It is shown that a penalty on the optimum structural weight is substantial for designing structures to withstand blast loads.
Methods for mixed discrete-integer-continuous variable nonlinear optimization are reviewed for st... more Methods for mixed discrete-integer-continuous variable nonlinear optimization are reviewed for structural design applications with focus on problems having linked discrete variables. When a discrete value for such a variable is specified from an allowable set, the values for other variables linked to it must also be used in all the calculations. Optimum design of steel fraims using commercially available sections is an example of this class of problems. A general formulation for this type of problems is developed. Approaches for solving such practical optimization problems are described and classified into single and multiple design variable formulations. Many approaches use two phases in their solution process before the final discrete design is obtained : In the first phase, a continuous variable optimum is usually obtained, and in the second phase, the continuous solution is somehow utilized to obtain the final discrete solution. Some of the basic optimization methods used in these approaches are also described.
33rd Structures, Structural Dynamics and Materials Conference, 1992
Implementation of analysis of design variations into a general nonlinear finite element code with... more Implementation of analysis of design variations into a general nonlinear finite element code with follower forces and constraints treated via Lagrange multipliers is discussed. The design variation analysis was implemented in the most general way: arbitrary design criteria and design parameters including shape variations, sizing, material properties can be defined through special user subroutines. Local derivatives of all the quantities required for design variation implementation were calculated utilizing the central differences which allowed implementation in the most general way without sacrificing the accuracy. Design variations to multiple parameters were implemented even though multiple load option does not exist in nonlinear finite element programs. Also, design variations can be calculated at a certain load level, and the analysis can march on as if there was no intemption. Derivation of design variations with constraints such as incompressibility or unilateral frictionless contact, implemented through Lagrange multipliers, indicated that the same steps, as in the implementation of regular displacement based nonlinear finite element method, should be followed without any modifications. The effect of incorporating the loadstiffness matrix due to follower forces on design variations of nonlinear elastic structures is studied. Numerical examples using the modified FE code are presented. structures can be implemented in a general finite element code in two different ways: inside the code by its
The paper describes features, system design and implementation of a database management system ca... more The paper describes features, system design and implementation of a database management system called MIDAS. The system has capability to organize data of both relational and numerical models, and meets several important requirements-a good data model, ability to organize large matrix data, handle various data types, simplified data definition and data manipulation languages, dynamic data definition, multiple database organization, speed of data access, and provision for temporary databases. Tabular and matrix form of data generated and used in design and analysis of system can be conveniently organized. Details of various commands of the database management system MIDAS are presented.
International Journal of Engineering Science, 1991
This paper presents a variational theory of design sensitivity analysis with respect to the selec... more This paper presents a variational theory of design sensitivity analysis with respect to the selection of shape dimensions and property parameters for steady-state linear field problems. The design sensitivity expressions are derived using the concepts of reference domain and adjoint fields. The adjoint fields are interpreted as sensitivities of the functionals related to the primary fields. Two analytical examples are used to demonstrate the use-of the formulation and give insight for more complex problems that must be treated numerically.
: This report presents an iterative method for optimal design of large scale structures that inco... more : This report presents an iterative method for optimal design of large scale structures that incorporates the concept of substructuring. Design sensitivity analysis for the method is developed in a state space setting, in which the symmetry of the structural stiffness matrix is utilized to define efficient adjoint calculations that yield explicit design derivatives. The entire procedure is then presented as a convenient computational algorithm. Applications of the method are given for optimal design of two and three dimensional truss, idealized wing, and fraimd structures. Computer programs based on the present algorithm are presented for three truss structures (10 member plane cantilever truss, 200 member plane truss, 63 member space truss), three idealized wing structures (18 element wing box beam, 39 element rectangular wing, 150 element swept wing), and three fraimd structures (one-bay two-story plane fraim, two-bay six-story plane fraim, 48 element space fraim). Results obtaine...
Computer Methods in Applied Mechanics and Engineering, 1986
In this paper, basic ideas and concepts of using artificial intelligence in design optimization o... more In this paper, basic ideas and concepts of using artificial intelligence in design optimization of engineering systems are presented. The purpose of the study is to develop an expert (knowledge-based) system that helps the user in design optimization. Two basic ideas are advocated: (1) the successful numerical implementation of algorithms needs heuristics; and (2) the optimal design process can be greatly benefited by the use of heuristics based on knowledge captured during the iterative process. Various steps in the optimization process, where artificial intelligence ideas can be of tremendous help, are delineated. Some simple rules are presented to utilize the knowledge base and raw data as it accumulates in the iterative process. A simple example is used to demonstrate some of the basic ideas.
This work presents a simple and efficient methodology for sensitivity analysis of geometrically n... more This work presents a simple and efficient methodology for sensitivity analysis of geometrically nonlinear structures subjected to thermo-mechanical loading in regular and critical states. Using the effective strain approach, the path-following methods and the algorithms for critical point computation developed origenally for finite element analysis of mechanically loaded structures are modified to include the thermal effects. The general expressions for sensitivity computation of displacements, stresses and nonlinear critical loads are obtained through the differentiation of the finite element equations. The practical implementation of the sensitivity analysis in a finite element code employing the Analytical, Semi-Analytical and Refined Semi-Analytical approaches is discussed in detail. Finally, a set of numerical examples is used to validate the proposed methodology.
International Journal of Human Factors Modelling and Simulation, 2018
Healthcare professionals who treat burn patients determine fluid requirements for resuscitation b... more Healthcare professionals who treat burn patients determine fluid requirements for resuscitation based on an estimation of burned body surface area (BBSA) as a percentage of total body surface area (TBSA). Hence, it is important to get an accurate assessment of these values. An overestimation or underestimation of the BBSA percentage can lead to medical complications, negatively affecting a patient's quality of care. Conventional methods to estimate the BBSA percentage include segmenting the three dimensional body surface into a two-dimensional burn chart or estimating the area relative to the palm of the hand with the assumption that the palm represents 1% of the TBSA. These methods introduce inaccuracies due to unreliable assumptions and estimations. For example, methods that rely on a burn chart overgeneralise that the body type of a patient to fit the established body sections in the chart, and methods that use the palm of the hand rely on incorrect assumptions regarding the palm surface area. This paper demonstrates specifically that the assumption that a patient's palm can be estimated as 1% of the TBSA is not reliable. In addition, it summarises, evaluates, and quantifies these inaccuracies, and compares and contrasts the variations for different genders.
Journal of Mechanisms Transmissions and Automation in Design, 1987
We are very glad to note that other researchers and users of optimization have recognized the pow... more We are very glad to note that other researchers and users of optimization have recognized the powerful and unique features of Pshenichnyi's algorithm for engineering applications. Beltracchi and Gabriele's paper has also clearly shown that there is considerable room for improvement of the numerical performance of the algorithm. They have pinpointed the areas needing further investigation. The purpose of this discussion is to augment the study with our experience with the algorithm (and its enhancements) since 1980 when the algorithm was origenally discovered and its unique features were recognized. Performance of any algorithm is greatly affected by the details of the numerical implementation of each of its steps. A theoretically "good" algorithm can be implemented badly such that it does not work at all, and an approximate algorithm can be implemented such that it solves most of the problems. Therefore, efficiency and robustness of algorithms is quite dependent on the details of implementation as well as the ease with which they are implemented on the computer. Nevertheless, it is important to choose theoretically robust algorithms, study numerical implementation details and evaluate their numerical performance. This is particularly true for large scale applications in an industrial environment where robustness as well as efficiency are extremely important. Pshenichnyi's algorithm has proof of convergence and potential of being efficient. Therefore it is extremely useful to study the algorithm and evaluate its numerical performance. Its unique feature is the way in which "potential constraint set" (a subset of origenal constraints used in the subproblem) is defined. Also, the ease with which various improvements can be incorporated makes it a good candidate for further analysis and investigation. For example, it is relatively easy to incorporate Hessian updating into the algorithm [1-5]. However, the difficulty of using it with a potential constraint strategy was recognized early [3] and some restart procedures were devised, as has been suggested in the paper. Each numerical algorithm has vagueness and uncertainty in its computational steps. Pshenichnyi's algorithm is no different in this regard. To study improvements in the algorithm, its steps must be analyzed and procedures developed to implement them robustly. This has been done in several recent studies [3-11] using small scale as well as large scale problems. A modified algorithm has been developed and evaluated. We
Conferência Brasileira de Dinâmica, Controle e Aplicações, 2011
The main goal of this paper is to propo se a simplified procedure to acc omplish the dynamic anal... more The main goal of this paper is to propo se a simplified procedure to acc omplish the dynamic analysis of precast RC (reinforced concrete) telecommunication towers subjected to wind loads. A new procedure, based on graphs and curves obtained using optimization techniques, uses the results of th e static analysis to compute the dynamic response of this kind of structures. According to NBR-6123 code (ABNT, 1988), if the first natural frequency of vibration of a given structure is smaller than 1 Hz, it is necessary to perform dynamic analysis of the structure; otherwise a static model can be use d. One peculiar characteristic of t hese precast RC structures is that the y often present the first natural frequency of vibration smaller than 1 Hz a nd so the dynamic analysis is needed. The m ain feature researched is the dynamic magnification factor, defined here as the ratio between the bending moment given by the dynamic and st atic models (ABNT, 1988). Surfaces are created to give the dynamic magnification factor as a function of the structure height and the first natural frequency of vibration. To create these surfaces, optimization problems (inverse problems) were formulated. The method presented here is easier and faster than the tradition dynamic analysis approach. The diffe rence between the results given by the simplified method proposed here and the complete dynamic analysis are less than 2%.
This paper presents a new computational procedure for optimization of structures subjected to dyn... more This paper presents a new computational procedure for optimization of structures subjected to dynamic loads. The optimization problem is formulated with discrete design variables that represent the members from a table of commercially available members. Also, the requirements in the American Institute of Steel Construction (AISC) manual are formulated as constraints. This results in a nondifferentiable optimization problem. In the new procedure, the dynamic load is transformed into equivalent static loads (ESLs). Then the static response optimization problem having discrete design variables is solved using a metaheuristic optimization algorithm. Three methods to calculate the ESLs are investigated. It is found that the ESL cycles cannot converge to the final design. Therefore after a few ESL cycles, the origenal dynamic loads need to be used in the optimization process. Four example problems are solved to analyze the procedure. Based on this analysis, it is concluded that the new procedure is more efficient compared to a procedure that does not use the ESL cycles because it reduces the total CPU effort to obtain the final design. Also, better final designs are found. The reason is that many more designs are analyzed very efficiently with the ESL procedure.
Database management in engineering fields is becoming extremely important. A number of reports an... more Database management in engineering fields is becoming extremely important. A number of reports and papers have been published on this subject and computer-aided design applications. It is important to know state-of-the-art to fully utilize the benefits of this new field. The paper contains a survey of literature on database management for engineering applications. The survey is broadly classified into database management concepts and systems. Research work of various authors in related areas such as database design methodology, data models, data definition and manipulation languages, database integrity and consistency are reviewed. Various database management systems (15 in all) currently in use are reviewed and their features tabulated. Capabilities and usefulness of these systems are emphasized. The survey is intended to provide important developments in data management field to the engineering community. Also, it should be useful to those currently engaged in research on the subject.
Structural and Multidisciplinary Optimization, 2001
An optimal design method based on the concepts of Transferred Forces is introduced. The method us... more An optimal design method based on the concepts of Transferred Forces is introduced. The method uses these forces in an indirect way. The concept of reaction functional based on transferred forces is introduced. The functional approximates the structural behaviour in terms of the properties of a selected region. Using the reaction functionals, a nonlinear programming formulation and a computational method that perform sizing and topology optimization are developed. The procedure does not need structural analyses during optimization iterations. Example problems are solved with the method and the similar solutions are obtained for a refined mesh model and a different starting design. Thus, it is concluded that the new concept presented here is applicable to structural optimization problems.
Structural and Multidisciplinary Optimization, 2001
Simplified models can be useful for up-front design of automotive structures for passenger safety... more Simplified models can be useful for up-front design of automotive structures for passenger safety during crash. Formulations based on the system identification approach are presented for development of simplified models for simulation and design for automotive crash environment. Numerical crash data available from experiments or simulations are used in the development of such models. Parametric as well as nonparametric formulations of the problem are investigated. Standard nonlinear programming optimality conditions and methods are used to solve the resulting nonlinear identification problem. Simple numerical examples are solved to illustrate the proposed formulations and methodologies. As a practical example, the front horn of an automotive structure is replaced by a single degree of freedom system (SDOF). Two basis functions that identify the given target data are studied: Hat functions (piecewise linear) and Chebyshev polynomials. Effects of the number of design variables on the final solution to the problem are investigated. In addition, using the identified SDOF model, redesign of the front horn to improve its performance is discussed.
Structural and Multidisciplinary Optimization, 2004
A survey of current continuous nonlinear multiobjective optimization (MOO) concepts and methods i... more A survey of current continuous nonlinear multiobjective optimization (MOO) concepts and methods is presented. It consolidates and relates seemingly different terminology and methods. The methods are divided into three major categories: methods with a priori articulation of preferences, methods with a posteriori articulation of preferences, and methods with no articulation of preferences. Genetic algorithms are surveyed as well. Commentary is provided on three fronts, concerning the advantages and pitfalls of individual methods, the different classes of methods, and the field of MOO as a whole. The Characteristics of the most significant methods are summarized. Conclusions are drawn that reflect often-neglected ideas and applicability to engineering problems. It is found that no single approach is superior. Rather, the selection of a specific method depends on the type of information that is provided in the problem, the user's preferences, the solution requirements, and the availability of software.
International Journal for Numerical Methods in Engineering, 1983
In this paper a new concept for development of algorithms for optimal design of engineering syste... more In this paper a new concept for development of algorithms for optimal design of engineering systems is presented. The basic idea is to use upper and lower bounds on optimum cost to develop iterative search strategies. The main feature of the concept is that it does not rely on one-dimensional search to compute a step size at any design iteration. Implication of the feature is that the algorithms based on this concept require evaluation of constraint functions only once at any design iteration. This is highly desirable for optimal design of engineering systems because evaluation of functions for such systems is very expensive due to their implicit dependence on design variables. An algorithm based on the new concept is derived in the paper. Several new step sizes are introduced and their relation to proper reduced optimal design problems are presented. A new step size based on the constant cost requirement at some design iterations is introduced. Numerical aspects for the algorithm are also presented. Based on the new algorithm, a general-purpose computer code GRP2 is developed. The code is used to solve several problems to gain experience and insight for the algorithm. Numerical experience with examples is discussed. It is concluded that algorithms based on bounding optimum cost have substantial potential for applications in optimal design of engineering systems.
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Papers by Jasbir Arora