Showing papers in "Structural Optimization in 1996"
TL;DR: A survey of recent publications in the field of aerospace where interest in MDO has been particularly intense is presented, focused on the interaction of the structures discipline with other disciplines.
Abstract: The increasing complexity of engineering systems has sparked increasing interest in multidisciplinary optimization (MDO). This paper presents a survey of recent publications in the field of aerospace where interest in MDO has been particularly intense. The two main challenges of MDO are computational expense and organizational complexity. Accordingly the survey is focused on various ways different researchers use to deal with these challenges. The survey is organized by a breakdown of MDO into its conceptual components. Accordingly, the survey includes sections on Mathematical Modeling, Design- oriented Analysis, Approximation Concepts, Optimization Procedures, System Sensitivity, and Human Interface. With the authors'' main expertise being in the structures area, the bulk of the references focus on the interaction of the structures discipline with other disciplines. In particular, two sections at the end focus on two such interactions that have recently been pursued with a particular vigor: Simultaneous Optimization of Structures and Aerodynamics, and Simultaneous Optimization of Structures Combined With Active Control.
1,049 citations
TL;DR: The perimeter method as mentioned in this paper allows the designer to control the number of holes in the optimal design and to establish their characteristic length scale, thus eliminating the need for relaxation, thereby circumventing many of the complexities and restrictions of other approaches to topology design.
Abstract: This paper introduces a method for variable-topology shape optimization of elastic structures called theperimeter method. An upper-bound constraint on the perimeter of the solid part of the structure ensures a well-posed design problem. The perimeter constraint allows the designer to control the number of holes in the optimal design and to establish their characteristic length scale. Finite element implementations generate practical designs that are convergent with respect to grid refinement. Thus, an arbitrary level of geometric resolution can be achieved, so single-step procedures for topology design and detailed shape design are possible. The perimeter method eliminates the need for relaxation, thereby circumventing many of the complexities and restrictions of other approaches to topology design.
476 citations
TL;DR: In this paper, global stress functions are used to approximate local stresses and the density method is employed for solving the topology optimization problems, and three numerical examples are used for this investigation.
Abstract: Previous research on topology optimization focussed primarily on global structural behaviour such as stiffness and frequencies. However, to obtain a true optimum design of a vehicle structure, stresses must be considered. The major difficulties in stress based topology optimization problems are two-fold. First, a large number of constraints must be considered, since unlike stiffness, stress is a local quantity. This problem increases the computational complexity of both the optimization and sensitivity analysis associated with the conventional topology optimization problem. The other difficulty is that since stress is highly nonlinear with respect to design variables, the move limit is essential for convergence in the optimization process. In this research, global stress functions are used to approximate local stresses. The density method is employed for solving the topology optimization problems. Three numerical examples are used for this investigation. The results show that a minimum stress design can be achieved and that a maximum stiffness design is not necessarily equivalent to a minimum stress design.
299 citations
TL;DR: In this paper, it is shown that the above modified procedures may also lead to erroneous solutions which cannot be avoided without changing the ground structure, which is a pitfall in topology optimization with only stress and local buckling constraints.
Abstract: A serlous difficulty in topology optimization with only stress andlocal buckling constraints was pointed out recently by Zhou (1996a). Possibilities for avoiding this pitfall are (i) inclusion of system stability constraints and (ii) application of imperfections in the ground structure. However, it is shown in this study that the above modified procedures may also lead to erroneous solutions which cannot be avoided without changing the ground structure.
163 citations
TL;DR: Key elements of how the functioning of the immune system can be modeled in the context of genetic search, and its applicability for handling constrained genetic search are described.
Abstract: Genetic search derives its computational advantage from an intrinsic pattern recognition capability. Patterns or schemata associated with a high level of fitness are rapidly identified and reproduced at a near-exponential growth rate through generations of simulated evolution. This highly exploitative search process has been shown to be extremely effective in searching for schema that represent an optimum, requiring only that an appropriate measure of fitness be defined. This exploitative pattern recognition process is also at work in another biological system-the immune system which recognizes antigens foreign to the system and generates antibodies to combat the growth of these antigens. The present paper describes key elements of how the functioning of the immune system can be modeled in the context of genetic search, and its applicability for handling constrained genetic search. Results from this simulation are compared with those obtained from the more traditional approach of handling constraints in genetic search, viz. through the use of a penalty function formulation.
102 citations
TL;DR: In this article, the author outlines further classes of problems for which Michell's original theory is valid and further classes for which it is not valid, including the following problems: (1)
Abstract: This reply outlines further classes of problems for which Michell's original theory is valid.
78 citations
TL;DR: This study presents the program Gendes (GENetic DEsign Sequencer), a sequencing tool based on a genetic algorithm that has the capability to minimize feedbacks as well as crossovers, and allows the potential for other considerations in the sequencing function.
Abstract: Methods in multidisciplinary design optimization rely on computer tools to manage the large amounts of information involved One such tool is DeMAID (DEsign Manager's Aide for Intelligent Decomposition), which incorporates planning and scheduling functions to analyse the effect of the information coupling between design tasks in complex systems on the efficiency of the design process Scheduling involves the formation of circuits of interdependent design tasks, and the minimization of feedbacks within these circuits Recently there has been interest in the incorporation of other considerations in the sequencing of tasks within circuits This study presents the program Gendes (GENetic DEsign Sequencer), a sequencing tool based on a genetic algorithm The program currently has the capability to minimize feedbacks as well as crossovers (intersections in the flow of design information which obscure straightforward evaluation), and allows the potential for other considerations in the sequencing function This paper presents the development of this tool and the methods used The results of computational studies to determine the most effective settings of the genetic algorithm for the task sequencing problem are presented, including population size, objective function weighting for the tradeoff between feedbacks and crossovers, mutation rate, and choice of selection operator and fitness function form The incorporation of Gendes into the DeMAID scheduling function is explored, and the method is applied to two test systems to show its feasibility
77 citations
TL;DR: In this paper, the authors discuss problems associated with local buckling constraints in the context of topology optimization and show that serious difficulties are encountered unless additional measures are introduced, which is not the case in this paper.
Abstract: The aim of this note is to discuss problems associated with local buckling constraints in the context of topology optimization. It is shown that serious difficulties are encountered unless additional measures are introduced.
76 citations
TL;DR: In this article, the problem of optimum truss topology design based on the ground structure approach is considered, and it is shown that any minimum weight truss design (computed subject to equilibrium of forces and stress constraints with the same yield stresses for tension and compression) is subject to static equilibrium and a weight constraint.
Abstract: The problem of optimum truss topology design based on the ground structure approach is considered. It is known that any minimum weight truss design (computed subject to equilibrium of forces and stress constraints with the same yield stresses for tension and compression) is—up to a scaling—the same as a minimum compliance truss design (subject to static equilibrium and a weight constraint). This relation is generalized to the case when different properties of the bars for tension and for compression additionally are taken into account. This situation particularly covers the case when a structure is optimized which consists of rigid (heavy) elements for bars under compression, and of (light) elements which are hardly/not able to carry compression (e.g. ropes). Analogously to the case when tension and compression is handled equally, an equivalence is established and proved which relates minimum weight trusses to minimum compliance structures. It is shown how properties different for tension and compression pop up in a modified global stiffness matrix now depending on tension and compression. A numerical example is included which shows optimal truss designs for different scenarios, and which proves (once more) the big influence of bar properties (different for tension and for compression) on the optimal design.
57 citations
TL;DR: In this article, an integrated design procedure which is composed of structural design, control design, and actuator locations design is proposed, where a composite objective function, formed by a structural and a control objective, is optimized in steady state through the homogenization design method.
Abstract: An integrated design procedure which is composed of structural design, control design, and actuator locations design is proposed in this paper. First, a composite objective function, formed by a structural and a control objective, is optimized in steady state through the homogenization design method. Then an independent modal space control algorithm (IMSC) is performed on this optimal structure to reduce the dynamic response. Finally, to minimize the control force while still obtaining the same modal response for the controlled modes, the optimal choice for actuator locations is discussed.
39 citations
TL;DR: In this paper, the authors extended the evolutionary structural optimization method to the solution for maximizing the natural frequencies of bending vibration thin plates, where two kinds of constraint conditions are considered in the EA method.
Abstract: This paper extends the evolutionary structural optimization method to the solution for maximizing the natural frequencies of bending vibration thin plates. Two kinds of constraint conditions are considered in the evolutionary structural optimization method. If the weight of a target structure is set as a constraint condition during the natural frequency optimization, the optimal structural topology can be found by removing the most ineffectively used material gradually from the initial design domain of a structure until the weight requirement is met for the target structure. However, if the specific value of a particular natural frequency is set as a constraint condition for a target structure, the optimal structural topology can be found by using a design chart. This design chart describes the evolutionary process of the structure and can be generated by the information associated with removing the most inefficiently used material gradually from the initial design domain of a structure until the minimum weight is met for maintaining the integrity of a structure. The main advantage in using the evolutionary structural optimization method lies in the fact that it is simple in concept and easy to be included into existing finite element codes. Through applying the extended evolutionary structural optimization method to the solution for the natural frequency optimization of a thin plate bending vibration problem, it has been demonstrated that the extended evolutionary structural optimization method is very useful in dealing with structural topology optimization problems.
TL;DR: In this article, a variational formulation of shape design sensitivity analysis is outlined, starting from a differential geometry-based representation of continuum mechanics, and a rigorous analysis using convected curvilinear coordinates yields a decomposition of all continuum mechanical functions into independent geometry and displacement mappings.
Abstract: A variational formulation of shape design sensitivity analysis is outlined, starting from a differential geometry-based representation of continuum mechanics. A rigorous analysis using convected curvilinear coordinates yields a decomposition of all continuum mechanical functions into independent geometry and displacement mappings. Using this representation of geometry and displacements defined on a fixed parameter space, their influence on physical quantities can easily be separated. Consequently, the variations of continuum mechanical quantities with respect to either geometry or displacements can be performed similarly using the well-known linearization techniques in nonlinear mechanics. The proposed methodology for performing variational design sensitivity analysis is formulated for general nonlinear hyperelastic material behaviour using either the Lagrangian or Eulerian description. The differences and similarities of the formulation presented compared with the material derivative approach and the domain parametrization approach are highlighted and discussed.
TL;DR: This paper presents a computer-based method for the optimal design of three-dimensional reinforced concrete (RC) skeletal structures having members subjected to biaxial moments, biaXial shears and axial loads.
Abstract: This paper presents a computer-based method for the optimal design of three-dimensional reinforced concrete (RC) skeletal structures having members subjected to biaxial moments, biaxial shears and axial loads The width, depth and area of longitudinal reinforcement of member sections are taken as the design variables The optimality criteria (OC) method is applied to minimize the cost of the concrete, steel and formwork for the structure The primary focus of the paper concerns fundamental issues related to the formulation of design performance constraints on combined axial load, biaxial moments and biaxial shears An example problem is solved with and without account for biaxial shear constraints to illustrate their influence on the design
TL;DR: A convex programming optimizer called GMMA (Generalized Method of Moving Asymptotes) is presented in this paper, which aims at solving engineering design problems including nonlinear equality and inequality constraints.
Abstract: A convex programming optimizer called GMMA (Generalized Method of Moving Asymptotes) is presented in this paper. This method aims at solving engineering design problems including nonlinear equality and inequality constraints. The basic feature of this optimizer is that the efficient dual solution strategy together with the flexible GMMA approximation scheme are used. Especially, nonlinear equality constraints can be exactly satisfied by the intermediate solution of each explicit subproblem because their linearization is updated in an internal loop of the subproblem. This method will be illustrated by a hydrodynamic design application.
TL;DR: This paper presents validated results of the optimization of cutouts in laminated carbon-fibre composite panels by adapting a recently developed optimization procedure known as Evolutionary Structural Optimization (ESO).
Abstract: This paper presents validated results of the optimization of cutouts in laminated carbon-fibre composite panels by adapting a recently developed optimization procedure known as Evolutionary Structural Optimization (ESO). An initial small cutout was introduced into each finite element model and elements were removed from around this cutout based on a predefined rejection criterion. In the examples presented, the limiting ply within each plate element around the cutout was determined based on the Tsai-Hill failure index. Plates with values below the product of the average Tsai-Hill number and a rejection ratio (RR) were subsequently removed. This process was iterated until a steady state was reached and the RR was then incremented by an evolutionary rate (ER). The above steps were repeated until a cutout of a desired area was achieved.
TL;DR: In this paper, the authors used Taguchi's orthogonal arrays for robust design in a nontraditional way to solve a mixed continuous-discrete structural optimization problem, where the factors of an Orthogonal array correspond to the members of a structure and the levels of each factor correspond to material choices of each member.
Abstract: Taguchi's orthogonal arrays for robust design are used in this paper in a nontraditional way to solve a mixed continuous-discrete structural optimization problem. The factors of an orthogonal array correspond to the members of a structure and the levels of each factor correspond to the material choices of each member. Based on the number of factors to be studied and the number of levels of each factor, an appropriate orthogonal array is selected for each specific problem. The number of rows of the orthogonal array correspond to the number of experiments (i.e. continuous sizing optimizations) to be conducted. The response of these experiments, which are the weight of the optimal designs corresponding to different material settings, are then used to calculate the mean effect of each factor level. Some possible optimal material settings can then be determined. Three examples are presented in this paper. Analysis using Taguchi's orthogonal arrays was able to isolate several near optimal or optimal designs. The accuracy and efficiency of the proposed method compared to more traditional solution methodologies are also discussed.
TL;DR: In this paper, ground structure approaches for topology optimization of trusses are discussed and the incorporation of stability constraints (buckling) into topology design is discussed, and the influence of buckling on the optimal layout is demonstrated by a bridge design example.
Abstract: This paper discusses ground structure approaches for topology optimization of trusses. These topology optimization methods select an optimal subset of bars from the set of all possible bars defined on a discrete grid. The objectives used are based either on minimum compliance or on minimum volume. Advantages and disadvantages are discussed and it is shown that constraints exist where the formulations become equivalent. The incorporation of stability constraints (buckling) into topology design is important. The influence of buckling on the optimal layout is demonstrated by a bridge design example. A second example shows the applicability of truss topology optimization to a real engineering stiffened membrane problem.
TL;DR: The optimization algorithm is developed based on the problem decomposition into three subproblems having as objectives the maximization of the structural efficiency atintact and degraded configurations of the structure and weight minimization subjected to allowable values for the structural reliability.
Abstract: Uncertainties in deviations of physical properties lead to a probabilistic failure analysis of the composite materials. The proposed optimization model for laminate composites is based on reliability analysis considering the ultimate failure state. To avoid difficulties associated with the complete analysis of the failure modes, bounds are established for the failure probability of the structural system. These bounds are related with theintact and degraded configurations of the structure. Using thefirst ply failure and thelast ply failure theories and a degradation model for the mechanical properties with load sharing rules we obtain the failure probabilities corresponding to the two above configurations. The failure probability of each configuration is obtained using level 2 reliability analysis and the Lind-Hasofer method.
TL;DR: A new heuristic method aimed at efficiently solving the mixed-discrete nonlinear programming (MDNLP) problem in structural optimization, and denoted selective dynamic rounding, is presented, which is effective in obtaining a low discrete approximation to the global optimum.
Abstract: A new heuristic method aimed at efficiently solving the mixed-discrete nonlinear programming (MDNLP) problem in structural optimization, and denotedselective dynamic rounding, is presented. The method is based on the sequential rounding of a continuous solution and is in its current form used for the optimal discrete sizing design of truss structures. A simple criterion based on discrete variable proximity is proposed for selecting the sequence in which variables are to be rounded, and allowance is made for both upward and downward rounding. While efficient in terms of the required number of function evaluations, the method is also effective in obtaining a low discrete approximation to the global optimum. Numerical results are presented to illustrate the effectiveness and efficiency of the method.
TL;DR: In this article, the problem of maximizing the overall stiffness of an elastic body comprised of given materials is treated, and variational methods of optimizing local composite structures in conjunction with a computational global minimization strategy are used.
Abstract: The problem of maximizing the overall stiffness of an elastic body comprised of given materials will be treated. Particular examples include the optimal shape and structure of shells, plates, domes, cantilevers, etc. The axisymmetry allows us to compute mathematically optimal out-of-plane examples. We will use recently developed variational methods of optimizing local composite structures in conjunction with a computational global minimization strategy. The optimal designs could be simplified into suboptimal projects subject to other practical considerations.
TL;DR: In this article, the authors explored the feasibility of applying topology optimization methods to the bead design of sheet panels and used a cantilever plate to perform a preliminary study for bead pattern design and a simplified vehicle structure is used to demonstrate the applicability of the proposed method.
Abstract: Plane sheet panels exhibit poor stiffness and NVH (noise, vibration, and harshness) performance due to their flexibility. A common and cost-effective approach in the automotive industry to improve the stiffness and NVH peformance of sheet panels is the addition of beads. However, no systematic methodology is available for determining the optimal pattern of beads in sheet metal. This research explores the feasibility of applying topology optimization methods to the bead design of sheet panels. The approach starts with adding beam elements to the shell element model of the sheet panel to simulate the stiffness improvement of the structure and then uses the topology optimization method to obtain the optimal layout of the beam elements. A cantilever plate is used to perform a preliminary study for bead pattern design and a simplified vehicle structure is used to demonstrate the applicability of the proposed method.
TL;DR: In this paper, a two-stage layout optimization procedure consisting of reduction and expansion processes is presented, where a reduced structure with a limited number of members and joints is established by solving large scale idealized problems.
Abstract: A tw0-stage layout optimization procedure, consisting of reduction and expansion processes, is presented. The object in developing this procedure is to use the advantages of both processes. In the reduction process, a reduced structure with a limited number of members and joints is established by solving large scale idealized problems. An expansion process is then employed, where members and joints are added to the initial reduced structure. At this stage, relatively small problems are solved, considering general variables, all relevant constraints and the real objective function.
TL;DR: A new method for the numerical realization of optimal shape design problems, called a fictitious domain approach, is presented and the use of a genetic type algorithm in the above mentioned approach is described.
Abstract: The aim of this paper is twofold: on the one hand to present a new method for the numerical realization of optimal shape design problems, called a fictitious domain approach and on the other hand to describe the use of a genetic type algorithm in the above mentioned approach.
TL;DR: In this paper, an improved semi-analytical method is presented for the accurate computation of shape design sensitivities, which is based on approximating the flexibility matrix by means of von Neumann series.
Abstract: The semi-analytical method is conveniently used to obtain design sensitivities. However, it may have serious accuracy problems in shape design. In this study, an improved semianalytical method is presented for the accurate computation of shape design sensitivities. The method is based on approximating the flexibility matrix by means of von Neumann series. In numerical examples, two cases for which the standard semianalytical method fails are considered. It is demonstrated that the sensitivities can be obtained very accurately by the improved method proposed.
TL;DR: In this article, a composite objective composed of structural and control objectives is introduced to find the optimal design of a controlled structure, and the effect of the control weighting is examined.
Abstract: A formulation that finds the optimal design of a controlled structure is proposed. To achieve this goal, a composite objective composed of structural and control objectives is introduced to be optimized, and the effect of the control weighting is examined. A feedback control law is defined before the structural optimization and then the composite objective will only become a function of structural design variables. As a result, optimal structural design and control forces in steady state are obtained.
TL;DR: A highly accurate heuristic algorithm, a relative difference quotient algorithm, is developed for a class of discrete optimization problems with monotonic objective functions and constraint functions and has been successfully applied to the discrete optimization of structures.
Abstract: According to the characteristics of discrete optimization, the concept of a relative difference quotient is proposed, and a highly accurate heuristic algorithm, a relative difference quotient algorithm, is developed for a class of discrete optimization problems with monotonic objective functions and constraint functions. The algorithm starts from the minimum point of the objective function outside the feasible region and advances along the direction of minimum increment of the objective function and maximum decrement of constraint functions to find a better approximate optimum solution. In order to evaluate the performance of the algorithm, a stochastic numerical test and a statistical analysis for the test results are also completed. The algorithm has been successfully applied to the discrete optimization of structures.
TL;DR: For a linearly elastic fiber reinforced composite disk, the first variation of an arbitrary stress, strain and displacement functional corresponding to variation of material parameters was derived by using the direct and adjoint approaches to sensitivity analysis as discussed by the authors.
Abstract: For a linearly elastic fiber reinforced composite disk, the first variation of an arbitrary stress, strain and displacement functional corresponding to variation of material parameters is derived by using the direct and adjoint approaches to sensitivity analysis. The results are particularized to the case of total potential and complementary energies. The relevant optimality conditions for optimal design and identification problems are then derived.
TL;DR: In this article, a new optimization method is presented that optimizes singular structures by reformulating the problem using the percent method so that the appropriate stress constraints are deleted as the member is removed.
Abstract: A new optimization method is presented that optimizes singular structures. An example of a singular problem is deleting an inefficient member from a structure. As the member is deleted, the stresses in the member may increase above the allowables. When a member is deleted the nature of the analysis changes because the member stiffness becomes zero. This causes a local optima because stress constraints prevent inefficient members from zeroing. The problem is reformulated using the percent method so that the appropriate stress constraints are deleted as the member is deleted. Several examples show that the global optimal design is reached. Other methods to reach the global optima are appropriate only if the optimal structure is statically determinate. The percent optimization is also useful for optimization of discrete problems.
TL;DR: In this article, the effectiveness of recently developed multipoint function approximations in the context of structural size, configuration and shape optimization is demonstrated using several structural optimization problems with stress, displacement and buckling constraints.
Abstract: The objective of this paper is to demonstrate the effectiveness of recently developed multipoint function approximations in the context of structural size, configuration and shape optimization. The developments include approximations built using just two points and also more than two-point information of optimization iterations. Intervening variables are used to control the nonlinearity of the approximations. Several structural optimization problems with stress, displacement and buckling constraints are used to demonstrate the validity and accuracy of the multipoint approximations. These examples include the size optimization of a 40 member frame, the configuration design of a 25-bar space truss and the shape design of a torque arm and a plate with a hole.
TL;DR: In this paper, a model for optimum design of three panel forms, namely tee stiffened, flat-bar stiffened and corrugated panels, to be used in ship structures is presented.
Abstract: 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