Minimum Weight Design Problem Research Articles

A novel minimum weight formulation of topology optimization implemented with reanalysis approach

SummaryIn this paper, we develop an efficient diagonal quadratic optimization formulation for minimum weight design problem subject to multiple constraints. A high‐efficiency computational approach of topology optimization is implemented within the framework of approximate reanalysis. The key point of the formulation is the introduction of the reciprocal‐type variables. The topology optimization seeking for minimum weight can be transformed as a sequence of quadratic program with separable and strictly positive definite Hessian matrix, thus can be solved by a sequential quadratic programming approach. A modified sensitivity filtering scheme is suggested to remove undesirable checkerboard patterns and mesh dependence. Several typical examples are provided to validate the presented approach. It is observed that the optimized structure can achieve lighter weight than those from the established method by the demonstrative numerical test. Considerable computational savings can be achieved without loss of accuracy of the final design for 3D structure. Moreover, the effects of multiple constraints and upper bound of the allowable compliance upon the optimized designs are investigated by numerical examples.

A Simple Mathematical Method for Optimal Preliminary Design of Tall Buildings with Peak Lateral Deflection Constraint

The classic methods of structural design based on trial-and-error are generally highly iterative and computationally intensive, especially in a tall building consisting of thousands of structural members. This paper presents a closed-form solution for a minimum weight design problem which may be used at the early-stage design of a high-rise and slender structure. Before considering the weight-based problem, an intervening optimization formulation is introduced in advance which for a fixed amount of material presents an optimal pattern for its distribution. The obtained pattern is then used in the main problem, in which the total weight is considered as the objective function while satisfying the peak lateral deflection constraint and some practical requirements. The flexural stiffness in its general form is selected here as the design variable, so the proposed method is not restricted to a particular system, and any structural system may be addressed. A braced-tube 61-storey building example is presented to be designed based on the proposed technique to illustrate the effectiveness and practicality of the method.

A new laminates encoding scheme for the genetic algorithm-based optimization of stiffened composite panels

Purpose – The genetic algorithm (GA) technique is widely used for the optimization of stiffened composite panels. It is based on sequential execution of a number of specific operators, including the encoding of particular design variables. For instance, in the case of a stiffened composite panel, the design variables that need to be encoded are: the number of plies and their stacking sequences in the panel skin and stiffeners. This paper aims to present a novel, implicit, heuristic approach for encoding composite laminates and, through its use, demonstrates an improvement in the optimization process. Design/methodology/approach – The stiffened panel optimization has been formulated as a constrained discrete minimum-weight design problem. GAs, which use both new encoding schemes and those previously described in the literature, have been used to find near-optimal solutions to the formulated problem. The influence of the new encoding scheme on the searching capabilities of the GA has been investigated using comparative analysis of the optimization results. Findings – The new encoding scheme allows the definition of stacking sequences in composites using shorter symbolic representations as compared with standard encoding operators and, as a result of this, a reduction in the problem design space. According to numerical experiments performed in this work, this feature enables GA to obtain near-optimal designs using smaller population sizes than those required if standard encoding schemes are used. Originality/value – The approach to encoding laminates presented in this paper is based on the original heuristics. In the context of GA-based optimization of stiffened composite panels, the use of the new approach rather than the standard encoding technique can lead to a significant reduction in computational time employed.

On the solution of the three forces problem and its application in optimal designing of a class of symmetric plane frameworks of least weight

Two problems of minimum weight design of plane trusses are dealt with. The first problem concerns construction of the lightest fully stressed truss subject to three self-equilibrated forces applied at three given points. This problem has been solved analytically by H.S.Y. Chan in 1966. This analytical solution is re-derived in the present paper. It compares favourably with new numerical solutions found here by the method developed recently by the first author. The solution to the three forces problem paves the way to half-analytical as well as numerical solutions to the problem of minimum weight design of plane symmetric frameworks transmitting two symmetrically located vertical forces to two fixed supports lying along the line linking the points of application of the forces.

Optimal weight design of a gear train using particle swarm optimization and simulated annealing algorithms

The problem of minimum weight design of simple and multi-stage spur gear trains has been a subject of considerable interest, since many high-performance power transmission applications (e.g., automotive, aerospace, machine tools, etc.) require low weight. This paper presents two advanced optimization algorithms known as particle swarm optimization (PSO) and simulated annealing (SA) to find the optimal combination of design parameters for minimum weight of a spur gear train. The results of the proposed algorithms are compared with the previously published results. It is observed that the proposed algorithms offer better gear design solutions.

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.

Optimal drift design model for multi‐story buildings subjected to dynamic lateral forces

AbstractAn optimal drift design model for a linear multi‐story building structure under dynamic lateral forces is presented. The drift design model is formulated into a minimum weight design problem subjected to constraints on stresses, the displacement at the top of a building, and inter‐story drift. The optimal drift design model consists of three main components: an optimizer, a response spectrum analysis module, and a sensitivity analysis module. Using a small example, the validation of the proposed model has been tested by a comparison of optimal solutions. Then, the performance of the optimal drift design model is demonstrated by application to three steel frame structures including a 40‐story building. Various structural responses including lateral displacement and inter‐story drift distributions along the height of the structure at the initial and final design stages are presented in figures and tables. Time‐consuming trial‐and‐error processes related to drift control of a tall building subjected to lateral loads is avoided by the proposed optimal drift design method. Copyright © 2003 John Wiley & Sons, Ltd.

Optimal structural design for flexible space structure with control system based on LMI

A simultaneous optimal design problem of structural and control systems is discussed by taking a 3-D truss structure as an object. We use descriptor forms for a controlled object and a generalized plant because the structural parameters appear naturally in these forms. We consider a minimum weight design problem for structural system and disturbance suppression problem for the control system. The structural objective function is the structural weight and the control objective function isH∞ norm from the disturbance input to the controlled output in the closed-loop system. The design variables are cross sectional areas of the truss members. The conditions for the existence of controller are expressed in terms of linear matrix inequalities (LMI). By minimizing the linear sum of the normalized structural objective function and control objective function, it is possible to make optimal design by which the balance of the structural weight and the control performance is taken. We showed in this paper the validity of simultaneous optimal design of structural and control systems.

Study on Structural Optimization Technique Using Evolutionary Cellular Automata. Local Direct Rule Based on New Transition Function.

In this paper, a local direct rule based on a new transition function of the Cellular Automata (CA) is presented. It is the structural optimization method by the Evolutionary Cellular Automata (ECA). The local direct rule uses the neighborhood states as the CA's input. The ECA is the CA optimized by the Genetic Algorithm (GA) for the certain problems. This new transition function makes to decrease drastically the degrees of local direct rule freedom depending on the number of the neighborhood cells. The design conditions of the structure are introduced as virtual cells to apply the same rule in all the design space. A local direct rule here is decided by the evolutionary calculation of GA. The method is applied to the minimum weight design problems and the adaptive solutions are obtained. From the results, it is observe that the local direct rule based on a new transition function is effective in the self-organization problem of the complex system.

216 分枝限定法による連層耐震壁の最適配置計画

The present paper deals with the allocation problem of multi-story shear walls in 3D RC frames. This problem is formulated as a minimum weight design problem under constraints of ultimate strength, relative story displacement and dynamic eccentric ratio. In the present paper, this problem is formulated as two combinatorial problems, which are searching problem of feasible solutions at each floor and minimization problem of total weight of walls. Optimality technique based upon the branch-and-bound method is applied to each problem. Several example of multi-story frames are optimally designed with discussion on influence of the number of stories, scale of plan, and allocation constraint at each floor upon computing efficiency.

Simultaneous Optimal Design of Structural and Control Systems in Flexible Structures

A simultaneous optimal design problem of structural and control systems is discussed for a 3-dimensional truss structure as an object. We use descriptor forms for a controlled object and a generalized plant because the structural parameters appear naturally in these forms. As the design purpose, we consider minimum weight design problem for structural system and suppression problem of the influence of disturbances for control system.

設計用水平力を受ける建築骨組の構造重量と保有水平耐力を指標とした満足度指定設計法

Specified grade design of multistory multispan frames under a set of horizontal loads is formulated Thls problem is an α-Levelfuzzy optlmum design problem in which both the fuzzy constraint relating to plastic collapse load factor and the fuzzy objective function relating to the weight of the structure are adopted. The above fuzzy design problem is verified to be a problem for mathematical programming, analogical to the crisp minimum weight design problem And an analogical method is proposed for derivation of exact closed form solutions to the fuzzy design variables of that problem The closed form solutions are very useful for determining members of a structure at the design process, as designers have only to select the members whose dimensions are within the range of fuzzy design variables

502 フレキシブルアームにおける構造系と制御系の統合設計(GS-10 制御)

An optimum structural design problem with control system is discussed taking a 1-Link structure as an object. We consider a minimum weight design problem for structural system and a suppression problem of the vibration for control system as the purpose of the design. A numerical example shows the validity of simultaneous optimum design of structural and control systems.

On the solution of a minimum weight elastoplastic problem involving displacement and complementarity constraints

This paper deals with a special class of minimum weight design problem involving discretized structures, holonomic (reversible) plasticity, and constraints on displacements. A key feature of the optimization problem is the presence of complementarity conditions, involving the orthogonality of two sign-constrained vectors. This problem falls within the important class of so-called Mathematical Programs with Equilibrium Constraints (MPECs). Two simple algorithms are proposed to solve our synthesis problem and application is illustrated by some examples concerning truss-like structures.

Simultaneous Optimum Design of Structural and Control Systems. Representation by Descriptor Forms and Use of LMI.

A simultaneous optimum design problem of structural and control systems is discussed taking a 3-dimensional truss structure as an object. We use descriptor forms for a controlled object and a generalized plant because the structural parameters appear naturally in these forms. We consider minimum weight design problem for structural system and suppression problem of the effect of disturbances for control system as the purpose of the design. The structural objective function is the structural weight and the control objective function is H∞ norm from the disturbance input to the controlled output in the closed-loop system. The design variables are cross sectional areas of the truss members. The conditions for the existence of controller are expressed in terms of linear matrix inequalities (LMI). By minimizing the linear sum of the normalized structural objective function and control objective function, it is possible to make optimum design by which the balance of structural weight and control performance is taken. We consider in this paper the validity of simultaneous optimum design of structural and control systems.

A stress analysis technique for plate and shell built-up structures with junctions and its application to minimum-weight design of stiffened structures

A finite element formulation using the penalty function method to analyse exactly the junctions of plate and shell built-up structures is suggested for an isoparametric shell element. The connectivity condition at the junction is added to the potential energy functional by the penalty parameter and the interpolating function of displacements. This formulation yields an integral-type stiffness matrix of the special junction elements, which can directly evaluate the surface tractions at the junction. For applying the technique suggested here to the optimum design of structures with junction parts, a design sensitivity analysis formulation for the adhesive special element is also developed. The technique is applied to the minimum-weight design problems of isotropic and composite laminated plates with a stiffener subjected to stress constraints.

On Optimization of Large-Scale Structures by Local Rule.

In the pevious paper, we proposed a generalized cellular automata for structural forming, that is a local rule as an analogy of the neural network system. It can be varied for adaptation to different problems. In this paper, a technique for designing large-scale structures using the generalized cellular automata is presented. By setting a small-scale problem that simulates a large-scale structure, a local rule is decided for adaptation to large-scale problems. By using this technique, minimum weight design problems of 2-dimensional continuous structures are analyzed and several solutions to the design problems are obtained.

Minimum weight and deflection design of thick sandwich laminates via symbolic computation

Optimal designs of thick laminated sandwich plates are given based on a higher-order theory of plates which include the effects of the normal and shear deformation. Two designs are considered, namely, the minimum weight design and minimum deflection design. The surface layers are made of a transversely isotropic composite material and the core is chosen as a honeycomb material. In the minimum weight design problem, the core thickness and the fibre content of the surface layers are optimally determined by using equations of micromechanics to express the elastic constants. In the minimum deflection problem, the thicknesses of surface layers are chosen as the design variables. The higher-order theory is implemented using special purpose symbolic computation routines developed in the C programming language. The analysis is incorporated into an optimization algorithm for the minimum weight and deflection design of a three-layered sandwich plate. Numerical results are given for plates under sinusoidal loading and the effects of various input parameters are investigated. The deflection behaviour is studied and it is shown that design analysis cannot be performed using a classical theory or a shear deformable theory only for the thick panels under consideration.

ALGEBRAIC LINEAR PROGRAMMING APPLIED TO OPTIMAL PLASTIC DESIGN OF STEEL PORTAL FRAMES

The paper is concerned with the minimum weight design of steel portal frames subject to the constraints of the kinematic theorem of plastic collapse. Minimum weight design is a classic linear programming problem which can be solved algebraically for classes of frames with arbitrary geometric dimensions and arbitrary load magnitudes. The solution for each class of frames is expressed in the form of a chart. This technique has been inhibited by the substantial amount of tedious algebraic manipulation necessary for each specified class of frames. In the paper, the process of algebraic linear programming is reduced to the repeated application of a number of vector formulas. A computer program is described which, using these formulas, derives the solution chart for specified classes of frames. Examples illustrate the use of the program to derive a design chart and the use of a chart to solve a specific minimum weight design problem.

Technique for Optimum Design of Truss Structures by Neural Network.

This paper describes an application of a mutual combination-type neural network to the optimum design problems of truss structures. The optimum design problems of truss structures are changed to some combinatorial optimization problems. The Hopfield model and the quadratic energy function are used to solve the design problems. The method is able to obtain feasible solutions for several optimum design problems. The effectiveness of this method is demonstrated by two examples of the minimum weight and maximum stiffness design problems of truss structures.