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1988 | Buch

Structural Optimization

Proceedings of the IUTAM Symposium on Structural Optimization, Melbourne, Australia, 9–13 February 1988

herausgegeben von: G. I. N. Rozvany, B. L. Karihaloo

Verlag: Springer Netherlands

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Inhaltsverzeichnis

Frontmatter

Contributed Papers

Practical Design of Shear and Compression Loaded Stiffened Panels

Many applications of optimization methods to structural design problems have been based on material strength. When buckling is considered, the problem is generally more complicated and difficult. In this paper, several of these difficulties and means to handle them for practical design will be described in the context of the development of the computer program PASCO (Panel Analysis and Sizing COde).

Melvin S. Anderson
Shape Optimization of Holes in Composite Shear Panels

The aim of this work is to find optimum shapes of holes in shear panels made of carbon/epoxy composite materials. The study is restricted to non-buckling shear panels, and a simplified fracture criterion is applied. Starting with a baseline square shear panel with a circular hole, the optimization results in a larger non-circular hole that gives the same maximum stress level in the laminate. Optimum shaped holes are determined for four different laminate configurations, the differences between the shapes being small.

Jan Bäcklund, Rikard Isby
Development of a Knowledge-Based System for Structural Optimization

In structural optimization, computer-based systems have been used to assist in the numerical aspects of the optimization process. However, structural optimization involves a number of tasks which require human expertise and are traditionally assisted by human designers. These include design optimization formulation, problem recognition and the selection of appropriate algorithm(s). This paper presents a framework for developing an integrated knowledge-based system for structural optimization. The operation of a prototype system, called OPTIMA, implemented in a combination of Lisp, Prolog and C on SUN workstations is described and demonstrated through an example problem. The system clearly demonstrates the potential of applying knowledge-based systems to structural optimization.

M. Balachandran, J. S. Gero
Modern Trend in Elastic-Plastic Design. Shape and Internal Structure Optimization

The paper deals with optimal design of anisotropic elastic-plastic structures. General formulations of the optimization problems are presented. Some results concerning solutions of the problems with strength and load capacity constraints are discussed.

N. V. Banichuk
Composite Materials as a Basis for Generating Optimal Topologies in Shape Design

Optimal shape design of structural elements based on boundary variations results in final designs that are topologically equivalent to the initial choice of design, and general, stable computational schemes for this approach often requires some kind of remeshing of the finite element approximation of the analysis problem. This paper presents a methodology for optimal shape design where both these drawbacks can be avoided. The method is related to modern production techniques and consists of computing the optimal distribution in space of a composite material, with the requirement that the resulting structure can carry the given loads as well as satisfy other design requirements.

Martin P. Bendsøe
Performance Characteristics of Optimality Criteria Methods

The formal development of the method is outlined emphasizing the utilization of the separability properties of the objective and constraint functions. Convergence properties are illustrated with examples of increasing numbers of independent size variables ranging from a few hundred to over a thousand.

Laszlo Berke, Narendra S. Khot
Optimal Shape of Cable Structures

The shape selection problem is formulated as the best approximation of a given not necessarily equilibrated configuration. This approximating configuration is achieved by minimizing the maximum value of suitably defined nodal distances under constraints which express equilibrium in terms of geometric and bounded pseudostress variables. The method seems to be very promising as a meaningful example shows.

M. Cannarozzi, C. Cinquini, R. Contro
Shape Optimization of Continuum with Crack

The present paper studies the problem of shape optimization from the viewpoint of structural design philosophy based on durability and damage tolerance. Initial cracks are assumed to exist or to occur at an early stage of fatigue life. The objective is to minimize the crack propagation rate, or the stress intensity factor range. Quadratic boundary elements are applied to discretize the continuum to be optimized. To obtain the stress intensity factor range, quarter-point singular elements are placed at the tip of the crack. The sensitivity of the stress intensity factor with respect to the structural shape is derived. A numerical example is presented and dicussed.

Gengdong Cheng, Biao Fu
Linear Complementarity Problems: A Cutting Plane Method Based on the Convex Hull of Polyhedra

Some structural engineering issues leading to linear complementarity problems (l.c.p.) are presented. Then the set of solutions of a linear complementarity system (l.c.s.) is represented as the union of a finite — but, unfortunately, large - number of polyhedra and the l.e.p. is reformulated as the problem of determining a supporting hyperplane of the closure of the convex hull of such union. The supporting hyperplane of any single polyhedron — which is obtained by means of parametric linear programming — generates a cut in the space of parameters, which can be so powerful as to eliminate half of the polyhedra that are to be considered in the resolution of the l.c.p..Besides, the parametric linear programming problem which has to be solved after the introduction of the cut has a smaller dimension.

V. De Angelis
Optimization of Vibrating Thin-Walled Structures

Thin-walled structures play an important role in structural engineering. These structures — due to the thinness of the walls — are very sensitive to external excitation which can be caused either by harmonically fluctuating loading or by impact. The aim of the paper is to determine optimality criteria for vibrating thin-walled structures. In deriving these conditions, one must be very careful since thin-walled structures exhibit a different mechanical behaviour to solid sections. These special effects are the influence of shear deformations and of the deformation of the cross-section. Moreover, for special cross-sections there is a coupling of bending and torsion. In order to consider all these effects, a system of differential equations is introduced. Then, optimization problems are discussed and optimality conditions are derived, including some known and several new results.

R. de Boer
Shape Optimization of Intersecting Pressure Vessels

A profile of variable thickness is sought which connects a spherical shell to a cylindrical one. The geometry of the mid-surface of the connecting shell of revolution is not known a priori, neither is the thickness variation. The profile and its thickness is obtained based on minimum material volume and a strength criterion. The ’optimum’ shape is obtained through a direct variation procedure — Rayleigh-Ritz method.

Fernand Ellyin
Optimization Procedure S A P 0 P Applied to Optimal Layouts of Complex Structures

For the treatment of problems of structural optimization, the “Three-Columns-Concept” is introduced along with the software system SAPOP (Structural Analysis Program and Optimization Procedure). SAPOP consists of an input module, a graphic module and a main module with subordinate sections containing several interchangeable software packages. Thus, it is possible to link various optimization algorithms via generally formulated optimization models with several structural analysis programs. The solution concept and the introduced definitions are illustrated by the example of a composite cantilever.

H. A. Eschenauer, P. U. Post
Structural Shape Optimization Using OASIS

OASIS is a code for structural optimization. This paper demonstrates the capibilities in shape optimization. The CAD system ALADDIN is used for shape description and generation of FE-meshes.

B. Esping, D. Holm
Optimal Design of R.C. Frames Based on Improved Inelastic Analysis Method

A general method for minimum cost design of R.C. frames has been presented. Constraints based on improved inelastic analysis method which can account for local unloading are used in framing optimization problem for minimizing the cost of material and the formwork used for a frame. The optimization problem is solved by extended interior penalty function technique using variable metric method of unconstrained minimization. A single dimension general computer program has been prepared based on the method and the procedure is demonstrated by solving four illustrative examples.

C. S. Gurujee, S. N. Agashe
Boundary Element Methods in Optimal Shape Design — An Integrated Approach

The present paper describes an implementation of the boundary element method (BEM) in optimal shape design. The computational advantages of the boundary element technique over the more traditionally used finite element method of analysis, are examined in context of the shape synthesis problem. An integrated analysis and optimization approach is also proposed for this problem. Approximate strategies that can be used in conjunction with boundary element techniques are briefly discussed. Numerical results are presented for shape design of torsional shafts and of structural components that can be characterized by a state of plane stress.

Prabhat Hajela, Junhaur Jih
A Michell Type Criterion for Shells

A lower bound, depending upon a restricted virtual displacement system, is found for the volume of material required by thin shells, which carry given loads, including hydrostatic pressure, to given supports. The loads are carried by membrane stress-resultants and Tresca’s safety criterion is satisfied. Sufficient conditions for the attainment of the bound lead to optimum designs in some simple cases, namely those for which the optimum structure is indeed a thin shell and not a three-dimentional continuum.

W. S. Hemp
Shape Optimization of the Cross-Sections of Thinwalled Beams Subjected to Bending and Shear

This paper presents the general condition for zero warping of symmetrical cross-sections of thinwalled beams under bending and shear. The condition derived within the linear elastic analysis is represented by a nonlinear functional equation coupling the function of the wall-thickness distribution with the Cartesian coordinates of points of the cross-sectional center line which are parallel to the plane of the bending moment. The solution of the corresponding functional problem, sought with the use of the discrete contracting mapping, makes it possible to determine the optimum cross-sections of beam-like structural elements which do not warp under bending and shear, the beam thus remaining free from shear-lag irrespective of the beam end conditions and the transverse loading variation.

M. Hýča
Optimization of Structures Using the Finite Element Method

The optimization code presented in this paper takes fullest advantage of the finite element modelling of structures. The link between the finite element model and the optimization problem is maintained by so-called design elements, which give this code a wide applicability and flexibility. Furthermore, the cost function and the constraints are regarded as a part of the finite element definition, rather than to be part of the optimization code. Therefore different cost functions and constraints can be used on structures, in order to meet the specific design requirements of the problem at hand. This is achieved by means of user-supplied routines on finite element level only. The gradient of the cost function and constraints are determined analytically, avoiding numerical differentiation. As a result a general purpose-structural optimization program, called Optisys, was obtained. As an example, simulation of bone remodelling will be discussed in this paper. This example can be regarded as a combined shape and material-property optimization problem, since bone remodelling is the change of shape and property of natural bone due to a change of external loading.

L. F. Jansen
Comparison of NLP Techniques in Optimum Structural Frame Design

The aim of this paper is to study the efficiency of three non-linear programming techniques for the solution of optimization problems of plane structural frames under multiple load systems. The problem is one of minimizing the mass of the frame subject to constraints on normal and shear stresses, the maximum transverse deflection and buckling load. Numerical examples are presented to indicate the efficiency of the various NLP techniques.

B. L. Karihaloo, S. Kanagasundaram
Structural and Control Optimization with Weight and Frobenius Norm as Performance Functions

A simultaneous structural and control optimization approach of flexible structures is presented. The constraints are imposed on the closed-loop eigenvalue distribution and the damping parameters. The design variables are the cross-sectional areas of the members. The effect of minimizing the weight of the structure and the Frobenius norm of the control gains is investigated. An ACOSS-FOUR structure is designed for numerical comparison.

N. S. Khot, R. V. Grandhi
Multicriterion Plate Optimization

A mu1ticriterion plate problem, where the material volume and the lowest natural frequency as well as some nodal displacements have been chosen as criteria, is formulated and methods for generating Pareto optima for it are discussed. A three-criterion plate example, where the static and dynamic analysis is based on the finite element method, is presented as an application.

J. Koski, R. Silvennoinen, M. Lawo
Optimization of Systems in Bending - Conjectures, Bounds and Estimates Relating to Moment Volume and Shape

One of the achievements of optimization theory for plate systems in bending has been the exact solution of a broad range of problems of technical interest. Some of these exact solutions are remarkably simple and could be regarded as moderately practical to actually achieve as built components. But many are complicated, and it is likely that at present unsolved problems will prove to be even more complicated.In the present study, the moment volume (V0) is the primary quantity of interest. For some shapes of plates in bending V0 is easily calculated; for others the task is much more difficult. For many problems which have been essentially solved, no V0 values have been calculated, presumably because of the difficulties involved.Certain conjectures which have been made previously are here applied to obtain V0 estimates, and also to study the role of plate shape as affecting moment volume. Some observations are made about the practicality of some basic solutions, since, it is argued, practicality must be taken into consideration if the potentials of optimization are to be more widely appreciated.

P. G. Lowe
On the Optimal Design of Columns Subjected to Circulatory Loads

Present paper is an extended review of results previously obtained by the authors, supplemented by some new results dealing with the Beck - Reut column optimization. The possibility of determination of a shape of column with the critical load higher than considered so far as “optimal” is presented.

O. Mahrenholtz, R. Bogacz
Structural Optimization in a Non- Deterministic Setting

For probabilistically described absolute structural optimization layout problems it is shown that using a simplified probabilistic framework (socalled First Order Second Moment), some classical solutions for optimal layout remain valid. Some remarks about the more general problem and the difficulty of its solution are made.

R. E. Melchers
On The Shape Optimization of Truss Structure Based on Reliability Concept

This paper is concerned with the shape optimization problems of truss structures based on the element and system reliabilities. The algorithmic procedure is proposed for determining the optimum configuration and size of members which minimize the structural weight under the constraints on the failure probabilities of the members. Numerical examples are provided to demonstrate the basic properties of the reliability based optimum design problem and the validity of the proposed method.

Y. Murotsu, M. Kishi, M. Yonezawa
On Optimality in Structural and Material Composition of Bamboo

In this paper the structural and material systems of bamboo are analyzed from the viewpoint of strength morphology. From the results, it appears that the node parts of bamboo not only are an optimum stiffener to prevent buckling fracture, but also an optimum arrester for any cracks initiated in the axial direction. The vascular bundles of bamboo, which correspond to the reinforced fiber of FRP,distribute uniquely in the axial and radial directions.The variation of volume percentage in the radial direction is based on the minimum weight design criterion.

J. Oda
Optimization of a Hollow Beam-Shaft with Prescribed Inner Contour

This paper considers the problem of minimizing the cross-sectional area of a prismatic bar with a hollow cross-section required to withstand either a twisting moment or a bending moment in a prescribed plane. In earlier work a first perturbation approximation was found. In this paper the second approximation is presented giving a significant improvement in some cases.

R. D. Parbery
Dynamic Optimization of Machine Systems Configuration

Speed, reliability and accuracy require new dynamic influences to be considered in system design, analysis and maintenance. These influences represent some dynamic interaction between the subsystems of a machine or structure, or any dynamic system, or between them and other machines or structures not included in the considered system and representing the environment [1].

Z. A. Parszewski, T. J. Chalko, D-X. Li
Design for Minimum Stress Concentration — Some Practical Aspects

The procedure necessary to obtain the shape which returns minimum stress concentration involves many choices, and we shall here sum up common personal experiences from solutions to different problems. Parametrization of the design shape is carried out using global expansion functions, very much like modal expansion in vibrational analysis. Finite element modelling is treated independent of design modelling and too simple finite elements are avoided. Linear stress elements are obtained from constant stress elements and this is utilized in the sensitivity analysis, that to a large extent is performed analytically.

Pauli Pedersen
Optimality Conditions for Multiple Loaded Structures — Integrating Control and Finite Element Method

The minimum cost design of structures (beam, truss or frame) is discussed. The structure has unknowns: area of cross section and location of some points (for example: supports). For the same structure multiple load is considered: vibration, buckling and static load — with prescribed frequency, buckling force and compliance, respectively.Optimality conditions for the unknowns are derived by variational approach. The problem is formulated in the optimal control form, so obtained results are valid for an arbitrary structure, load and boundary conditions. Optimality equations for specific structure can be solved numerically: by combination of the finite element method and the iterative algorithm. An illustrative example is presented and efficiency of the optimal design is judged by comparing it with a uniform cross-sectional area design.

Alija Pičuga
A Variational Principle Useful in Optimizing Rectangular-Base Shallow Shells

Thin, elastic, shallow shells with constant thickness and rectangular base are considered. The edges are clamped or simply supported, with no in-plane displacements. Buckling under a uniformly distributed load is analyzed. A variational principle is presented and then utilized to optimize the forms of shells with given surface areas. In some cases, the optimal forms possess significantly higher buckling loads than standard forms.

Raymond H. Plaut, David T. Young
Minimax Algorithms for Structural Optimization

In this paper we highlight the salient features of our recently developed theory for the construction of broad classes of nondifferentiable optimization algorithms. These algorithms can be used for the solution of a wide variety of unconstrained and constrained minimax problems, such as those occurring in the design of structures subjected to dynamic loads, floor planning and layout problems, control system and electronic circuit design.

E. Polak
Discrete-Continuous Structural Optimization

Methods for structural optimization problems having discrete variables, or a mix of discrete and continuous variables, are treated. The original problem is replaced by a sequence of approximate, sub-problems of a more favourable structure. A method using a generalized Lagrangian function is presented. The primal minimization over the discrete variables is done using neighbourhood searches. The performance of the method is demonstrated on numerical examples. A branch and bound algorithm is used, for comparison, to obtain global minima for a convex structural optimization problem.

Ulf Torbjörn Ringertz
Optimality Criteria and Layout Theory in Structural Design: Recent Developments and Applications

After outlining current difficulties in structural optimization and a way of overcoming them by employing optimality criteria and layout theory, the above concepts are discussed in greater detail and illustrated by simple examples. Finally, a brief review of recent developments in these fields is presented.

G. I. N. Rozvany
Shape Optimization: Creating a Useful Design Tool

Several new areas of research are presented which seek to eliminate some of the barriers to achieving a useful design optimization tool. These areas include consideration of geometrical and topological optimization as well as crossectional optimization, design for latitude uncertainty in loading conditions and problem formulation, member insertion and deletion, new elements for optimization and fundamental new approaches to combine analysis and optimization. The role new computing hardware will play in the implementation of the next generation design tool is investigated. Work in several of these areas will be described. Results for shape optimization using the boundary integral method with substructuring, zero-one integer programming for decision support and a means of performing the analysis within the shape optimization formulation are presented.

E. Sandgren, Mohamed El Sayed
Optimal Shape of Pendulum Links

Pendulums with a few links are found in many technical applications like robot arm assemblies and torsional vibration absorbers. Such pendulum devices are characterized by instationary motions ranging from the equilibrium position under gravity forces via irregular chaotic motions to steady-state rotations under centrifugal forces. The method of multibody systems is well qualified for the analysis of such motions as well as for the estimation of corresponding stresses. An optimization of the shape will result in a more homogeneous stress distribution and lower weight. A method for the shape optimization of instationary moving pendulum links is proposed and some results will be shown in detail.

Werner O. Schiehlen
An Integrated Knowledge-Based Problem Solving System for Structural Optimization

LAGRANGE is an interactive integrated programming system supporting the whole life cycle of the solution process of a mechanical structural optimization problem. Providing the geometry of the structure by means of a finite element formulation, the system guides a user to define the optimization problem, e.g. the type of constraints and their numerical data, the variable linking of the design variables, the selection of a suitable optimization routine, the generation of a formatted input file, the automatic execution of the corresponding main program and the evaluation of the results. The system is selflearning and uses rules for proposing a suitable optimization algorithm or for proposing remedies in an error situation.

K. Schittkowski
A Method of Feasible Direction with FEM for Shape Optimization

The avoidance of cracks in zones of stress concentrations by minimizing the maximal von Mises stress is very important in practical problems for the industry. In many applications it is necessary to allow for the change of traction vectors in large time intervals. So, one gets as result a multiple loading problem with a finite number of traction vectors, which will be formulated here as a discrete dynamic programming problem. The proposed algorithm is based on the method of feasible directions. It means, in effect, that one has a non-gradient method, combined with FEM, for which the search direction vector is known from physical reasons, see SCHNACK 1979 and SPÖRL 1986 [1, 2].

Eckart Schnack
Experimental Design and Structural Optimization

Structural optimization problems are mostly solved iteratively by combining finite element and mathematical progamming methods.An alternative approach can be used in which the FEM-analyses are planned a priori, both with regard to their number and the values of the design variables, applying techniques used for planning of experiments. From the outcome of the computations an approximate mathematical model is derived by means of regression analysis. This model can in turn be used as a fast analysis module in optimization software. In this paper the use of experimental design in structural optimization is discussed.The methods have been tested and used extensively for shape optimization of carillon bells, resulting in a new bell which is musically very interesting. They have also been applied successfully to several mechanical engineering problems.

A. J. G. Schoofs
On the Shape Determination of Non-Conservative System: A Case of Column Under Follower Force

The shape of a column subject to dissipative and follower forces is determined by the response-based procedure using the space-time finite element scheme. The shape improvement process is derived from the inverse problem of the adjoint variational principle combined with the energy-ratio method. By shifting the time domain included in the functional, the shape is determined in a step-by-step procedure suggesting the possibility of an adaptive shape improvement. The case study shows that the response of improved column is remarkably calm even in unstable region for the uniform column.

Y. Seguchi, S. Kojima
A Mathematical Programming Approach for Finding the Stochastically Most Relevant Failure Mechanism

In calculating the failure probability of structural systems, the most important operation is the search for the stochasticly most relevant failure mechanism. The nodal and mesh description for the modelling of a flexural frame with fully plastic behaviour and slabs discretized into triangular finite elements whose behaviour conforms the yield line theory are considered. The mathematical programming method arising from these models can be formulated as the minimization of a quadratic concave function over a linear domain.

L. M. C. SimÕes
Structural Shape Optimization in Multidisciplinary System Synthesis

Structural shape optimization couples with other discipline optimization in the design of complex engineering systems. For instance, the wing structural weight and elastic deformations couple to aerodynamic loads and aircraft performance through drag. This coupling makes structural shape optimization a subtask in the overall vehicle synthesis. Decomposition methods for optimization and sensitivity analysis allow the specialized disciplinary methods to be used while the disciplines are temporarily decoupled, after which the interdisciplinary couplings are restored at the system level. Application of decomposition methods to structures-aerodynamics coupling in aircraft is outlined and illustrated with a numerical example of a transport aircraft. It is concluded that these methods may integrate structural and aerodynamic shape optimizations with the unified objective of the maximum aircraft performance.

Jaroslaw Sobieszczanski-Sobieski
Boundary Element Approach to Optimal Structural Design Based on the Inverse Variational Principle

This paper proposes the use of the boundary element method inthe optimal structural design based on the inverse variational principle. The Condition for optimum in the inverse variational shape determination method can be expressed in terms of the boundary data alone. Firstly, using the displacements obtained by BEM, the shape of a body is reformed so that the strain energy density might become uniform everywhere on the designed surface. Volume changes in the iterative process are calculated by the movements of the extreme points of the BEM. Optimum shapes are obtained by a comparable number of iterations with the finite element approach. The boundary element approach has the merit that tne initial division into elements and redivision for reanalysis can be more easily performed than in FEM.

Yukio Tada, Hideki Taketani
Optimal Shape of Least Weight Arches

The paper concerns the shape optimization of plastically designed arches under bending and axial compression. In addition to the arch shape being unknown a priori, the problem is further made difficult by a nonsmooth objective functional. A method for solving this class of nonlinearly constrained nonsmooth optimization problem is presented and illustrated with some numerical examples.

K. L. Teo, C. M. Wang
Optimization of Conical Shells for Static and Dynamic Loads

Optimization of conical shells under static or dynamic loads is treated herein. Volume minimization subject to constraints on either allowable stresses or fundamental frequency and frequency maximization subject to a constraint on volume are studied. Piecewise linear variation in shell thickness is allowed in the study. A numerical procedure incorporating the finite element method and direct search optimization techniques is used. Results indicate that considerable saving in material and elevation in frequency are possible.

David P. Thambiratnam
Optimum Designs of Rotating Shaft Systems for Nonlinear Dynamic Responses
Optimum Shape Design and Optimum Operating Curve

Two recent studies of optimum designs of rotating shaft systems are shown here for nonlinear dynamic transient responses when the operating speeds pass through the critical ones. One is an optimum design problem to find a optimum shape of a rotating shaft which gives the minimum transient response where the shaft is supported by nonlinear bearings. The other is a optimum design problem to find an optimum operating curve for a rotating shaft system which yields the minimum transient response where the system is subjected to the operation with a limited power supply. To analyse the nonlinearities, the step-by-step integration techniques are used. Numerical results obtained by the gradient-based optimization methods are examined and discussed.

H. Yamakawa
Minimum Compliance Stiffener Layout of a Plate

An optimum design technique of stiffener layout to achieve the minimum compliance is developed. A thin plate with stiffeners is treated as anisotropic pseudo-continuum and discretized into finite elements. The minimum compliance design problem subjected to constant volume in which angles of stiffener arrangement and its density distributions in the orthogonal directions are varied is solved by a recursive quadratic programming technique. Optimal stiffener layouts of a rectangular plate under some typical loading and supporting conditions are obtained numerically.

K. Yamazaki
Recent Investigations of Structural Optimization by Analytic Methods

In this paper, we discuss two analytic methods suggested by the author for solving structural optimization problems, viz. the “stepped reduction method [1, 3–5] and a method based on the principle of complementary energy [2]. In the former, we discretize first the Young’s modulus E(x) and the thickness of h(x) of structural elements. We use the initial parameter method and the Heaviside function for descriving results in analytic form and then we use a combination of homogeneous solutions to eliminate discontinuities of bending moment and shearing force at element boundaries. This means that we need to solve only simultaneous algebraic linear equations with a finite number of unknowns. The above methods will be illustrated on the following problems: 1.Optimal design of thin elastic solid annular plate under an arbitrary load (stepped reduction method) [6]; and2.Uniform strength for statically indeterminate beams [2,7].

Yeh Kai-yuan
Detailed Machine Structural Shapes Generated from Simplified Models

In order to effectively obtain the optimum design for high precision machines requiring the evaluation of dynamic characteristics, two design optimization methods based on different simplification concepts have been proposed. In this paper a systematic methodology in which the two methods are synthesized is presented for obtaining more effectively the optimum detailed structural shapes of machine structural systems.

M. Yoshimura

Abstracts of the papers presented at the Symposium which are likely to appear in an early issue of the Journal “Structural Optimization”, (Springer-Verlag).)

On Shape Optimization of Satelite Tanks

In order to reduce the transportation cost incurred when sending a satellite into orbit, the weight of the satellite should be as low as possible. Even small reductions in the weight of the individual components lead to a decrease in the costs. One of these components is the satellite fuel tank, which stores the fuel required for positioning purposes for the entire lifetime of the satellite.

H. A. Eschenauer
Divergence Instability Conditions in the Optimum Design of Nonlinear Elastic Systems Under Follower Forces

Nonlinearly elastic discrete systems under nonconservative, compressive loading [1,2,3] of follower type, that may lose their stability through divergence, are considered. Using a general mathematical formulation a thorough parametric discussion of the critical, prebuckling and postbuckling, large displacement response, is comprehensively presented. The predominant effects on the nonlinear divergence instability of the material nonlinearity as well as of the loading parameters defining the degree of nonconservativeness, are completely revealed. Necessary and sufficient conditions for the existence of regions of devergence instability, are properly established. By means of these conditions the boundary between divergence (static) and flutter (dynamic) instability is found. The case of existence of a double critical point (coincidence of the first and second static buckling eigenmodes), obtained as a result of the linear stability analysis [4–6], is also discussed. At the aforementioned boundary, the (critical) buckling load corresponds to the maximum load-carrying capacity that can be determined by means of a nonlinear (static) stability analysis. Thus, a further insight into the role of certain parameters of paramount importance for the change of mechanism of instability from divergence to flutter, and vice-versa, is also gained.

A. N. Kounadis, O. Mahrenholtz
Solution of Max-Min Problems via Bound Formulation and Mathematical Programming

Structural optimization problems pertaining to maximization of the minimum (or minimization of the maximum) of a set of weighted criteria for given cost, are considered. It is shown that maximization of the initially smaller of the (weighted) criteria and using this as a lower bound in an iterative mathematical programming formulation leads to a very efficient method for solution of problems with global as well as local objectives.

Niels Olhoff
Natural Structural Shapes of Membrane Shells

The concept of natural structural shapes is based on the simultaneous “minimization” of the mass and the strain energy of the loaded structure, a multicriteria optimization problem. Natural structural shapes are represented by “proper” Pareto optimal designs in the sense that the limiting minimum weight and minimum stored energy designs are omitted. The method here is used to obtain optimal shell designs within the membrane theory of shells. In order to make full use of standard control theoretic methods, the problems are restricted to axisymmetrically loaded shells of revolution, a formulation involving only one independent variable. The meridional radius of curvature is used as the design variable with the Cartesian coordinates of the midsurface and a modified meridional force per unit length of the midsurface as state variables. Necessary conditions for an Edgeworth-Pareto optimum are derived and only extremal solutions based on this condition are considered.

W. Stadler, V. Krishnan
Optimal Design of Structures Under Creep Conditions

Optimal design of structures, or rather just of simple structural elements working under creep conditions, belongs to the most recent branches of structural optimization: it was initiated by four papers published in the years 1967–8 (Reytman, Prager, Nemirovsky, Zyczkowski). The most important differences with respect to elastic or plastic design are as follows: factor of time appearing in the constraints, a great variety of constitutive equations of creep or viscoplasticity, of creep rupture hypotheses, creep buckling theories, various definitions of creep stiffness etc. Moreover, the constraints related to stress relaxation are quite new. So, it is almost impossible to establish a sufficiently general theory and various types of problems must be treated separately by appropriate methods.

Michal Zyczkowski
Backmatter
Metadaten
Titel
Structural Optimization
herausgegeben von
G. I. N. Rozvany
B. L. Karihaloo
Copyright-Jahr
1988
Verlag
Springer Netherlands
Electronic ISBN
978-94-009-1413-1
Print ISBN
978-94-010-7132-1
DOI
https://doi.org/10.1007/978-94-009-1413-1