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The plated structures are one of the most frequently used engineering structures. The object of this research work is the optimal design of curved folded plates. This work is an ongoing investigation. There are various solution methods to analyze this type of structures. Here the finite strip method is used. At first single load condition is considered, but later the multiple load conditions are used for the design. The base formulation is a minimum volume design with displacement constraint what is represented by the compliance. For the multiple loading two equivalent topology optimization algorithms are elaborated: minimization of the maximum strain energy with respect to a given volume or minimization of the volume of the structure subjected to displacement constraints. The numerical procedures are based on iterative formula which are formed by the use of the first order optimality condition of the Lagrangian-functions. The application is illustrated by numerical examples.

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... The extended formulations are presented, but the algorithm is derived for single load case. This paper is an extended version of the conference presentation of Balogh and Lógó [1]. ...

The plated structures are one of the most frequently used engineering structures. The object of this research work is the optimal design of curved folded plates. This work is an ongoing investigation. There are various solution methods to analyze this type of structures. Here the finite strip method is used. At first single load condition is considered, but later the multiple load conditions are used for the design. The base formulation is a minimum volume design with displacement constraint what is represented by the compliance. For the multiple loading two equivalent topology optimization algorithms can be elaborated: minimization of the maximum strain energy with respect to a given volume or minimization of the volume of the structure subjected to displacement constraints. The numerical procedures are based on iterative formulas which is formed by the use of the first order optimality condition of the Lagrangian-functions. The application is illustrated by numerical examples.

Simulating the material behavior on the basis of a rigid-plastic body, a method for optimal design of reinforced cylinderical shells is presented herein. Both fiber-reinforced and rib-reinforced shells are incorporated into the study. The influence of geometrical changes is retained in the analysis, but elastic effects, as well as strain hardening, are disregarded. From the mathematical point of view, the optimal design problem is referred to as an optimal control problem with state-variable inequality constraints. Two particular cases of optimal design are examined in greater detail. The optimal continuous thickness distribution of the shell is determined for a specified displacement field. The optimal design is assigned for a shell of piece-wise constant thickness.

A procedure is developed for obtaining the design of an elastic, perfectly plastic shell or structure which will support prescribed loads and which is the optimum design for a given criterion. The action of body forces is included in the analysis. Some problems in the minimum volume design of a circular cylindrical sandwich shell are solved to illustrate the method, and it is found that only for relatively short shells does the minimum volume design effect an appreciable saving over the membrane design.

The paper investigates implications of some recent mathematical developments in the fields of shape optimization and relaxation of variational problems. Considering the least-weight design of perforated elastic plates in either flexure or plane stress for a prescribed compliance, it is shown that at low rib densities microstructures consisting of a combination of first- and second-order infinitesimal ribs is superior to those consisting of purely first-order infinitesimal ribs. Moreover, it is indicated that thin ribs of infinite length/thickness ratio do not contribute significantly to the stiffness in a direction normal to their plane. On the basis of this conclusion, a simple specific cost function is derived and then it is used in the design of circular, uniformly loaded perforated plates with zero value of Poisson's ratio. As a basis for comparison several intuitively selected topographies are optimized for the case of simply supported plates, and in Part II of this study a variational analysis is used to obtain the optimal solutions for plates with simply supported, clamped or loaded edges.

Optimal design with thousands of variables is a great challenge in engineering calculations. In this paper beside the short history of optimality criteria methods, a solution technique is introduced for the topology optimization of elastic disks under single parametric static loading. Different boundary conditions and thousands of design variables are applied. Due to a simple mesh construction technique, the checker-board pattern is avoided. The Michell-type problem is investigated minimizing the weight of the structure subjected to a compliance condition. The numerical procedure is based on an iterative formula that is formed by the use of the. first-order optimality condition of the Lagrangian function. The application is illustrated by numerical examples. The effect of the different loading conditions is studied for the Michell-type topologies as well.

The aim of this paper is to introduce a new type of stochastic optimal topology design method where the loads are given randomly. The standard stochastic mathematical programming problem is based on penalized minimum weight design procedure subjected to a probabilistic compliance constraint due to the loading uncertainties. If the probability of the compliance constraint is given by the use of recommendation of Prekopa this probabilistic expression can be substituted with an equivalent one and used as a deterministic constraint in the original problem. In the numerical method, optimality criteria procedure is applied. The application is illustrated by numerical examples.

Das Dimensionierungsverfahren vonDrucker undShield [1, 2] wurde krzlich auf die Dimensionierung rotationssymmetrisch belasteter Kreisplatten fr Mindestgewicht angewandt [3], wobei sowohl gelenkig gesttzte als auch eingespannte Sandwichplatten betrachtet wurden. In der vorliegenden Arbeit werden diese Untersuchungen auf kreisfrmige Sandwichplatten unter nicht rotationssymmetrischer Belastung ausgedehnt. Es zeigt sich, dass auch fr solche Lasten der Dimensionierung fr Mindestgewicht diejenigen Verformungszustnde zugrunde gelegt werden knne, welche schon zur Lsung der entsprechenden Aufgabe bei rotationssymmetrischer Belastung konstruiert wurden. Fr Belastung einer gelenkig gesttzten oder eingespannten Kreisplatte durch eine Einzellast mit beliebigem Angriffspunkt werden explizite Dimensionierungsformeln gewonnen, fr beliebig verteilte Belastung werden Integraldarstellungen der optimalen Dimensionierung gegeben.

A non-linear programming method is developed for optimization of inelastic cylindrical shells with internal ring supports.
The shells under consideration are subjected to internal pressure loading and axial tension. The material of shells is a composite
which is considered as an anisotropic inelastic material obeying the yield condition suggested by Lance and Robinson. Taking
geometrical non/linearity of the structure into account optimal locations of internal ring supports are determined so that
the cost function attains its minimum value. A particular problem of minimization of the mean deflection of the shell with
weakened singular cross sections is treated in a greater detail.
KeywordsCylindrical shell-Plasticity-Optimization-Internal support