OPTIMASI BENTUK OVAL CANGKANG SIMETRI SUMBU

Wibowo, Fx. Nurwadji (1996) OPTIMASI BENTUK OVAL CANGKANG SIMETRI SUMBU. Phd thesis, UAJY.

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Abstract

The study of this dissertation is concerned with the oval shape optimization of ax symmetric shells. An oval shape equation which is able to represent circles, an ellipse and egg shape is found successfully in this study. Coordinates of shell nodes are represented by parameters of the oval shape equation. Shell thickness at the nodes and the parameters of the oval shape equation become design variables, while a minimum shell material volume is the objective function of this shape optimization problem. Actual stresses at the shell nodes which are less or equal to allowable stress becomes inequality constraints which must be satisfied. A content in the shell which is equal to a constant become an equality constraint which must be satisfied too. A Gauss quadrature method is used to solve integration problems of the shell material volume and the content in the shell numerically. A finite element method which uses a curve element is used to calculate the actual stresses at the shell nodes. A displacement function which indirectly includes by rigid body motions is used in this study. The displacement function has two additional constants which explain a strain value decrease due to the rigid body motions, such that a condensation of element stiffness matrices and element load vectors are needed before the element stiffness matrices and the element load vectors are assembled into a structure stiffness matrix and a structure load vector respectively. Genetic algorithms are based on genetics and Darwin theory "survival of the fittest" is used to know characteristics of the problems and to solve the oval shape optimization of ax symmetric shells. In this study, continuous genetic algorithms are developed, and then the continuous genetic algorithms are combined with a flexible polyhedron method and an arranged mutation technique. The optimization methods which form the combination of some methods are called a hybrid method. A computer program is written based on the oval shape equation, the finite element formulation, the continuous genetic algorithms and the hybrid method. The computer program is used to solve the oval shape optimization of ax symmetric shells on a roll support and a continuous elastic support, with a uniform pressure load, a water load and a combination of the water load and a shell self weight. The optimization results show that: • The optimum shapes of the shape optimization problem of ax symmetric shells on a roll support with the uniform pressure load are the shape of a ball. • The optimum shapes of the shape optimization problem of ax symmetric shells on a roll support with the water load and the combination of the water load and the shell self weight are nearly of an egg shape. • The optimum shapes of the shape optimization problem of ax symmetric shells on the continuous elastic support with the water load and the combination of the water load and the shell self weight are the shape of a flat oval.

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