Mustafa Özakça

Optimization of arches using genetic algorithm

Abstract An optimization procedure is presented for the minimum weight and strain energy optimization for arch structures subjected to constraints on stress, displacement and weight responses. Both thickness and shape variables defining the natural line of the arch are considered. The computer program which is developed in this study can be used to optimize thick, thin and variable thickness curved beams/arches. An automated optimization procedure is adopted which integrates finite element analysis, parametric cubic spline geometry definition, automatic mesh generation and genetic algorithm methods. Several examples are presented to illustrate optimal arch structures with smooth shapes and thickness variations. The changes in the relative contributions of the bending, membrane and shear strain energies are monitored during the whole process of optimization.

Basic Finite Element Formulation for Vibrating Axisymmetric Shells

This chapter deals with the free vibration analysis of SORs using the FE method. A family of variable-thickness, curved, C(0), MR axisymmetric FEs that include shear deformation and rotatory inertia effects is presented. The accuracy, convergence and efficiency of these newly developed elements are explored through a series of free-vibration analyses of axisymmetric shell structures and the results are compared with those obtained by other analytical and numerical methods. An interesting feature of the chapter is a brief study of the vibrational behaviour of church bells and a hand bell.

A COMPUTATIONAL TOOL BASED ON GENETIC ALGORITHM FOR DETERMINING OPTIMUM SHAPES OF VIBRATING PLANAR AND SPACE TRUSSES

This paper deals with the structural optimization of vibrating planar and space trusses. The objective of the present study is to develop a robust and reliable shape optimization tool for vibrating trusses. Natural frequencies are determined using standard finite element matrixdisplacement method. The fundamental concept is to generate structural shapes for trusses in which certain vibration characteristics are improved. The results of comparative studies of the Genetic Algorithm (GA) against other continuous optimization algorithms for truss problems are reported to show the efficiency of the structural optimization.

OPTIMIZATION OF VIBRATING ARCHES BASED ON GENETIC ALGORITHM

The present work is concerned with the structural shape optimization of vibrating arches. Natural frequencies and mode shapes are determined using curved, variable thickness, C(0) continuity Mindlin-Reissner finite elements. The whole shape optimization process is carried out by integrating finite element analysis, cubic spline shape and thickness definition, automatic mesh generation and Genetic Algorithm (GA). An example is included to highlight various features of the optimization procedure.

Basic Finite Strip Formulation for Prismatic Shells

This chapter deals with the linear elastic analysis of prismatic folded plate and shell structures supported on diaphragms at two opposite edges with the other two edges arbitrarily restrained. The analysis is carried out using curved, variable-thickness, MR FSs.

Finite Strip Formulation for Vibrating Prismatic Shells

This chapter deals with the free-vibration analysis of prismatic folded plate and shell structures supported on diaphragms at two opposite edges with the other two edges arbitrarily restrained. The analysis is carried out using curved, variable-thickness FSs based on MR shell theory. The theoretical formulations are presented for families of C(0) strips for prismatic structures with rectangular and curved planform. The accuracy and relative performance of both families are then examined for a series of problems including plates, cylindrical shells and box girders.

Buckling Analysis and Optimization of Plates and Shells

This chapter deals with the buckling analysis and optimization of prismatic and axisymmetric plate and shell structures. The analysis of prismatic folded plate structures supported on diaphragms at two opposite edges is carried out using variable-thickness FSs based on MR assumptions, which allow for transverse shear deformation effects. The theoretical formulation is presented for a family of C(0) strips and the accuracy and relative performance of the strips are examined.

Basic Dynamic Analysis of Plates, Solids of Revolution and Finite Prism Type Structures

In this chapter we consider some additional approaches to the analysis of axisymmetric and prismatic shells. Focusing on the dynamic analysis of MR rectangular plates with simply supported edges, we present exact, Navier-type solutions based on double Fourier series representations of the plate lateral displacement and normal rotations.

Basic Finite Element Formulation for Shells of Revolution

In this chapter the basic FE formulation of a newly developed family of linear, quadratic and cubic, variable-thickness, C(0) elements for SORs based on MR shell theory is described. Only axisymmetric behaviour is considered. A method for evaluating the SE is presented and several benchmark examples are studied to verify the performance of the elements.

Structural Shape Optimization of Vibrating Axisymmetric and Prismatic Shells

Chapter 9 is concerned with structural shape and thickness optimization of vibrating axisymmetric and prismatic plates and shells. The basic algorithm for SSO is described first. Details are subsequently presented concerning the problem definition. Attention is then focused on the sensitivity calculations and problems connected with their accuracy. In the penultimate section some details regarding mathematical programming are given. Finally, various practical aspects of SSO are discussed, such as specification of end conditions, scaling and bounds on design variables. This chapter is also concerned with the SSO of vibrating axisymmetric and prismatic shells. Natural frequencies and mode shapes are determined using curved, variable-thickness, MR FSs and FEs introduced and bench-marked in Chapters 7 and 8. The whole shape optimization process is carried out by integrating FE and FS analysis, cubic spline shape and thickness definitions, sensitivity analysis and mathematical programming. In most cases, the objective is either the maximization of the fundamental frequency or the minimization of the volume by changing the shape or thickness variation of the cross-section of the structure with constraints on the volume or natural frequencies. The SAM and FDM are used to determine the sensitivities of the objective function and constraints to changes in the design variables. Several examples are considered to illustrate and highlight various features of the optimization, including plates, conical shells, box-girder bridges with rectangular or curved planform, axisymmetric branched shells, bells and cylindrical shells.