Optimization Of Laminated Composite Plates And Shells Using Genetic Algorithms, Neural Networks And Finite Elements

Proceedings of COBEM 2009
Copyright c 2009 by ABCM

20th International Congress of Mechanical Engineering
November 15-20, 2009, Gramado, RS, Brazil

OPTIMIZATION OF LAMINATED COMPOSITE PLATES AND SHELLS
USING GENETIC ALGORITHMS, NEURAL NETWORKS AND FINITE
ELEMENTS
Sergio D. Cardozo, sergiocardozo@gmail.com
Armando. M. Awruch, amawruch@ufrgs.br
Graduate Program in Civil Engineering,Federal University of Rio Grande do Sul, Av. Osvaldo Aranha, 99, 90035-190 Porto Alegre,
RS, Brazil

Abstract. Structural optimization using computational tools has become a major research field in recent years. Methods
commonly used in structural analysis and optimization may demand considerable computational cost, depending on
the problem complexity. Therefore, many techniques have beenevaluated in order to diminish such impact. Among
these various techniques, artificial neural networks may be considered as one of the main alternatives, when combined
with classic analysis and optimization methods, to reduce the computational effort without affecting the final solution
quality. Use of laminated composite structures has been continuously growing in the last decades due to the excellentmechanical properties and low weight characterizing these materials. Taken into account the increasing scientific effort in
the different topics of this area, the aim of the present work is the formulation and implementation of a computational code
to optimize manufactured complex laminated structures with a relatively low computational cost by combining the Finite
Element Method (FEM) forstructural analysis, Genetic Algorithms (GA) for structural optimization and Artificial Neural
Networks (ANN) to approximate the finite element solutions. The modules for linear and geometrically non-linear static
finite element analysis and for optimize laminated composite plates and shells, using GA, were previously implemented.
Here, the finite element module is extended to analyze dynamic responsesto optimize problems based in frequencies and
modal criteria, and a module with perceptron ANN is added to approximate finite element analyses. Several examples are
presented to show the effectiveness of ANN to approximate solutions obtained using the FEM and to reduce significatively
the computational cost.
Keywords: Laminated composite plates and shells, Artificial Neural Networks,Optimization, Genetic Algorithms, Finite
Element
1. INTRODUCTION
The structural optimization is not a new field. Galileo in his text “Discorsi e Dimostrazioni Matematiche intorno a due
Nuove Scienze” (1638) studied the problem which consist to find the shape of a beam in which every transversal section
have the same stress distribution.
In composite materials structures, some experiences has shown thatthe GA performs better than traditional gradient
based techniques due to the discrete approach of the design variables.
A problem that arises when GA are used is the high computational cost demanded by this method. For this reason
some techniques to reduce this cost have been tested. One of them, consist to replace the complete FEM analyses by some
approximation technique. The ANN have beenshown to be a good alternative to avoid the large number of FEM analyses
involved in the GA approach.
In this work these two techniques are combined to make the process faster and cheaper in terms of computational cost.
This work is based on Almeida and Awruch (2009) from which some GA parameters, objective functions and results
are taken in order to compare the effectiveness of ANN substitutinga complete FE analyse.
2. STRUCTURAL OPTIMIZATION
The structural optimization can be understand as a process to search the configuration which gives the best performance, within some criteria and subjected to certain design constraints.
To model the structural optimization as a mathematical optimization problem, the following concepts are used:
Design variables: they are the characteristics...