COBEM99

S24 Mecânica dos Sólidos

Title:

A HEURISTIC METHOD TO OPTIMIZE THE SHAPE OF STRUCTURAL ELEMENTS

Summary :

RESEARCHERS HAVE SOUGHT TO DEVELOP MATHEMATICAL METHODS AND/OR NUMERICAL METHODS TO OPTIMIZE THE GEOMETRIC CONFIGURATION OF A STRUCTURE. STRUCTURAL ANALYSIS IS PART OF THE PROCESS OF SHAPE OPTIMIZATION AND IN OUR APPROACH ITS DEPENDS ON THE DEVELOPMENT OF AN ADEQUATE FINITE ELEMENT MODEL. ASSUMING THAT THE GEOMETRICAL AND PHYSICAL DISCRETIZATION OF THE MODEL IS ESTABLISHED, IT IS POSSIBLE TO IMPLEMENT AN ITERACTIVE ALGORITHM TO SEEK THE OPTIMAL SHAPE OF A STRUCTURAL COMPONENT USING A HEURISTIC PRINCIPLE. A BALANCING METHOD TO THE ERROR OF EACH ELEMENT IN THE PLANE STRESS STATE IS EXTRAPOLED. THIS METHOD IS USED TO BALANCE THE ENERGY OF DISTORTION DEFORMATION FUNCTION (VON MISES) OF EACH ELEMENT AND THE CRITERION TO STOP THE EXTRAPOLATION IS THE MAXIMUM DISTORTION ENERGY FUNCTION IN THE UNIAXIAL TENSION TEST. A NUMERICAL CODE USING FORTRAN F32 LANGUAGE IS IMPLEMENTED. THE MAINL CHARACTERISTIC OF THIS CODE IS THE EXECUTION OF TWO DISTINCT STRUCTURAL MODULES (PHYSICAL AND GEOMETRIC MODEL). IN THE GEOMETRIC MODEL THE NODES ARE REALOCATED CONSIDERING THE HOMOGENIZATION THE DISTORTION DEFORMATION ENERGY DENSITY PER ELEMENT. THE POTENTIALITY OF THE PROPOSED METHOD IS EVALUATED THROUGH SOME EXAMPLES FROM THE LITERATURE. WITH THE RESULTS THE EFFICIENCY AND THE CONVERGENCE OF THE METHOD ARE CHECKED. KEYWORDS:R METHOD, SHAPE OPTIMIZATION, FINITE ELEMENTS

Author :

Clapis, Antonio Pedro
Iguti, Fernando 0

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