XII ADM International Conference - Grand Hotel - Rimini – Italy - Sept. 5th-7th, 2001
Shape Optimisation For Structural Design By Means Of Finite Elements Method Marco Evangelos Biancolini, Carlo Brutti, Eugenio Pezzuti Università degli Studi di Roma “Tor Vergata” Dipartimento di Ingegneria Meccanica Via di Tor Vergata 110, 00133 Roma E-mail:
[email protected]
Abstract In this paper a shape optimisation method is exposed. The optimum shape of a threedimensional structure was searched to obtain the minimum weight with prescribed constraint on stiffness and maximum stress. The calculations were performed directly on the FEM model of the structure without links to the original geometric model: shape evolution was generated as a linear combination of vectors belonging to the FEM model nodal positions space. A suitable vector basis is obtained by a set of fictitious FEM analyses in which the new shapes that respect design symmetry and fixed dimensions result imposing proper constraints, materials and load conditions. Of course vector basis plays a crucial role on the results both for structural performance and for aesthetic. A typical application of the method was exposed concerning the optimisation of a motorbike frame.
1. INTRODUCTION Structure design is a continuos challenge toward the best for strength, minimum weight and cost. Actual power of calculation available even on inexpensive personal computer has introduced powerful simulation tools as CAD, FEA, MB in every design fields. New tools are able to reproduce reality in a more and more reliable way so that the engineer is able to know physical quantities in a detail degree that in many cases is not accessible even experimentally. Simulation tools are the keys to reduce time to market, getting the best performance reducing the number of hard prototypes; the term “Virtual Prototyping” explain very well the actual design trend. Obviously the optimisation of a “virtual prototype” could be conducted with lower efforts saving time and money against the “hard prototype”. Shape optimisation is a very interesting tool in many fields of mechanical engineering for structural aspects (FEM), fluidodynamic (CFD), acoustic, and many other. Shape optimisation, together with emerging new techniques of topological optimisation can lead to new design solutions that at a first glance could not even supposed by the engineer. Simulation of physic, combined with geometric and topologic optimisation, can lead to new shapes and new ideas in design. Functional optimisation has to be performed under expert designer judgement, taking into account aesthetic aspects and construction feasibility.
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XII ADM International Conference - Grand Hotel - Rimini – Italy - Sept. 5th-7th, 2001
Shape evolution need a parameterisation of a starting model. This parameterisation could be achieved at various level. Geometric parameterisation is a standard tool available in advanced solid modeller and is very useful for integrated design CAD/CAE/CAM. Many FEA packages are directly connected with solid modeller [1]. A different approach consists in the local parameterisation of boundary surfaces, subdividing the boundary in regular patches connected at moveable key points; prescribed continuity order could be imposed in the local displacements fields [2]. A simpler approach consists in the parameterisation of the discrete representation of the structure. Within a FEA model of a structure, a lot of starting geometry information are preserved, and overall model belongs to a finite dimension space (order 3*N in the space, if N is the number of nodes). Parameterisation could be easily achieved by means of a base for a subspace of the model (order
