Title: Fair surface creation using FEM and optimisation

Authors: S . Teppola, A. Pramila

Addresses: Univerity of Oulu, Department of Mechanical Engineering, Oulu, Finland. ' Univerity of Oulu, Department of Mechanical Engineering, Oulu, Finland

Abstract: Creation or the form for an engineering object - e.g. a car - is, from a mathematical point of view, an underdetermined problem if the form is specified using finite number or points to be passed and using requirements on enclosed volumes, etc., because a curve or a surface consists always of an infinite number or points. In this paper, the form creation problem is formulated as a constrained minimisation problem. The functional under minimisation describes the unfairness of the curve or surface. The continuous problem is discretised using the FEM. Some examples created using the present technique are also given.

Keywords: constraints; cost functions; finite element method; FEM; integrals; form creation; constrained minimisation; optimisation; shape function matrix; vectors.

DOI: 10.1504/IJVD.1991.061670

International Journal of Vehicle Design, 1991 Vol.12 No.1, pp.40 - 49

Published online: 27 May 2014 *

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