On the use of the P–TFE method for panel flutter optimization

Abstract

A numerical approach for structural analysis based on the concept of parameter transfer finite elements (P–TFE) was proposed by the authors in previous papers Barboni R, Castellani A, Mannini A. Un metodo analitico-numerico per l'analisi strutturale. Atti del Dipartimento Aerospaziale, Roma, Novembre, 1988; Barboni R, Gaudenzi P, Mannini A, Santini P. An application to the dynamics of large space structures of a new semi-analytic method for structural analysis. 17th Congress ICAS, Stockholm, September, 1990; Barboni R, Gaudenzi P, Mannini A. Parameter-transfer finite element method for structural analysis. AIAA Journal 1993; 31:923–9; Barboni R, Mannini A, Scarponi C. Structural optimization with parameter-transfer finite element. Meccania 1995; 30: 291–304. Such elements are able to take into account, like a transfer function, the whole behaviour of the structure under concern, subject to dynamic, aerodynamic or thermal actions, and to produce, in analogy with the finite element method, a numerical technique of discretization of a continuum. The purpose of this paper is to apply this methodology to optimization problems, in particular to the design of a minimum-weight monodimensional panel under critical flutter pressure constraint. The use of P–TFE in this aeroelastic optimization problem overcomes most difficulties of the usual techniques of solution, in particular, the evaluation of the sensitivity matrix, the terms of which can be calculated analytically in the frame of the proposed approach. Moreover, the critical conditions are directly imposed by the solution of a non-linear system of two equations in the eigenfrequency and the dynamic pressure unknowns. Several examples relevant to different boundary conditions are presented and the results compared with those obtained by other authors, using different methodologies.