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Computers and Structures 74 (2000) 649±666
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Structural design optimization of wind turbine towers
Hani M. Negm a, Karam Y. Maalawi b,*
aAerospace Engineering Department, Cairo University, Cairo, Egypt
bMechanical Engineering Department, National Research Center, Cairo, Egypt
Received 22 May 1998; accepted 18 February 1999
Abstract
This paper describes several optimization models for the design of a typical wind turbine tower structure. The
main tower body is considered to be built from uniform segments where the eective design variables are chosen to
be the cross-sectional area, radius of gyration and height of each segment. The nacelle/bination is
regarded as a rigid non-rotating mass attached at the top of the tower. Five optimization strategies are developed
and tested. The last one concerning reduction of vibration level by direct maximization of the system natural
frequencies works very well and has shown excellent results for both tower alone and bined tower/rotor
model. puter experimentation has shown that global optimality is attainable from the proposed
discretized model and a new mathematical concept is given for the exact placement of the system frequencies. The
normal mode method is applied to obtain forced response for dierent types of excitations. The optimization
problem is formulated as a nonlinear mathematical programming problem solved by the interior penalty function
technique. Finally, the model is applied to the design of a 100-kW horizontal axis wind turbine (ERDA-NASA
MOD-0). It has eeded in arriving at the optimum solutions showing signi®cant improvements in the overall
system performance pared with a reference or baseline design. # 2000 Elsevier Science Ltd. All rights
reserved.
Keywords: Renewable energy; Wind turbine; Vibration; Tower structures; Dynamics; Optimization
1. Introduction be found that deals with the problem of structural de-
sign optimization. It is the main intent of the present