Hani M. Negm

Structural design optimization of wind turbine towers

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 effective design variables are chosen to be the cross-sectional area, radius of gyration and height of each segment. The nacelle/rotor combination 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 the combined tower/rotor model. Extensive computer 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 different 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 succeeded in arriving at the optimum solutions showing significant improvements in the overall system performance as compared with a reference or baseline design.

OPTIMAL FREQUENCY DESIGN OF WIND TURBINE BLADES

Abstract An optimization model for the design of a typical blade structure of horizontal-axis wind turbines is presented. The main spar is represented by thin-walled tubular beam composed of uniform segments each of which has different cross-sectional properties and length. The optimization variables are chosen to be the cross-sectional area, radius of gyration and length of each segment. The optimal design is pursued with respect to maximum frequency design criterion. Global optimality is attainable by the proposed model and a novel mathematical concept is given for placing the system frequencies. The problem is formulated as a non-linear mathematical programming problem solved by multi-dimensional search techniques. Structural analysis is restricted to the case of uncoupled flapping motion of the rotating blade, where an exact method of solution is given for calculating the natural vibration characteristics. Aeroelastic stability boundaries and steady-state response are calculated using Floquets transition matrix theory. The results show that the approach used in this study is efficient and produces improved designs as compared with a reference or baseline design.

Thermal buckling and nonlinear flutter behavior of shape memory alloy hybrid composite plates

A new nonlinear finite element model is provided for the nonlinear flutter response of shape memory alloy (SMA) hybrid composite plates under the combined effect of thermal and aerodynamic loads. The nonlinear governing equations for moderately thick rectangular plates are obtained using first-order shear-deformable plate theory, von Karman strain-displacement relations and the principle of virtual work. To account for the temperature dependence of material properties, the thermal strain is stated as an integral quantity of thermal expansion coefficient with respect to temperature. The aerodynamic pressure is modeled using the quasi-steady first-order piston theory. Newton-Raphson iteration method is employed to obtain the thermal post-buckling deflection, while the linearized updated mode method is implemented in predicting the limit-cycle oscillation at elevated temperatures. Numerical results are presented to show the thermal buckling and flutter characteristics of SMA hybrid composite plates, illustrating the effect of the SMA volume fraction and pre-strain value on the aero-thermo-mechanical response of such plates.

Calculation of the natural frequencies and steady state response of thin plates in bending by an improved rectangular element

Abstract This paper presents an application of a new improved rectangular finite element to the problems of free and forced harmonic oscillations of thin plates in bending. The proposed element, called the parametric element, has been presented in a previous paper by the same authors and applied to the problem of static bending of plates. The shape functions corresponding to the various nodal movements are expressed in simple parametric forms which scan the space between the Adini-Clough-Melosh model and the Papenfuss model. The performance of the parametric element is found to be at its best in both the statical and dynamical applications when the parameters included in the shape functions assume certain values. Like what happened in the statical application, the optimal parametric element has shown remarkable superiority over other simple elements when used in the prediction of the natural frequencies and harmonic response of several plates having different boundary conditions.

Thermoacoustic Random Response of Shape Memory Alloy Hybrid Composite Plates

Random dynamic response and thermal buckling of a shape memory alloy hybrid composite plate subjected to combined thermal and random acoustic loads are investigated. A nonlinear finite element model was developed using the first-order shear-deformable plate theory, von Karman strain-displacement relations, and the principle of virtual work. The thermal load was assumed to be a steady-state constant-temperature distribution, whereas the acoustic excitation was modeled as a white-Gaussian pressure with zero mean and uniform magnitude over the plate surface. To account for the nonlinear temperature dependence of material properties, the thermal strain was stated as an integral quantity of the thermal expansion coefficient with respect to temperature. The static nonlinear equations of motion are solved by the Newton-Raphson iteration technique to obtain the thermal postbuckling deflection, whereas the dynamic nonlinear equations of motion were transformed to modal coordinates and solved by employing Newmark implicit integration scheme. Finally, the critical buckling temperatures, static thermal postbuckling deflections, and random dynamic responses of a shape memory alloy hybrid-composite-plate panel are presented, illustrating the effect of shape memory alloy fiber embedding, sound pressure level, and temperature rise on the panel response.

An improved rectangular element for plate bending analysis

Abstract This paper presents a new, simple, rectangular finite element with twelve degrees of freedom for the bending analysis of thin plates. Three interpolation functions corresponding to the normal deflections and tangential slopes at the nodal points are written in parametric form. Convergence requirements are then used to find relationships among the parameters included in these functions. To identify the optimal values of the still undetermined parameters extensive comparisons are carried out using plate problems with different loading and boundary conditions. Certain values of the unknown parameters are found to produce displacement results with faster rate of convergence than those of other simple elements. When comparisons are based on a measure representing the actual computational effort rather than the mesh size the proposed element is found to excell higher-order elements as well. Stress results are also calculated for the proposed element and found to be fairly close to the exact values.

Aerothermoacoustic Response of Shape Memory Alloy Hybrid Composite Panels

theacousticexcitationisconsideredtobeawhite-Gaussianrandompressurewithzeromeananduniformmagnitude over the panel surface. Nonlinear temperature-dependence of material properties is considered in the formulation. The dynamic nonlinear equations of motion are transformed to modal coordinates to reduce the computational efforts. The Newton–Raphson iteration method is employed to obtain the dynamic response at each time step of the Newmark numerical integration scheme. Finally, the nonlinear response of a shape memory alloy hybrid composite panel is presented, illustrating the effect of shape memory alloy fiber embeddings, aerodynamic pressure, sound pressure level, and temperature rise on the panel response.

Limit-Cycle Oscillation of Shape Memory Alloy Hybrid Composite Plates at Elevated Temperatures

A traditional composite plate impregnated with pre-strained shape memory alloy fibers and subject to combined thermal and aerodynamic loads is investigated to demonstrate the effectiveness of using the SMA fiber embeddings in improving the static and dynamic response of composite plates. The problems investigated can be categorized into: thermal buckling subject to aerodynamic loading, linear flutter boundary at elevated temperatures, nonlinear flutter limit-cycle, and chaotic oscillations at elevated temperatures. A nonlinear finite element model based on the von Karman strain displacement relations and first-order shear deformable plate theory is derived. Aerodynamic pressure is modeled using the quasi-steady first-order piston theory. The governing equations are obtained using the principle of virtual work based on thermal strain being a cumulative physical quantity. Newton-Raphson iteration is employed to obtain the static aero-thermal large deflection at each temperature step and the dynamic response at each time step of the Newmark numerical integration scheme. A frequency domain solution is presented for predicting the flutter boundary at elevated temperatures, while the time domain method along with modal transformation is applied to numerically investigate periodic, non-periodic, and chaotic limit-cycle oscillations. The results show that the critical buckling temperature of the plate is greatly increased, and hence the thermal post-buckling deflection is suppressed by using SMA fiber embeddings. The SMA fiber embeddings caused an increase in the critical dynamic pressure at elevated temperatures, and enlargement of the static flat and dynamically stable region of the panel.

A comparison between different finite elements for elastic and aero-elastic analyses

Graphical abstract