Fred F. Afagh

Boundary element analysis of interface cracks between dissimilar anisotropic materials

Abstract In this paper, the boundary element method (BEM) is applied to the analysis of interface cracks between dissimilar anisotropic materials in plane elasticity. It is based on the quadratic element formulation and special crack-tip elements which incorporate the proper O(r−12+1γ) oscillatory traction singularity are employed. A simple expression relating the stress intensity factors to the BEM computed traction coefficients is derived, and this procedure for determining stress intensity factors is validated by several examples. The numerical results obtained are shown to be very satisfactory even with relatively coarse mesh discretizations.

Optimization of Piezoelectric Actuator Configuration on a Flexible Fin for Vibration Control using Genetic Algorithms

This study presents a novel approach to optimizing the configuration of piezoelectric actuators for vibration control of a flexible aircraft fin. The fitness (cost) function for optimization using a genetic algorithm is derived directly from the frequency response function (FRF) obtained from a finite element model of the fin. In comparison to existing approaches, this method allows optimization on much more complex geometries where the derivation of an analytical fitness function is prohibitive or impossible. This technique is applied to two optimization problems for vibration control of the fin. First, the position of a single actuator is optimized anywhere within a judiciously pre-determined area of the fin using a genetic algorithm for polynomial surface fitting of the FRF in order to obtain a continuous fitness function. Next, the configuration of a pre-determined number of up to 48 separate actuators is optimized within the same area. The optimization approach is verified against experimental results obtained from a set of 12 actuators fixed to an experimental model of the fin.

Optimized grouping of piezoelectric actuators on a flexible fin

This paper presents a new method used to determine the optimum group configuration of any specified number of piezoelectric actuators for vibration control of a flexible aircraft fin. A finite element model of the fin was used to obtain the frequency response function (FRF). The fitness function for optimization using a genetic algorithm was derived directly from this FRF, eliminating the need for a closed-form analytical solution. In comparison to the existing approaches, the novelty of this method is in that it allows optimization on much more complex geometries where the derivation of an analytical fitness (cost) function is prohibitive or impossible. Optimum configurations of pre-determined numbers of actuators are presented for single mode and multi-modal acceleration and displacement control criteria. Group efficiency and control authority are also examined, allowing a suitable number of actuators to be selected for any application. Actuator efficiency was higher for single mode control; however, actuation authority was much higher in multi modal control, reflecting the fact that it is desirable to select actuators that are able to exert substantial control authority over several modes.

Asymptotically-Correct Structural Modelling Of Thin-Walled Anisotropic Closed Cross-Section Rotating Slender Beams

An application of a comprehensive and compact methodology to obtain the asymptotically-correct stiffness matrix of anisotropic, thin-walled, closed cross-section, and rotating slender beams is presented. The Variational Asymptotic Method (VAM), which utilizes small geometrical parameters inherent to thin-walled slender beams, is used to obtain the displacement and strain fields, and the cross-sectional stiffness matrix without any ad hoc assumptions. The advantage of this approach is that the asymptotically-correct and populated 4 × 4 cross-sectional stiffness matrix provides all the necessary information about the elastic behavior of the rotating beam, thereby nullifying the need for refined beam theories that incorporate higher order deformation modes, like the Vlasovs mode. The implementation of the theory usingMATLAB was validated against the Vartiational Asymptotic Beam Sectional Analysis (VABS) computer software, a two-dimensional finite element program that utilizes a more general approach to the VAM that is applicable to thick/thin-walled anisotropic crosssections with arbitrary geometry. Sample applications of the theory to rotor blades are presented. The paper concludes with a discussion of how the presented material would be used directly in the dynamic modelling of rotating helicopter blades.

Dynamic response of elastic rods subjected to uniformly distributed, tangential follower forces

SummaryThis paper treats the solution of separable non-selfadjoint initial-boundary-value problems using Greens function approach. Specifically, the dynamic response of an isotropic, homogeneous and linearly elastic clamped-free rod when perturbed by a time varying driving force and under constant uniformly distributed tangential follower forces is determined.ÜbersichtIn dieser Arbeit wird die separable Lösung nicht-selbstadjungierter Anfangs-Randwertprobleme mittels Anwendung der Greenschen Funktion behandelt. Insbesondere wird das dynamische Verhalten eines isotropen, homogenen und linear elastischen Stabes betrachtet, der unten eingespannt, oben frei ist und der einer zeitlich veränderlichen Erregerkraft sowie konstanten, tangential mitgehenden Kräften unterworfen worden ist.

Actuation of Slender Thin-wall Anisotropic Open Cross-section Beams Based on Asymptotically Correct Vlasov theory

An asymptotically correct analysis of passive anisotropic thin-walled open cross-section beam-like structures using the variational asymptotic method (VAM) is extended to include embedded macro fiber composites. Application of the VAM to beam-like structures splits the problem into non-linear 1D theory along the selected beam reference line and linear 2D generalized 5 × 5 Vlasov theory augmented by a 5 × 1 actuation vector over the cross-section. The linear 2D cross-sectional theory is validated against the University of Michigan/variational beam sectional analysis 2D finite element software. The validation examples selected were based on practical cross-sectional geometry and material anisotropy under DC actuation voltage. Actuation-induced deformations predicted at the beam reference line are obtained using an intrinsic geometrically exact beam theory for open cross-sections. The predicted generalized deformations are compared with those obtained using the 3D finite element analysis software ANSYS Multiphysics, which further validates the extended theory. The analytical theory is shown to be straightforward to implement and efficient, yet sufficiently reliable to perform interdisciplinary studies and optimization of various engineering applications of such structures.

Analysis of active closed cross-section slender beams based on asymptotically correct thin-wall beam theory

An asymptotically correct theory for multi-cell thin-wall anisotropic slender beams that includes the shell bending strain measures is extended to include embedded active fibre composites (AFCs). A closed-form solution of the asymptotically correct cross-sectional actuation force and moments is obtained. Active thin-wall beam theories found in the literature neglect the shell bending strains, which lead to incorrect predictions for certain cross-sections, while the theory presented is shown to overcome this shortcoming. The theory is implemented and verified against single-cell examples that were solved using the University of Michigan/Variational Beam Sectional Analysis (UM/VABS) software. The stiffness constants and the actuation vector are obtained for two-cell and three-cell active cross-sections. The theory is argued to be reliable for efficient initial design analysis and interdisciplinary parametric or optimization studies of thin-wall closed cross-section slender beams with no initial twist or obliqueness.

Simulation of non-selfadjoint control of thin elastic plates in the presence of conservative in-plane forces

Summary Based on the analysis presented in [1], a closed-form solution for the response of a controlled plate to a transversely applied dynamic loading is presented. Both the applied loading and the control are considered to be continuously distributed. The results and the corresponding parametric study are presented for two common boundary conditions of SSSS and SFSF in the plates.

On the dynamic response of certain separable and non-selfadjoint systems

SummaryIn this paper the dynamic response of certain separable and non-selfadjoint systems has been investigated. Specifically, the dynamic characteristics of isotropic, homogeneous, linearly elastic and spatially one-dimensional systems such as clamped-free rods under constant uniformly distributed tangential follower forces have been determined and presented. The dynamic response of such a system when perturbed by a time varying driving force has also been determined and numerical examples are presented.ÜbersichtIn dieser Arbeit wird das dynamische Verhalten bestimmter separierbarer und nicht-selbstadjungierte Systeme untersucht. Insbesondere wird das dynamische Verhalten von isotropen, homogenen, linear elastischen und räumlich eindimensionalen Systemen untersucht, wie z. B. unten eingespannte und oben freie Stäbe, die konstanten tangentialen mitgehenden Kräften unterworfen sind. Die Ergebnisse sind in Tabellen und in graphischer Form dargestellt. Auch einbegriffen wird das dynamische Verhalten von Systemen, die einer zeitlich veränderlichen Erregerkraft ausgesetzt sind.

Efficient Identification of Naval High-Speed Craft Shock Mitigation Seat Modal Parameters From Drop-Test Data

Naval high-speed craft (HSC) operating in moderate to high seas experiences high-g and repeated shock loading at the seat–deck interface. These conditions are known to pose a serious potential for injury to the occupants. While various shock-mitigating seats are commercially available; their designs are in many cases quite different, and quantifying their shock attenuation characteristics can be challenging. The need for a standard test platform and experimental analysis methodology to investigate HSC seat effectiveness is a major objective of research being conducted by Carleton Universitys Applied Dynamics Laboratory (ADL) in partnership with Defence Research and Development Canada-Atlantic (DRDC Atlantic). A drop tower was designed and manufactured for testing HSC seats in order to characterize their shock-mitigating effectiveness by simulating the severe conditions of a slam impact at sea. Further, in order to identify seat dynamic parameters from drop-test data, the eigensystem realization algorithm (ERA), a modal-analysis-based system identification method, was applied to efficiently extract the modal parameters. The technique was shown to successfully extract the damping ratio as well as the damped and undamped natural frequencies of the seats from impact test data. The evaluated dynamic properties of the seats can subsequently inform decisions related to the design and/or procurement of commercially available seats.