A combined finite element-transfer matrix structural analysis method

The current emphasis on increasing aeronautical efficiency is leading the way to a new class of lighter more flexible airplane materials and structures, which unfortunately can result in aeroelastic instabilities. To effectively control the wings deformation and shape, appropriate modeling is necessary. Wings are often modeled as cantilever beams using finite element analysis. The drawback of this approach is that large aeroelastic models cannot be used for embedded controllers. Therefore, to effectively control wings shape, a simple, stable and fast equivalent predictive model that can capture the physical problem and could be used for in-flight control is required. The current paper proposes a Discrete Time Finite Element Transfer Matrix (DT-FETMM) model beam deformation and use it to design a regulator. The advantage of the proposed approach over existing methods is that the proposed controller could be designed to suppress a larger number of vibration modes within the fidelity of the selected time step. We will extend the discrete time transfer matrix method to finite element models and present the decentralized models and controllers for structural control.

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AN APPLICATION OF THE MODIFIED FINITE ELEMENT TRANSFER MATRIX METHOD FOR A HEAT TRANSFER PROBLEM

Kırklareli Üniversitesi Mühendislik ve Fen Bilimleri Dergisi ◽

10.34186/klujes.564004 ◽

2019 ◽

pp. 15-28

Author(s):

Kanat Burak BOZDOĞAN ◽

Farshid KHOSRAVI MALEKI

Keyword(s):

Heat Transfer ◽

Finite Element ◽

Transfer Matrix ◽

Transfer Matrix Method ◽

Matrix Method ◽

Transfer Problem ◽

Heat Transfer Problem ◽

Element Transfer

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Saint-Venant Decay Rates for the Rectangular Cross Section Rod

Journal of Applied Mechanics ◽

10.1115/1.1687794 ◽

2004 ◽

Vol 71 (3) ◽

pp. 429-433 ◽

Cited By ~ 2

Author(s):

N. G. Stephen ◽

P. J. Wang

Keyword(s):

Finite Element ◽

Aspect Ratio ◽

Transfer Matrix ◽

Cross Section ◽

Cross Sections ◽

Rectangular Cross Section ◽

Decay Rates ◽

Elastic Rod ◽

Cross Sectional ◽

Element Transfer

A finite element-transfer matrix procedure developed for determination of Saint-Venant decay rates of self-equilibrated loading at one end of a semi-infinite prismatic elastic rod of general cross section, which are the eigenvalues of a single repeating cell transfer matrix, is applied to the case of a rectangular cross section. First, a characteristic length of the rod is modelled within a finite element code; a superelement stiffness matrix relating force and displacement components at the master nodes at the ends of the length is then constructed, and its manipulation provides the transfer matrix, from which the eigenvalues and eigenvectors are determined. Over the range from plane stress to plane strain, which are the extremes of aspect ratio, there are always eigenmodes which decay slower than the generalized Papkovitch-Fadle modes, the latter being largely insensitive to aspect ratio. For compact cross sections, close to square, the slowest decay is for a mode having a distribution of axial displacement reminiscent of that associated with warping during torsion; for less compact cross sections, slowest decay is for a mode characterized by cross-sectional bending, caused by self-equilibrated twisting moment.

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