Matrix Methods in Elastomechanics

Pestel, Eduard; Leckie, F. A.; Kurtz, E. F.

doi:10.1115/1.3629714

Cited by 234 publications

(153 citation statements)

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“…The transfer-matrix method is a classic approach [23]. Here, we first review its application to a periodic laminated hollow sphere proposed in [22] and next extend the obtained results to the case of imperfect contact between the layers.…”

Section: Fig 2 Comparison Of the Effective Coefficients Hmentioning

confidence: 99%

Behavior of laminated shell composite with imperfect contact between the layers

Guinovart-Sanjuán

Rizzoni

Rodrı́guez-Ramos

et al. 2017

Composite Structures

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The paper focuses on the calculation of the effective elastic properties of a laminated composite shell with imperfect contact between the layers. To achieve this goal, first the two-scale asymptotic homogenization method (AHM) is applied to derive the solutions for the local problems and to obtain the effective elastic properties of a two-layer spherical shell with imperfect contact between the layers. The results are compared with the numerical solution obtained by finite elements method (FEM). The limit case of a laminate shell composite with perfect contact at the interface is recovered. Second, the elastic properties of a spherical heterogeneous structure with isotropic periodic microstructure and imperfect contact is analyzed with the spherical assemblage model (SAM). The homogenized equilibrium equation for a spherical composite is solved using AHM and the results are compared with the exact analytical solution obtained with SAM.

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Section: Fig 2 Comparison Of the Effective Coefficients Hmentioning

confidence: 99%

Behavior of laminated shell composite with imperfect contact between the layers

Guinovart-Sanjuán

Rizzoni

Rodrı́guez-Ramos

et al. 2017

Composite Structures

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“…The TMM principle is to break up the structure into smaller components across which one calculates the transfer of a state vector (displacements and forces). Pestel and Leckie [7] introduced the TMM [8] used TMM to calculate the vibration of helicopter blades modeled as rotating Timoshenko beams. Bois et al [9,10] used TMM to calculate the electromechanical (E/M) impedance of a PWAS mounted on a composite beam with internal delaminations.…”

Section: Transfer Matrix Methods Modeling Of Pwas Electromechanical (Ementioning

confidence: 99%

Predictive modeling of piezoelectric wafer active sensors interaction with high-frequency structural waves and vibration

et al. 2012

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The modeling of the interaction between piezoelectric wafer active sensors (PWAS) and structural waves and vibration is addressed. Three main issues are discussed: (a) modeling of pitch-catch ultrasonic waves between a PWAS transmitter and a PWAS receiver by comparison between exact Lamb wave solutions and various finite element method (FEM) results; (b) analytical modeling of the power and energy transduction between PWAS and ultrasonic guided waves highlighting the tuning opportunities between PWAS and the waves; (c) the use of the transfer matrix method to model the electromechanical (E/M) impedance method for direct reading of high-frequency local structural vibration and comparison with FEM results. The paper ends with a summary and conclusions followed by recommendations for further work.

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“…Vlasov used cartesian coordinates and the so-called method of initial functions. This method is similar to the transfer matrix method of structural mechanics [14] which has been applied to multilayered media by the author [8]- [11 ]. Kuo started from Muki's theory [13] of asymmetric loaded thick plates and used transfer matrices too.…”

Section: Introductionmentioning

confidence: 99%

Theory of elasticity of a multilayered medium

Bufler

1971

J Elasticity

165

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Though the basic equations of the linear theory of elasticity are well known, it is rather cumbersome to evaluate the exact state of stress and displacement for a multilayered medium. In this paper we discuss a formal solution based on integral transforms and matrix analysis. Essentially the problem is reduced to the evaluation of some basic matrices and thus the calculation takes place in a clearly arranged way. Here we restrict ourselves to plane elastic and isotropic layers and use cartesian coordinates. ZUSAMMENFASSUNGObwohl die Grundgleichungen der linearen Elastizit~itstheorie wohlbekannt sind, ist die Ermittlung des genauen Spannungs-und Verschiebungszustandes eines vielschichtigen Mediums ziemlich miihsam. In der vorliegenden Arbeit wird mithilfe yon Integraltransformationen und der Matrizenrechnung eine formale LOsung entwickelt. Das Problem wird im wesentlichen auf die Bestimmung einiger Grundmatrizen zuriickgefiihrt, die eine iibersichtliche Berechnung gestattet. Die Untersuchung beschr/inkt sich auf ebene elastisch-isotrope Schichten, wobei kartesische Koordinaten verwendet werden.

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Matrix Methods in Elastomechanics

Cited by 234 publications

References 0 publications

Behavior of laminated shell composite with imperfect contact between the layers

Behavior of laminated shell composite with imperfect contact between the layers

Predictive modeling of piezoelectric wafer active sensors interaction with high-frequency structural waves and vibration

Theory of elasticity of a multilayered medium

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