Refined engineering beam theory based on the asymptotic expansion approach

Fan, Hui; Widera, G. E. O.

doi:10.2514/3.10598

Cited by 20 publications

(12 citation statements)

References 11 publications

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“…Accurate results are obtained for n = 4 and higher. Similar solutions may also be obtained using the theory presented in [26], resulting in displacements that are inferior to the Timoshenko theory (not presented here). Note in this static case that the exact results may not be obtained directly from the static counterpart of the dynamic solution presented in Section 7.2.…”

Section: Boundary Value Problemssupporting

confidence: 62%

“…Consequently there are n z − 1 BCs at each end in the normal direction as expected. For a prescribed stress using (26) and (29) this results in the set {σ zz,{m,m} , . .…”

Section: End Boundary Conditionsmentioning

confidence: 99%

“…There are several other more advanced beam theories in use. Some of these concern only rectangular cross sections [16,17,18,19,20,21,22,23], while others are applicable for circular cross sections [24,25,26,27,28,29].…”

Section: Introductionmentioning

confidence: 99%

“…Other higher order power series expansion flexural theories are presented in the literature [24,25,26,28,20]. Here, Martin [28] uses an approach on cylindrically anisotropic cylinders that in many respects is similar to the present method.…”

Section: Introductionmentioning

confidence: 99%

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A hierarchy of dynamic equations for solid isotropic circular cylinders

Abadikhah

Folkow

2014

Wave Motion

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This work considers homogeneous isotropic circular cylinders adopting a power series expansion method in the radial coordinate. Equations of motion together with consistent sets of end boundary conditions are derived in a systematic fashion up to arbitrary order using a generalized Hamilton's principle. Time domain partial differential equations are obtained for longitudinal, torsional, and flexural modes, where these equations are asymptotically correct to all studied orders. Numerical examples are presented for different sorts of problems, using exact theory, the present series expansion theories of different order, and various classical theories. These results cover dispersion curves, eigenfrequencies and the corresponding displacement and stress distributions, as well as fix frequency motion due to prescribed end displacement or lateral distributed forces. The results illustrate that the present approach may render benchmark solutions provided higher order truncations are used, and act as engineering cylinder equations using low order truncation.

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Section: Boundary Value Problemssupporting

confidence: 62%

“…Consequently there are n z − 1 BCs at each end in the normal direction as expected. For a prescribed stress using (26) and (29) this results in the set {σ zz,{m,m} , . .…”

Section: End Boundary Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A hierarchy of dynamic equations for solid isotropic circular cylinders

Abadikhah

Folkow

2014

Wave Motion

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“…This is done without assumptions on the displacement field, which is approximated as part of the asymptotic solution process. The problem can be posed from either a weak [3][4][5] or a strong [6][7][8] form of the equations of elasticity and its solution, except for a few particular configurations, needs to be obtained numerically. In general, this problem can be seen as the estimation of how much the actual displacement field in the slender solid deviates from the rigid cross sections along a deformable reference line (which corresponds to the limit h=L !…”

mentioning

confidence: 99%

Geometrically Nonlinear Theory of Composite Beams with Deformable Cross Sections

Palacios

Cesnik

2008

AIAA Journal

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A one-dimensional theory of slender structures with heterogeneous anisotropic material distribution is presented. It expands Cosserat's description of beam kinematics by allowing deformation of the beam cross sections. For that purpose, a Ritz approximation is introduced on the cross-sectional displacement field, which defines additional elastic degrees of freedom (finite-section modes) in the one-dimensional model. This results in an extended set of beam dynamic equations that includes direct measures of both the large global displacement and rotations of a reference line, and the small local deformations of the cross sections. Two situations are studied in which this approach provides a simpler alternative to shell models with comparable fidelity. First, we look at the detailed structural response of composite beams with distributed loads. In particular, the case of a composite box beam with embedded piezoelectric actuators is considered. Second, this methodology is applied to study the low-frequency response characterization of composite beams. Numerical results in both cases show that a reduced set of finite-section modes allows a full description of the actual three-dimensional displacement field using a strictly one-dimensional formulation.

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Numerical Algorithms for Dynamics of Thermopiezoceramic Bars

Altay

Dökmeci

1997

Z Angew Math Mech

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This paper is concerned with the numerical algorithms for the macromechanical analysis of a ceramic bar in which account is taken of mechanical, electrical, and thermal fields. In the first part of the paper, a hierarchic system of one‐dimensional equations of the thermopiezoceramic bar is deduced by a direct method of integration from the three‐dimensional equations of thermopiezoelectricity. Also, in a similar way, the method of moments is described for the macromechanical analysis. The second part is addressed to a direct method of solution which is essentially based on Kantorovich's method, as an alternative, for the macromechanical analysis. The resulting equations incorporate all the significant effects of ceramic bar under a general state of mechanical, electrical, and thermal loads. They accommodate the extensional, flexural, and torsional as well as coupled motions of thermopiezoceramic bar at both low and high frequencies. Lastly, in the third part, attention is confined to the cases involving special fields, motions, and material properties.

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Refined engineering beam theory based on the asymptotic expansion approach

Cited by 20 publications

References 11 publications

A hierarchy of dynamic equations for solid isotropic circular cylinders

A hierarchy of dynamic equations for solid isotropic circular cylinders

Geometrically Nonlinear Theory of Composite Beams with Deformable Cross Sections

Numerical Algorithms for Dynamics of Thermopiezoceramic Bars

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