A superconvergent finite element for composite beams with embedded magnetostrictive patches

Ghosh, Debi Prasad; Gopalakrishnan, S.

doi:10.1016/j.compstruct.2006.01.007

Cited by 8 publications

(3 citation statements)

References 32 publications

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“…In this article, we present the super convergent beam element formulation for sandwich beam with soft core, which uses the exact solution to the strong form of the governing equation as interpolating function for element formulation. Such formulation for higher order rod [16], beam [17], thin-walled beam [18], higher order composite beam [19,20] were reported in the literature. Through this procedure, the continuity and completeness of the displacement polynomial, which is essential to obtain shear locking free performance, can be achieved.…”

Section: Introductionmentioning

confidence: 86%

Development of a New Finite Element for the Analysis of Sandwich Beams with Soft Core

Sudhakar

Vijayaraju

Gopalakrishnan

2010

Jnl of Sandwich Structures & Materials

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A new super convergent sandwich beam finite element formulation is presented in this article. This element is a two-nodded, six degrees of freedom (dof) per node (3 dof u0, w, φ for top and bottom face sheets each), which assumes that all the axial and flexural loads are taken by face sheets, while the core takes only the shear loads. The beam element is formulated based on first-order shear deformation theory for the face sheets and the core displacements are assumed to vary linearly across the thickness. A number of numerical experiments involving static, free vibration, and wave propagation analysis examples are solved with an aim to show the super convergent property of the formulated element. The examples presented in this article consider both metallic and composite face sheets. The formulated element is verified in most cases with the results available in the published literature.

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Section: Introductionmentioning

confidence: 86%

Development of a New Finite Element for the Analysis of Sandwich Beams with Soft Core

Sudhakar

Vijayaraju

Gopalakrishnan

2010

Jnl of Sandwich Structures & Materials

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“…Writing the solution of the differential equation (36) for axial deformation in terms of λ 4 , we get,…”

Section: Shape Functions For Axial Deflectionmentioning

confidence: 99%

“…Generally, locking may be avoided if inter-dependence of the approximated fields is not neglected; for example, by considering exact solutions. Following Reddy's work, Gopalakrishnan and his co-workers ( [33]- [34], [36]) applied the idea to more complex structures. In general, these studies consider a uniform structure when developing the shape functions, which can then be used for non-uniform finite element analysis.…”

Section: Introductionmentioning

confidence: 99%

Superconvergent Finite Element for Coupled Torsional-Flexural-Axial Vibration Analysis of Rotating Blades

Chhabra

Ganguli

2010

International Journal for Computational Methods in Engineering

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A new two-noded, twelve degree of freedom finite element is developed for rotating blades. The shape functions are derived from the exact solutions of the governing static homogenous differential equations for the rotating blades. Such an approach leads to superconvergent elements. These differential equations include out-ofplane bending, in-plane bending, axial deformation, and torsion. The axial and torsion equations yield exact solutions and the flap and lag equations are solved by assuming a constant centrifugal force within the element. Differing from the conventional polynomial shape functions, the new shape functions account for the centrifugal stiffening effect as they depend upon the rotation speed, material properties, and the element position along the length of the blade. The finite element formulation is derived from the energy expressions using the Hamilton's principle. A convergence study for the natural frequencies is performed using the new shape functions and the polynomial shape functions for a coupled and an uncoupled blade. It is observed that the new shape functions lead to much more rapid convergence than the conventional polynomial shape functions for the first few modes at higher rotation speeds, where the effect of centrifugal stiffening is higher. The basis functions can also be used for finite element analysis of rotating rods and beams, and for energy methods.

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Rotor Blade Finite Element

Ganguli

2016

Foundations of Engineering Mechanics

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A superconvergent finite element for composite beams with embedded magnetostrictive patches

Cited by 8 publications

References 32 publications

Development of a New Finite Element for the Analysis of Sandwich Beams with Soft Core

Development of a New Finite Element for the Analysis of Sandwich Beams with Soft Core

Superconvergent Finite Element for Coupled Torsional-Flexural-Axial Vibration Analysis of Rotating Blades

Rotor Blade Finite Element

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