Geometrically Non-Linear Analysis of Doubly Curved Laminated and Sandwich Fibre Reinforced Composite Shells with a Higher Order Theory and C° Finite Elements

A higher order theory is presented for symmetrical, non-linear gravity waves As a consequence of the generality employed, the theory includes the full range of possible wave lengths, water depths and wave heights that may be encountered, and brings them into one unified formulation Thus, the theory encompasses both linear and non-linear waves, including Airy waves, Stokes waves, cnoidal waves and the solitary wave Based on the work of Nekrasov, a complex potential in the form of an infinite series is developed to describe the flow field The potential satisfies the bottom (horizontal) condition as well as the kinematic surface condition exactly Furthermore, the dynamic surface condition is satisfied by numerical calculation of the series coefficients which appear in the complex potential The calculation of these coefficients is accomplished by solving a set of non-linear algebraic equations, with the aid of a Newton-Raphson iteration procedure and matrix inversion Coefficients of the complex potential have been obtained for a fifth order analysis and preliminary results are presented in tabular form A brief discussion of the characteristics of the waves, including wave speed, wave shape and the height of the highest possible wave follows.

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Boundary discontinuous Fourier solution for plates and doubly curved panels using a higher order theory

Composites Part B Engineering ◽

10.1016/j.compositesb.2011.01.014 ◽

2011 ◽

Vol 42 (4) ◽

pp. 842-850 ◽

Cited By ~ 17

Author(s):

Ahmet Sinan Oktem ◽

C. Guedes Soares

Keyword(s):

Order Theory ◽

Higher Order ◽

Higher Order Theory ◽

Doubly Curved ◽

Curved Panels

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A Finite Element Model for Thick-Walled Axisymmetric Shells

Journal of Pressure Vessel Technology ◽

10.1115/1.3264207 ◽

1982 ◽

Vol 104 (3) ◽

pp. 215-222 ◽

Cited By ~ 4

Author(s):

D. J. Barrett ◽

A. Soler

Keyword(s):

Finite Element ◽

Finite Elements ◽

Finite Element Model ◽

Thin Shell ◽

Element Model ◽

Order Theory ◽

Higher Order ◽

Shells Of Revolution ◽

Geometric Conditions ◽

Higher Order Theory

The symmetrically loaded moderately thick-walled shell of revolution can be treated by general finite elements, or for certain geometric conditions, by extended thin shell finite elements that have incorporated transverse shear deformation. In this work, we develop a higher order theory finite element model for symmetrically loaded shells of revolution which is useful for configurations which are out of the range of validity of the extended thin shell elements. Legendre polynomial series expansions are key features of the development and lead to nonlinear distributions of both stress and deformation in the thickness variable. Problems are solved to yield some initial data for comparison of the cost and accuracy of the higher order theory finite element model to other shell element models.

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