A new doubly-curved shell element for the free vibrations of arbitrarily shaped laminated structures based on Weak Formulation IsoGeometric Analysis

AbstractA hybrid-mixed ANS four-node shell element by using the sampling surfaces (SaS) technique is developed. The SaS formulation is based on choosing inside the nth layer In not equally spaced SaS parallel to the middle surface of the shell in order to introduce the displacements of these surfaces as basic shell variables. Such choice of unknowns with the consequent use of Lagrange polynomials of degree In − 1 in the thickness direction for each layer permits the presentation of the layered shell formulation in a very compact form. The SaS are located inside each layer at Chebyshev polynomial nodes that allows one to minimize uniformly the error due to the Lagrange interpolation. To implement the efficient analytical integration throughout the element, the enhanced ANS method is employed. The proposed hybrid-mixed four-node shell element is based on the Hu-Washizu variational equation and exhibits a superior performance in the case of coarse meshes. It could be useful for the 3D stress analysis of thick and thin doubly-curved shells since the SaS formulation gives the possibility to obtain numerical solutions with a prescribed accuracy, which asymptotically approach the exact solutions of elasticity as the number of SaS tends to infinity.

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Thermo-Mechanical Stability Analysis of Composite Cylindrical Panels

ASME 2013 Gas Turbine India Conference ◽

10.1115/gtindia2013-3651 ◽

2013 ◽

Author(s):

P. V. Katariya ◽

S. K. Panda

Keyword(s):

Mechanical Stability ◽

Shear Deformation Theory ◽

Laminated Composite ◽

Shell Element ◽

Element Model ◽

Computer Code ◽

Substantial Effect ◽

Stability Behavior ◽

Support Conditions ◽

Laminated Structures

In this article, stability behavior of laminated composite curved panels under thermo-mechanical loading is analyzed. A generalized panel model is developed based on higher order shear deformation theory by taking the nonlinearity in Green-Lagrange sense for thermal distortion. The critical buckling load (mechanical/thermal) parameters are obtained by using the developed finite element model validated for both ANSYS and homemade computer code. The model has been discretized in ANSYS using an eight-noded serendipity shell element (shell281) and a nine noded isoparametric element for the computer code. The convergence test has been carried out and the results are compared with those available published literature. In this analysis, a uniform temperature distribution through the thickness is taken and the material properties for the composites are assumed to be temperature invariant. We note substantial effect of different parameters (support conditions, number of layers, thickness ratio and modular ratio) on thermo-mechanical stability behavior of laminated structures.

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Efficient three-node finite shell element for linear and geometrically nonlinear analyses of piezoelectric laminated structures

Journal of Intelligent Material Systems and Structures ◽

10.1177/1045389x17705538 ◽

2017 ◽

Vol 29 (3) ◽

pp. 345-357 ◽

Cited By ~ 9

Author(s):

Gil Rama ◽

Dragan Marinković ◽

Manfred Zehn

Keyword(s):

Shell Element ◽

Geometrically Nonlinear ◽

Nonlinear Analyses ◽

Laminated Structures ◽

Finite Shell

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On Free Vibrations of Fiber Reinforced Doubly Curved Panels, Part 2: Applications

Journal of Vibration and Acoustics ◽

10.1115/1.2893820 ◽

1998 ◽

Vol 120 (1) ◽

pp. 295-300 ◽

Cited By ~ 4

Author(s):

A. V. Singh ◽

V. Kumar

Keyword(s):

Natural Frequencies ◽

Shear Deformation Theory ◽

Free Vibrations ◽

Cylindrical Panel ◽

Curvilinear Coordinates ◽

Displacement Fields ◽

Element Analysis ◽

Surface Patches ◽

Orthogonal Curvilinear Coordinates ◽

Doubly Curved

The applications of a Ritz-type numerical scheme, in which the displacement fields are prescribed by Bezier surface patches, are presented for the analysis of doubly curved laminated open panels. The fundamental strain-displacement relations and energy expressions are developed in orthogonal curvilinear coordinates. The higher-order shear deformation theory and the effects of rotary inertia are considered in the formulation. Good comparisons of the results are obtained for a class of open panels. For example, values of the natural frequencies of open cylindrical and spherical panels made of isotropic material are compared with the results from the finite element analysis. Cases of cantilevered and simply supported angle-ply laminated cylindrical panel and a fully clamped isotropic conical panel are also examined for comparison with the available sources in the literature. In addition, the natural frequencies are presented for angle-ply laminated circular cylindrical, conical and spherical panels and the influence of the fiber orientation on the fundamental frequency is also examined for the angle ply having one, two [φ/−φ] and four [φ/−φ/φ/−φ] laminae arrangements.

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Elastic Analysis of a Skull

Journal of Applied Mechanics ◽

10.1115/1.3423172 ◽

1973 ◽

Vol 40 (4) ◽

pp. 838-842 ◽

Cited By ~ 22

Author(s):

C. H. Hardy ◽

P. V. Marcal

Keyword(s):

Finite Element ◽

Composite Material ◽

Elastic Stress ◽

Shell Element ◽

Elastic Analysis ◽

Triangular Shell Element ◽

Skull Measurements ◽

Doubly Curved

A finite-element elastic analysis is made of a skull. Measurements were made of the geometry and thickness of a skull. The skull was then idealized with a doubly curved and arbitrary triangular shell element. Results suggest that the skull is well built for resistance to front loads. The importance of using a composite material through the thickness of the shell was established. On the basis of tensile cracking at maximum elastic stress, loads of 3500 lb and 1400 lb were predicted for the first cracking of the skull due to front and side loading, respectively.

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