On Free Vibrations of Fiber Reinforced Doubly Curved Panels, Part 1: Formulation/Convergence Study

1998 ◽  
Vol 120 (1) ◽  
pp. 287-294 ◽  
Author(s):  
A. V. Singh ◽  
V. Kumar
Keyword(s):  
Shear Deformation Theory ◽  
Solution Procedure ◽  
Free Vibrations ◽  
Curvilinear Coordinates ◽  
Displacement Fields ◽  
Eighth Order ◽  
Bézier Surface ◽  
Surface Patches ◽  
Bezier Surface ◽  
Doubly Curved

This paper presents a Ritz-type numerical scheme for the analysis of doubly curved laminated open panels. The fundamental strain-displacement relations and energy expressions are developed in orthogonal curvilinear coordinates. Higher-order shear deformation theory and the effects of rotary inertia are included in the formulation. The displacement fields are prescribed by Bezier surface patches and the procedure to implement the boundary conditions in this context is also described. The numerical method is developed such that any arbitrary open panel bounded by four curved edges can be analyzed. Two examples namely: cantilevered cross-ply cylindrical and spherical panels are used to demonstrate the convergence of the solution procedure. Bezier surface patches formed by the eighth order polynomials yield good values of the natural frequencies.

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

1998 ◽  
Vol 120 (1) ◽  
pp. 295-300 ◽  
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.

On the existence of biharmonic tensor-product Bézier surface patches

2006 ◽  
Vol 23 (7) ◽  
pp. 612-615 ◽  
Author(s):  
Bert Jüttler ◽  
Margot Oberneder ◽  
Astrid Sinwel
Keyword(s):  
Tensor Product ◽  
Bézier Surface ◽  
Surface Patches ◽  
Bezier Surface

scholarly journals Intersecting Biquadratic Bézier Surface Patches

2008 ◽  
pp. 161-180 ◽  
Author(s):  
Stéphane Chau ◽  
Margot Oberneder ◽  
André Galligo ◽  
Bert Jüttler
Keyword(s):  
Bézier Surface ◽  
Surface Patches ◽  
Bezier Surface

scholarly journals Computing exact rational offsets of quadratic triangular Bézier surface patches

2008 ◽  
Vol 40 (2) ◽  
pp. 197-209 ◽  
Author(s):  
Bohumír Bastl ◽  
Bert Jüttler ◽  
Jiří Kosinka ◽  
Miroslav Lávička
Keyword(s):  
Bézier Surface ◽  
Surface Patches ◽  
Bezier Surface ◽  
Triangular Bézier Surface ◽  
Triangular Bézier Surface Patches

Vibrations of Fiber-Reinforced Laminated Deep Shells

1996 ◽  
Vol 118 (4) ◽  
pp. 407-414 ◽  
Author(s):  
V. Kumar ◽  
A. V. Singh
Keyword(s):  
Natural Frequencies ◽  
Vibrational Analysis ◽  
Solution Procedure ◽  
Curvilinear Coordinates ◽  
Material Strength ◽  
Shear Stresses ◽  
Control Points ◽  
Eighth Order ◽  
Good Convergence ◽  
Eigen Analysis

This paper deals with a numerical method for the free vibrational analysis of laminated deep shells. The strain-displacement relations are obtained for a general laminated shell geometry described by orthogonal curvilinear coordinates. Parabolic variation of transverse shear stresses along the thickness and the effects of rotary inertia are included in the formulation. The displacement fields are represented by Bezier patches. The shape and size of these patches are controlled by certain arbitrary points called control points. Owing to the special characteristics of these control points, the treatment of displacements, slopes, curvatures, etc., at a particular edge becomes very simple. Hence, the enforcement of boundary conditions along the edges is straightforward. Ritz-type solution procedure is used for the eigen-analysis of the shell structure. Numerical examples involving laminated spherical, conical, and cylindrical shells are investigated in detail. Such shell geometries usually have planes of symmetry; hence, only one-quarter of the shell is analyzed in this study. Good convergence of the natural frequencies is observed by using eighth-order Bezier functions. The results are compared with the existing sources in the literature. The influences of material strength and number of layers on the natural frequencies are also examined.

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