Nonelement boundary representation with Bézier surface patches for 3D linear elasticity problems in parametric integral equation system (PIES) and its solving using Lagrange polynomials

2017 ◽  
Vol 34 (1) ◽  
pp. 51-79 ◽  
Author(s):  
Eugeniusz Zieniuk ◽  
Krzysztof Szerszeń
Keyword(s):  
Integral Equation ◽  
Linear Elasticity ◽  
Equation System ◽  
Boundary Representation ◽  
Lagrange Polynomials ◽  
Bézier Surface ◽  
Surface Patches ◽  
Bezier Surface ◽  
Elasticity Problems

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

Construction of Bézier surface patches with Bézier curves as geodesic boundaries

2009 ◽  
Vol 41 (11) ◽  
pp. 772-781 ◽  
Author(s):  
R.T. Farouki ◽  
N. Szafran ◽  
L. Biard
Keyword(s):  
Bezier Curves ◽  
Bézier Curves ◽  
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

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.

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