Rational B-spline and PDE surfaces with unstructured grids for aerospace-vehicle design

The accuracy of B-spline finite element approximations to PDE surfaces

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/s0045-7825(98)00252-7 ◽

1998 ◽

Vol 158 (3-4) ◽

pp. 221-234 ◽

Cited By ~ 16

Author(s):

Joanna M. Brown ◽

Malcolm I.G. Bloor ◽

M.Susan Bloor ◽

Michael J. Wilson

Keyword(s):

Finite Element ◽

B Spline ◽

Finite Element Approximations ◽

Spline Finite Element ◽

Pde Surfaces

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The Use of Multiple Knots for B-spline Finite Element Approximations to PDE Surfaces

Geometric Modelling - Computing Supplement ◽

10.1007/978-3-7091-7584-2_6 ◽

1995 ◽

pp. 87-99

Author(s):

J. M. Brown ◽

M. S. Bloor ◽

M. I. G. Bloor ◽

M. J. Wilson

Keyword(s):

Finite Element ◽

B Spline ◽

Finite Element Approximations ◽

Spline Finite Element ◽

Pde Surfaces

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B-Spline Solutions of General Euler-Lagrange Equations

Mathematics ◽

10.3390/math7040365 ◽

2019 ◽

Vol 7 (4) ◽

pp. 365

Author(s):

Lanyin Sun ◽

Chungang Zhu

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Fourth Order ◽

Optimization Problems ◽

Lagrange Equations ◽

Surface Design ◽

B Spline ◽

Special Cases ◽

Pde Surfaces ◽

General Method

The Euler-Lagrange equations are useful for solving optimization problems in mechanics. In this paper, we study the B-spline solutions of the Euler-Lagrange equations associated with the general functionals. The existing conditions of B-spline solutions to general Euler-Lagrange equations are given. As part of this work, we present a general method for generating B-spline solutions of the second- and fourth-order Euler-Lagrange equations. Furthermore, we show that some existing techniques for surface design, such as Coons patches, are exactly the special cases of the generalized Partial differential equations (PDE) surfaces with appropriate choices of the constants.

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