Given a prescribed boundary of a Bézier surface, we compare the Bézier surfaces generated by two different methods, i.e., the Bézier surface minimising the biharmonic functional and the unique Bézier surface solution of the biharmonic equation with prescribed boundary. Although often the two types of surfaces look visually the same, we show that they are indeed different. In this paper, we prov...

In this paper we give an enclosure for the solution of the biharmonic problem and also for its gradient and Laplacian in the L2-norm, respectively.

fies the biharmonic equation. The detailed behavior of solutions to the biharmonic equation on regions with corners has been historically difficult to characterize. The problem was first examined by Lord Rayleigh in 1920; in 1973, the existence of infinite oscillations in the domain Green’s function was proven in the case of the right angle by S. Osher. In this paper, we observe that, when the ...

In this article we prove the regularity of weakly biharmonic maps of domains in Euclidean four space into spheres, as well as the corresponding partial regularity result of stationary biharmonic maps of higher-dimensional domains into spheres. c © 1999 John Wiley & Sons, Inc. Introduction In this article we consider the notion of biharmonic maps and begin an analytic study of the regularity pro...

This paper reports a new spectral collocation method for numerically solving two-dimensional biharmonic boundary-value problems. The construction of the Chebyshev approximations is based on integration rather than conventional differentiation. This use of integration allows: (i) the imposition of the governing equation at the whole set of grid points including the boundary points and (ii) the s...

Time-dependent creep stress redistribution analysis of thick-walled FGM spheres subjected to an internal pressure and a uniform temperature field is investigated. The material creep and mechanical properties through the radial graded direction are assumed to obey the simple power-law variation throughout the thickness. Total strains are assumed to be the sum of elastic, thermal and creep strain...