2 The Calculus of Variations 2 2.1 Functionals of f and f ′ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Functionals of f , f ′, and f ′′ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Cubic Splines and Green’s Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 Euler-Lagrange Equations for Multi...

Thin plate splines have been used successfully to model curves and surfaces. A new application is in data mining where they are used to model interaction terms. These interaction splines break the \curse of di-mensionality" by reducing the high-dimensional nonparametric regression problem to the determination of a set of interdependent surfaces. However , the determination of the corresponding ...

I discuss the production of low rank smoothers for d ≥ 1 dimensional data, which can be fitted by regression or penalized regression methods. The smoothers are constructed by a simple transformation and truncation of the basis that arises from the solution of the thinplate spline smoothing problem, and are optimal in the sense that the truncation is designed to result in the minimum possible pe...

This paper describes single point micro incremental forming (SPMIF) applied to the fabrication of meso-scale shell structures. The authors have developed SPMIF without using any die and backing plate for flexible micro forming of miniature 3D products in a range of micro meters to sub-millimeters. A desk-top type of CNC milling machine was constructed as an experimental apparatus. Thin aluminum...

A fast multipole boundary element method (BEM) for solving large-scale thin plate bending problems is presented in this paper. The method is based on the Kirchhoff thin plate bending theory and the biharmonic equation governing the deflection of the plate. First, the direct boundary integral equations and the conventional BEM for thin plate bending problems are reviewed. Second, the complex not...

Recent failure information from research teams in NASA Langley and others has shown that CTOA based fracture models calibrated on large C(T) and M(T) specimens can be transferred successfully to cracked aircraft fuselage structures for the assessment of their residual strength. A major difficulty that could limit the more extensive use of this failure parameter is its experimental measurement e...

In order to simulate the mechanical behavior of large structures assembled from thin composite panels, we propose a coupling technique which substitutes local 3D models for the global plate model in the critical zones where plate modeling is inadequate. The transition from 3D to 2D is based on stress and displacement distributions associated with Saint-Venant problems which are precalculated au...

Fig. 1 a —c. Motion sensitive neurons of the lobula plate of Calliphora erythrocephala stained by intracellular injection of procion yellow. The tracings (a, b) were obtained from 12 «m frontal sections and show the injected cells drawn into a semi-schematic vertical elevation of the brain (lateral structures, indicated by thin lines: lobula plate and medulla; oval structure in the center: oeso...

We present a methodology for the efficient numerical solution of eigenvalue problems of full three-dimensional elasticity for thin elastic structures, such as shells, plates and rods of arbitrary geometry, discretized by the finite element method. Such problems are solved by iterative methods, which, however, are known to suffer from slow convergence or even convergence failure, when the thickn...

Thin plate splines provide smooth interpolation of the given data in two or more dimensions. These are analogous to cubic splines in one dimension. The main objectives of this report is to provide an implementation of the thin plate spine interpolation of data using various efficient methods and to investigate the possibility of using thin plate splines in adaptive optics. In this report, we co...