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B-spline Functions (b-spline + function)

Distribution by Scientific Domains
Engineering80%

Selected Abstracts

On optimal income taxation with heterogeneous work preferences

INTERNATIONAL JOURNAL OF ECONOMIC THEORY, Issue 1 2007
Ritva Tarkiainen
C63; H21; H24 This paper considers the problem of optimal income taxation when individuals are assumed to differ with respect to their earnings potential and work preferences. A numerical method for solving this two-dimensional problem has been developed. We assume an additive utility function, and utilitarian social objectives. Rather than solve the first order conditions associated with the problem, we directly compute the best tax function, which can be written in terms of a second order B-spline function. Our findings show that marginal tax rates are higher than might be anticipated, and that very little bunching occurs at the optimum. Our simulation results show that the correlation between taste for work and productivity has a crucial role in determining the extent of redistribution in our model. [source]

Integration of geometric design and mechanical analysis using B-spline functions on surface

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2005
Hee Yuel Roh
Abstract B-spline finite element method which integrates geometric design and mechanical analysis of shell structures is presented. To link geometric design and analysis modules completely, the non-periodic cubic B-spline functions are used for the description of geometry and for the displacement interpolation function in the formulation of an isoparametric B-spline finite element. Non-periodic B-spline functions satisfy Kronecker delta properties at the boundaries of domain intervals and allow the handling of the boundary conditions in a conventional finite element formulation. In addition, in this interpolation, interior supports such as nodes can be introduced in a conventional finite element formulation. In the formulation of the mechanical analysis of shells, a general tensor-based shell element with geometrically exact surface representation is employed. In addition, assumed natural strain fields are proposed to alleviate the locking problems. Various numerical examples are provided to assess the performance of the present B-spline finite element. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Free vibration of sandwich plates with laminated faces

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2002
W. X. Yuan
Description is given of the development of a spline finite strip method for predicting the natural frequencies and modes of conventional rectangular sandwich plates. The faceplates are treated as being classically thin and may be of composite laminated construction. The core is modelled as a three-dimensional body. Finite strip stiffness and mass properties are based on a displacement field which represents eight fundamental through-thickness displacements as a series of products of longitudinal B-spline functions and crosswise Lagrangian or Hermitian polynominal shape functions. The solution procedure utilizes the efficient superstrip concept in conjunction with the extended Sturm sequence-bisection approach. A variety of applications of the developed analysis capability is described which demonstrates the nature of the convergence of the finite strip predictions of natural frequencies and the close comparison of these predictions with available results in the literature, and also the use of the capability in parametric studies. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Natural gradient-projection algorithm for distribution control

OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 5 2009
Zhenning Zhang
Abstract In this paper, we use an information geometric algorithm to solve the distribution control problem. Here, we consider the distribution of the output determined by the control input only. We set up two manifolds that are formed by the B-spline functions and the system output probability density functions, and we call them the B-spline manifold(B) and the system output manifold(M), respectively. Moreover, we call the new designed algorithm natural gradient-projection algorithm. In the natural gradient step, we use natural gradient algorithm to obtain an optimal trajectory of the weight vector on the B-spline manifold from the viewpoint of information geometry. In the projection step, we project the selected points on B onto M. The coordinates of the projections on M give the trajectory of the control input u. Copyright © 2008 John Wiley & Sons, Ltd. [source]