Constrained Minimization Of Incomplete
Quadratic Functions And Its Applications
Author(s)
Q. Zheng & R. J. Gu
Abstract
In an ordinary minimization problem, the quadratic function contains both
quadratic and linear terms. Through minimization, a system of linear equations
is yielded. The right-hand side vector of such a system is normally a known
input. In a special type of elasticity problem in which coerced deformation of an
elastic body is sought, the applied load becomes unknown. In other words, the
quadratic function does not have a linear term. The objective function has two
quadratic terms, and the minimization is conducted to satisfy some constraints.
In another application where the amount of springback of a stamped metal is to
be determined, the applied force giving the metal the least strain energy is
sought. In this paper, the mathematical formulation as well as the approach to
solve the problems is presented. Several numerical examples are presented.
Keywords: constrained minimization, quadratic, coerced deformation,
springback, minimum strain energy, Lagrange multipliers.
1 Introduction
In some disciplines such as finding the displacements of a deformable elastic
object, a solution xi is sought by finding the minimum of the following quadratic
function.
i x i b j x i x ij a i x U += 2
1 ) ( . (1)
Keywords
constrained minimization, quadratic, coerced deformation,
springback, minimum strain energy, Lagrange multipliers.
Related Book
Other papers in this volume
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