Lars-Erik Andersson

A quasistatic frictional problem with normal compliance

A friction and contact problem will be considered for an elastic solid body, which under the influence of volume and surface forces is in contact with a rigid foundation

Existence results for quasistatic contact problems with Coulomb friction

Abstract. We prove the existence of a solution for an elastic frictional, quasistatic, contact problem with a Signorini non-penetration condition and a local Coulomb friction law. The problem is formulated as a time-dependent variational problem and is solved by the aid of an established shifting technique used to obtain increased regularity at the contact surface. The analysis is carried out by the aid of auxiliary problems involving regularized friction terms and a so-called normal compliance penalization technique. \par

An algorithm for computing constrained smoothing spline functions

SummaryThe problem of computing constrained spline functions, both for ideal data and noisy data, is considered. Two types of constriints are treated, namely convexity and convexity together with monotonity. A characterization result for constrained smoothing splines is derived. Based on this result a Newton-type algorithm is defined for computing the constrained spline function. Thereby it is possible to apply the constraints over a whole interval rather than at a discrete set of points. Results from numerical experiments are included.

Selfintersection of composite curves and surfaces

Abstract This paper provides computationally tractable conditions to determine whether a composite spline curve or patch selfintersects, according to a definition that includes the important limiting cases of cusps, singularities, and tangential intersections of adjacent components. These results follow upon our exposition of necessary and sufficient conditions to preclude such selfintersections. The paper includes a numerical example illustrating the results, and discusses an important application, namely, guaranteeing that a finite curvilinear simplicial complex in R 3 , made up of properly-joined parametric patches, will retain its original topological form when its control points are perturbed.

Polyhedral perturbations that preserve topological form

Abstract The idea, that we are willing to accept variation in an object but that we insist it should retain its original topological form, has powerful intuitive appeal, and the concept appears in many applied fields. Some of the most important of these are tolerancing and metrology, solid modeling, engineering design, finite element analysis, surface reconstruction, computer graphics, path planning in robotics, fairing procedures, image analysis, and medical imaging. In this paper we focus on the field of tolerancing and metrology. The requirement that two objects or sets should have the same topological form requires a precise definition. We specify “same topological form” to mean that there exists a “space homeomorphism” from R 3 onto R 3 that carries a nominal object S onto another design object. In general, establishing the existence of such space homeomorphisms can be considerably more difficult than demonstrating classical topological equivalence by a homeomorphism. In the special case when the boundary of S is a polyhedral two-sphere in R 3 , one of the authors has previously given a simple sufficient condition for the existence of a space homeomorphism mapping S onto another design object. This paper presents an analogous sufficient condition for the case when S is a finite polyhedron in R 3 . The result relies upon a triangulation of the boundary and upon a dependent parameter that specifies the maximum size of permissible perturbations of the vertices of the polyhedron.

Criteria for copositive matrices using simplices and barycentric coordinates

Abstract We present criteria for verifying the copositivity of an n × n matrix, given that all its principal submatrices of order n − 1 are copositive. For n = 4, 5 necessary and sufficient conditions for copositivity are given, based on the sign distribution of the off-diagonal elements of a single row. Here it is only assumed that one principal submatrix is copositive.

Interpolation and approximation by monotone cubic splines

Abstract We study the reconstruction of a function defined on the real line from given, possibly noisy, data values and given shape constraints. Based on two abstract minimization problems characterization results are given for interpolation and approximation (in the euclidean norm) under monotonicity constraints. We derive from these results Newton-type algorithms for the computation of the monotone spline approximant.

EQUIVALENCE OF TOPOLOGICAL FORM FOR CURVILINEAR GEOMETRIC OBJECTS

Given a curvilinear geometric object in R3, made up of properly-joined parametric patches defined in terms of control points, it is of interest to know under what conditions the object will retain its original topological form when the control points are perturbed. For example, the patches might be triangular BΘzier surface patches, and the geometric object may represent the boundary of a solid in a solid-modeling application. In this paper we give sufficient conditions guaranteeing that topological form is preserved by an ambient isotopy. The main conditions to be satisfied are that the original object should be continuously perturbed in a way that introduces no self-intersections of any patch, and such that the patches remain properly joined. The patches need only have C0 continuity along the boundaries joining adjacent patches. The results apply directly to most surface modeling schemes, and they are of interest in several areas of application.

A Constrained Procrustes Problem

The following constrained matrix problem is studied. Find the matrix

Am algorithm for constrained interpolation

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