Approximate Fitting of a Circular Arc When Two Points Are Known

The task of approximating points with circular arcs is performed in many applications, such as polyline compression, noise filtering, and feature recognition. However, the development of algorithms that perform a significant amount of circular arcs fitting requires an efficient way of fitting circular arcs with complexity O(1). The elegant solution to this task based on an eigenvector problem for a square nonsymmetrical matrix is described in [1]. For the compression algorithm described in [2], it is necessary to solve this task when two points on the arc are known. This paper describes a different approach to efficiently fitting the arcs and solves the task when one or two points are known.Comment: 15 pages, 4 figures, extended abstract published at the conferenc

A kinematically exact finite element formulation of planar elastic-plastic frames

A finite element formulation of finite deformation static analysis of plane elastic-plastic frames subjected to static loads is presented, in which the only function to be interpolated is the rotation of the centroid axis of the beam. One of the advantages of such a formulation is that the problem of the field-consistency does not arise. Exact non-linear kinematic relationships of the finite-strain beam theory are used, which assume the Bernoulli hypothesis of plane cross-sections. Finite displacements and rotations as well as finite extensional and bending strains are accounted for. The effects of shear strains and non-conservative loads are at present neglected, yet they can simply be incorporated in the formulation. Because the potential energy of internal forces does not exist with elastic-plastic material, the principle of virtual work is introduced as the basis of the finite element formulation. A generalized principle of virtual work is proposed in which the displacements, rotation, extensional and bending strains, and the Lagrangian multipliers are independent variables. By exploiting the special structure of the equations of the problem, the displacements, the strains and the multipliers are eliminated from the generalized principle of virtual work. A novel principle is obtained in which the rotation becomes the only function to be approximated in its finite element implementation. It is shown that (N-1)-point numerical integration must be employed in conjunction with N-node interpolation polynomials for the rotation, and the Lobatto rule is recommended. Regarding the integration over the cross-section, it is demonstrated by numerical examples that, due to discontinuous integrands, no integration order defined as `computationally efficient yet accurate enough' could be suggested. The theoretical findings and a nice performance of the derived finite elements are illustrated by numerical examples

A kinematically exact finite element formulation of elastic-plastic curved beams

A finite element, large displacement formulation of static elastic-plastic analysis of slender arbitrarily curved planar beams is presented. Non-conservative and dynamic loads are sit present not included. The Bernoulli hypothesis of plane cross-sections is assumed and the effect of hear strains is neglected. Exact non-linear kinematic equations of curved beams, derived by Reissner are incorporated into;a generalized principle of virtual work through Lagrangian multipliers. The only function that has to be interpolated in the finite element implementation is the rotation of the centroid axis of a beam. This is an important advantage over other classical displacement approaches since the field consistency problem and related locking phenomena do not arise. Numerical examples, comprising elastic and elastic-plastic, curved and straight beams, at large displacements and rotations, show very nice computational and accuracy characteristics of the present family of finite elements. The comparisons with other published results very clearly show the superior performance of the present elements. (C) 1998 Elsevier Science Ltd. All rights reserved

Condition number analysis and preconditioning of the finite cell method

The (Isogeometric) Finite Cell Method - in which a domain is immersed in a structured background mesh - suffers from conditioning problems when cells with small volume fractions occur. In this contribution, we establish a rigorous scaling relation between the condition number of (I)FCM system matrices and the smallest cell volume fraction. Ill-conditioning stems either from basis functions being small on cells with small volume fractions, or from basis functions being nearly linearly dependent on such cells. Based on these two sources of ill-conditioning, an algebraic preconditioning technique is developed, which is referred to as Symmetric Incomplete Permuted Inverse Cholesky (SIPIC). A detailed numerical investigation of the effectivity of the SIPIC preconditioner in improving (I)FCM condition numbers and in improving the convergence speed and accuracy of iterative solvers is presented for the Poisson problem and for two- and three-dimensional problems in linear elasticity, in which Nitche's method is applied in either the normal or tangential direction. The accuracy of the preconditioned iterative solver enables mesh convergence studies of the finite cell method

3D modeling of the vane test on a power-law cement paste by means of the proper generalized decomposition

The effective modeling of the flow of fresh concrete materials in settings such as that of the vane test is a challenging process that is the object of ongoing research. Previous works modeled concrete and cement pastes as solids subjected to yielding or as Bingham or power-law fluids, both in two or three dimensions [1, 2]. Of the existing models, those implementing power-law fluids in three dimensions carry the best predictive ability considering the typically heterogeneous composition of concrete suspensions and the relatively complex three-dimensional features of their flows. In this work, we model the vane test in a power-law cement paste using the Proper Generalized Decomposition (PGD). In this framework, the three-dimensional problem is solved as a sequence of 2D × 1D problems, thus alleviating the curse of dimensionality. This choice is supported by experience from previous works using the PGD to simulate Non-Newtonian behavior using iterative resolutions [3, 4]. It is also particularly useful in addressing the inverse problem corresponding to the identification of the material properties of cement pastes from experimental data, as this requires many direct resolutions of the forward problem. The use of the PGD is also appealing because the model parameters can be introduced as extra coordinates of the problem [5]