Abstract-An alternating method, in conjunction with the finite element method and a solution for multiple coplanar elliptical cracks in an intinite solid, is used to determine stress intensity factors for semi-elliptical surface flaws in cylindrical pressure vessels. The solution technique for multiple cracks in an infinite body has recently been developed by the prese.nt authors which implemen...

Problem 1. Infinite Products and Coproducts in Ab. We have seen that finite products and coproducts agree in Ab. However, the same is not true for infinite products and coproducts. Let I be a set and let {Ai}i∈I be a family of abelian groups, each equal to some fixed group A. (a) Show that the set AI := HomSet(I, A) is an abelian group. Furthermore, show that we can think of this group as the i...

The Arnold–Winther element successfully discretizes the Hellinger–Reissner variational formulation of linear elasticity; its development was one key early breakthroughs finite exterior calculus. Despite great utility, it is not available in standard software, because degrees freedom are preserved under Piola push-forward. In this work we apply novel transformation theory recently developed by K...

In the automotive industry, predicting noise during design cycle is a necessary step. Well-known methods exist to answer this issue in low frequency domain. Among these, Finite Element Methods, adapted to closed domains, are quite easy to implement whereas Boundary Element Methods are more adapted to infinite domains, but may induce singularity problems. In this article, the described method, t...

A tournament is acyclically indecomposable if no acyclic autonomous set of vertices has more than one element. We identify twelve infinite acyclically indecomposable tournaments and prove that every infinite acyclically indecomposable tournament contains a subtournament isomorphic to one of these tournaments. The profile of a tournament T is the function φT which counts for each integer n the n...

Finite element meshes are large, richly structured sets whose internal relationships must be visible to diierent parts of a nite element program. This causes software engineerings problems that increase when adaptive mesh reenement and multilevel preconditioners are applied. Even more problems arise when nite element methods have to be implemented for parallel computers since the meshes have to...

In this paper we present error estimates for the finite element approximation of linear elliptic problems in unbounded domains that are outside an obstacle and a semi-infinite strip in the plane. The finite element approximation is formulated on a bounded domain using a nonlocal approximate artificial boundary condition. In fact there is a family of approximate boundary conditions with increasi...

the concept of “infinite essence” that is both philosophically and theologically important, has passed many different evolutions in western history of thought. presocratics has evaluated it in two different ways. anaximender and melissus agree that the principle substance is infinite and divine, but neither absolutly transcendent nor anthropomorphic. the infinite is the fusis in its substantial...