4,316 research outputs found
Qualitative Analysis of Polycycles in Filippov Systems
In this paper, we are concerned about the qualitative behaviour of planar
Filippov systems around some typical minimal sets, namely, polycycles. In the
smooth context, a polycycle is a simple closed curve composed by a collection
of singularities and regular orbits, inducing a first return map. Here, this
concept is extended to Filippov systems by allowing typical singularities lying
on the switching manifold. Our main goal consists in developing a method to
investigate the unfolding of polycycles in Filippov systems. In addition, we
applied this method to describe bifurcation diagrams of Filippov systems around
certain polycycles
An improved return-mapping scheme for nonsmooth yield surfaces: PART I - the Haigh-Westergaard coordinates
The paper is devoted to the numerical solution of elastoplastic constitutive
initial value problems. An improved form of the implicit return-mapping scheme
for nonsmooth yield surfaces is proposed that systematically builds on a
subdifferential formulation of the flow rule. The main advantage of this
approach is that the treatment of singular points, such as apices or edges at
which the flow direction is multivalued involves only a uniquely defined set of
non-linear equations, similarly to smooth yield surfaces. This paper (PART I)
is focused on isotropic models containing: yield surfaces with one or two
apices (singular points) laying on the hydrostatic axis; plastic
pseudo-potentials that are independent of the Lode angle; nonlinear
isotropic hardening (optionally). It is shown that for some models the improved
integration scheme also enables to a priori decide about a type of the return
and investigate existence, uniqueness and semismoothness of discretized
constitutive operators in implicit form. Further, the semismooth Newton method
is introduced to solve incremental boundary-value problems. The paper also
contains numerical examples related to slope stability with available Matlab
implementation.Comment: 25 pages, 10 figure
On a global implicit function theorem for locally Lipschitz maps via nonsmooth critical point theory
We prove a non-smooth generalization of the global implicit function theorem.
More precisely we use the non-smooth local implicit function theorem and the
non-smooth critical point theory in order to prove a non-smooth global implicit
function theorem for locally Lipschitz functions. A comparison between several
global inversion theorems is discussed
Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems
The present article presents a summarizing view at differential-algebraic
equations (DAEs) and analyzes how new application fields and corresponding
mathematical models lead to innovations both in theory and in numerical
analysis for this problem class. Recent numerical methods for nonsmooth
dynamical systems subject to unilateral contact and friction illustrate the
topicality of this development.Comment: Preprint of Book Chapte
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