相关论文: Metric Independent Analysis of Second Order Stress…
A geometric analysis of high order stresses in continuum mechanics is presented. Virtual velocity fields take their values in a vector bundle \vbts over the n-dimensional space manifold. A stress field of order k is represented…
The paper considers the formulation of higher-order continuum mechanics on differentiable manifolds devoid of any metric or parallelism structure. For generalized velocities modeled as sections of some vector bundle, a variational kth order…
The energy-based definition provides a viable resolution to the longstanding confusion on the proper definition of $n$-th order rigidity and flexibility in geometric constraint systems. Applying an energy-based local rigidity analysis to…
This paper deals with the problem of describing the vector spaces of divergence-free, natural tensors on a pseudo-Riemannian manifold that are second-order; i.e., that are defined using only second derivatives of the metric. The main result…
The fundamental ideas and tools of the global geometric formulation of stress and hyper-stress theory of continuum mechanics are introduced. The proposed framework is the infinite dimensional counterpart of statics of systems having finite…
We restrict our attention to space-time point pattern data for which we have a single realisation within a finite region. Second-order characteristics are used to analyse the spatio-temporal structure of the underlying point process. In…
For high-order continuum mechanics and classical field theories configurations are modeled as sections of general fiber bundles and generalized velocities are modeled as variations thereof. Smooth stress fields are considered and it is…
The second order tangent bundle $T^{2}M$ of a smooth manifold $M$ consists of the equivalent classes of curves on $M$ that agree up to their acceleration. It is known that in the case of a finite $n$-dimensional manifold $M$, $T^{2}M$…
In a previous paper, field theory in curved space was considered, and a formula that expresses the first order variation of correlation functions with respect to the external metric was postulated. The formula is given as an integral of the…
Rank two momentum tensors, free of mass singularities, are often used for identification and analysis of two and three hadronic jet events. Based on Monte-Carlo generated events, we find that for sufficiently high energies, the tensor…
Classical field theories together with the Lagrangian and Eulerian approaches to continuum mechanics are embraced under a geometric setting of a fiber bundle. The base manifold can be either the body manifold of continuum mechanics, space…
Second-order structured deformations of continua provide an extension of the multiscale geometry of first-order structured deformations by taking into account the effects of submacroscopic bending and curving. We derive here an integral…
This paper presents asymptotic covariance formulae and central limit theorems for geometric functionals, including volume, surface area, and all Minkowski functionals and translation invariant Minkowski tensors as prominent examples, of…
We investigate the existence of coordinate transformations which bring a given vector field on a manifold equipped with an involutive distribution into the form of a second-order differential equation field with parameters. We define…
Let $P$ be a set of points and $L$ a set of lines in the (extended) Euclidean plane, and $I \subseteq P\times L$, where $i =(p,l) \in I$ means that point $p$ and line $l$ are incident. The incidences can be interpreted as quadratic…
The mechanical problem discussed in this paper focuses on the stress state estimation in a composite laminate in the vicinity of a free edge or microcracks. To calculate these stresses, we use two models called Multiparticle Models of…
In this paper we address the vector problem of a 2D half-plane interfacial crack loaded by a general asymmetric distribution of forces acting on its faces. It is shown that the general integral formula for the evaluation of stress intensity…
We derive the evolution equation for the second order curvature perturbation using standard techniques of cosmological perturbation theory. We do this for different definitions of the gauge invariant curvature perturbation, arising from…
This paper deals with iteration stable (STIT) tessellations, and, more generally, with a certain class of tessellations that are infinitely divisible with respect to iteration. They form a new, rich and flexible class of spatio-temporal…
In his work on stress functions Maxwell noted that given a planar truss the internal force distribution may be described by a piecewise linear, $C^0$ continuous version of the Airy stress function. Later Williams and McRobie proposed that…