Search results for "tangent"
showing 10 items of 123 documents
Singular systems in dimension 3: Cuspidal case and tangent elliptic flat case
2007
We study two singular systems in R3. The first one is affine in control and we achieve weighted blowings-up to prove that singular trajectories exist and that they are not locally time optimal. The second one is linear in control. The characteristic vector field in sub-Riemannian geometry is generically singular at isolated points in dimension 3. We define a case with symmetries, which we call flat, and we parametrize the sub-Riemannian sphere. This sphere is subanalytic.
Tangency conditions for multivalued mappings
1996
We prove that interiority conditions imply tangency conditions for two multivalued mappings from a topological space into a normed vector space. As a consequence, we obtain the lower semicontinuity of the intersection of two multivalued mappings. An application to the epi-upper semicontinuity of the sum of convex vector-valued mappings is given.
Simplified model for compressive response of RC column footing with square cross-section
2017
Abstract In this paper, a simplified calculus model for the prediction of the compressive response of RC column footing with a square cross-section is presented. As it is well-known RC concrete footing are designed adopting uniform contact pressures on the substrate and assuming a strut and tie model in deep members and a cantilever beam or slab model in flexible members. Deep and flexible members are distinguished in literature only based on the tangent of the angle expressed as the ratio between the depth and the shear span of the footing. In this paper, several subgrade contact pressures distribution for column footings (rigid or soft soils) were considered in developing a mechanical mod…
On the dynamic behavior of piezoelectric active repair by the boundary element method
2011
The dynamic behavior of piezoelectric active repair bonded on cracked structures is analyzed in this article. The boundary element code used to perform the simulations is implemented in the framework of piezoelectricity in order to model the coupling between the elastic and the electric fields, which represents the most important feature of piezoelectric media. The fracture mechanics problem, i.e. the crack, as well as the bonding layer between the host structure and the active patch is modeled by means of the multidomain technique provided with an interface spring model. More particularly, the spring interface model allows considering the bonding layer as a zero-thickness elastic ply char…
Affine varieties and lie algebras of vector fields
1993
In this article, we associate to affine algebraic or local analytic varieties their tangent algebra. This is the Lie algebra of all vector fields on the ambient space which are tangent to the variety. Properties of the relation between varieties and tangent algebras are studied. Being the tangent algebra of some variety is shown to be equivalent to a purely Lie algebra theoretic property of subalgebras of the Lie algebra of all vector fields on the ambient space. This allows to prove that the isomorphism type of the variety is determinde by its tangent algebra.
Analysis of microsphere oblique impact with planar surfaces based on the independent friction-restitution approach
2020
The independent friction restitution closure (IFR) previously applied to describe planar oblique impact of a homogeneous sphere on an infinitely massive rough plane is applied here to microsphere collisions and is extended to describe horizontal launch experiments. The model provides analytical solutions of the motion equations based on a unique set of values of the coefficients of normal and tangential restitution and friction. Comparison with experimental data in literature for the impact of microspheres of diameter <100 mu m yields a satisfactory agreement between experimentation and theory.
Espaces tangents pour les formes auto-similaires
2013
The fractal geometry is a relatively new branch of mathematics that studies complex objects of non-integer dimensions. It finds applications in many branches of science as objects of such complex structure often poses interesting properties. In 1988 Barnsley presented the Iterative Func-tion System (IFS) model that allows modelling complex fractal shapes with only a limited set of contractive transformations. Later many other models were based on the IFS model such as Language-Restricted IFS,Projective IFS, Controlled IFS and Boundary Controlled IFS. The lastto allow modelling complex shapes with control points and specific topol-ogy. These models cover classical geometric models such as B-…
Harmonicity and minimality of oriented distributions
2004
We consider an oriented distribution as a section of the corresponding Grassmann bundle and, by computing the tension of this map for conveniently chosen metrics, we obtain the conditions which the distribution must satisfy in order to be critical for the functionals related to the volume or the energy of the map. We show that the three-dimensional distribution ofS4m+3 tangent to the quaternionic Hopf fibration defines a harmonic map and a minimal immersion and we extend these results to more general situations coming from 3-Sasakian and quaternionic geometry.
Meshless meso-modeling of masonry in the computational homogenization framework
2017
In the present study a multi-scale computational strategy for the analysis of structures made-up of masonry material is presented. The structural macroscopic behavior is obtained making use of the Computational Homogenization (CH) technique based on the solution of the Boundary Value Problem (BVP) of a detailed Unit Cell (UC) chosen at the mesoscale and representative of the heterogeneous material. The attention is focused on those materials that can be regarded as an assembly of units interfaced by adhesive/cohesive joints. Therefore, the smallest UC is composed by the aggregate and the surrounding joints, the former assumed to behave elastically while the latter show an elastoplastic soft…
Extra tension at electrode-nanowire adhesive contacts in nano-electromechanical devices
2017
Abstract We report a strong tangential component of the reaction force at electrode to nanowire adhesive contact which was previously established using electrostatic attraction. The reaction force tangential component absolute value was found to be comparable to or even bigger than the corresponding normal component. This effect is important for understanding of the mechanics of nano-electromechanical devices. Both the experiment and the corresponding theory are presented. Fitting of the obtained analytical solutions to experimental data was used to measure the reaction force acting at the contact for several nanowire-electrode configurations.