Wave cancellation conditions for the double impact of finite duration in an arbitrary structure

Resonance phenomena in impacting systems can be defined as an amplitude increasing during periodically applied impacts. Thewave cancellation phenomenon is defined as application of certain conditions to cancel the wave fully. The double impact system is defined as the application of the first impact with a certain duration τ and then the application of a counter impact in a certain time τ$_{1}$ such that the vibrations caused by the first impact are fully disappearing. In the current contribution this phenomenon is first studied for the simplest 1D bar vibration. The response function is introduced as a characteristic for such a phenomenon and, by studying its properties, it is possible to find both an impact duration time τ and an application time τ$_{1}$ for the counter impact leading to the wave cancellation. The result is generalized for any arbitrary homogeneous linear non-dissipative mechanical structure described by a semi-elliptic operator Lu. The counter impact can be determined in the same way as in the opposite direction. This general result is numerically illustrated for various operators Lu possessing relatively simple analytical solutions: for a simply supported and a clamped Bernoulli beam, for a fixed membrane and for a Kirchhoff plate. Three potential applications are discussed at the end: a set of verification examples for further analysis of time integration numerical schemes with the energy conservation property; straightforward transfer of cancellation conditions for the double impact to any convenient numerical method in mechanics, e.g. finite element method, iso-geometric method etc.; application of the result in engineering design of impacting devices (hammering etc.) in order to prevent recoil

Some remarks on load modeling in nonlinear structural analysis–Statics with large deformations–Consistent treatment of follower load effects and load control

Load modeling in nonlinear statics, particularly incorporating large deformations differs significantly from the treatment in linear analysis. As in structural dynamics masses in a gravity field generate the loading, their location, and their modifications within the deformation process must be considered in a nonlinear simulation. A specific view besides loading by masses is on gas and fluid interaction with structures. In addition, load control using specifically designed algorithms is evaluated with respect to realistic applications. Within the load modeling an unavoidable, however side aspect, is the general discussion about the so-called follower forces and non-conservative loading. As an example of real-world applications, the specifics of inflated rubber dams are presented

Geometrically exact theory for contact interactions

The intuitive understanding of contact bodies is based on the geometry and adjoining surfaces. A powerful approach to solve the contact problem is to take advantage of the geometry of an analyzed object and describe the problem in the best coordinate system. This book is a systematical analysis of geometrical situations leading to contact pairs: suface-to-surface, curve-to-surface, point-to-surface a.s.o. resultingin the corresponding computational algorithms to solve the contact problem

On contact between curves and rigid surfaces – from verification of the euler-eytelwein problem to knots

A general theory for the Curve-To-Curve contact is applied to develop a special contact algorithm between curves and rigid surfaces. In this case contact kinematics are formulated in the local coordinate system attached to the curve, however, contact is defined at integration points of the curve line (Mortar type contact). The corresponding Closest Point Projection (CPP) procedure is used to define then a shortest distance between the integration point on a curve and the rigid surface. For some simple approximations of the rigid surface closed form solutions are possible. Within the finite element implementation the isogeometric approach is used to model curvilinear cables and the rigid surfaces can be defined in general via NURB surface splines. Verification of the finite element algorithm is given using the well-known analytical solution of the Euler-Eytelwein problem – a rope on a cylindrical surface. The original 2D formula is generalized into the 3D case considering an additional parameter H-pitch for the helix. Finally, applications to knot mechanics are shown

Finite element analysis on multi-chamber tensairity-like structures filled with fluid and/or gas

The concept of Tensairity-structures [6] developed by the company Airlight in Biasca, Switzerland, has been known since 2004. The advantages of the airbeams with a compression element and a spiraled cable are essentially their light weight and that such beams can be used for wide span structures. To achieve a further weight reduction Pronk et al [8] proposed to replace the compression element by an additional slim chamber filled with water. Experiments with these multi-chamber beams with and without cables showed a stiffer behavior in bending tests compared to only air filled beams. In the current contribution different tests like - primarily - the bending of multi-chamber beams will be simulated with finite elements. Explicit and implicit finite element simulations with LS-DYNA [7] and FEAP-MeKa [11] respectively will be performed with a special focus on the interaction of structural deformations and the gas/fluid filling in combination with the cables contacting the membranes. The specific features have been implemented in the above codes. The fluid and/or gas filling is replaced by an energetically equivalent load and corresponding stiffness matrix contributions to simulate quasi-static fluid-structure interaction taking the effect of the deformations of the chambers on the fluid/gas filling into account. This approach has already been introduced for fluid-structure interaction problems with large deformations and stability analysis in [1], [2]. For the implicit simulation the cables will be added using special solid-beam finite elements [5]. A new curve-to-surface contact algorithm is developed to model the contact interaction between cables and the deformable shell structure

Quantifying the Density of mmWave NR Deployments for Provisioning Multi-Layer VR Services

The 5G New Radio (NR) technology operating in millimeter wave (mmWave) frequency band is designed for support bandwidth-greedy applications requiring extraordinary rates at the access interface. However, the use of directional antenna radiation patterns, as well as extremely large path losses and blockage phenomenon, requires efficient algorithms to support these services. In this study, we consider the multi-layer virtual reality (VR) service that utilizes multicast capabilities for baseline layer and unicast transmissions for delivering an enhanced experience. By utilizing the tools of stochastic geometry and queuing theory we develop a simple algorithm allowing to estimate the deployment density of mmWave NR base stations (BS) supporting prescribed delivery guarantees. Our numerical results show that the highest gains of utilizing multicast service for distributing base layer is observed for high UE densities. Despite of its simplicity, the proposed multicast group formation scheme operates close to the state-of-the-art algorithms utilizing the widest beams with longest coverage distance in approximately 50-70% of cases when UE density is lambda >= 0.3. Among other parameters, QoS profile and UE density have a profound impact on the required density of NR BSs while the effect of blockers density is non-linear having the greatest impact on strict QoS profiles. Depending on the system and service parameters the required density of NR BSs may vary in the range of 20-250 BS/km(2).publishedVersionPeer reviewe

Geometry and Mechanics

IASS-IACM 2008 Session: Geometry and Mechanics -- Session Organizers: Kai-Uwe BLETZINGER (TU Munich), Fehmi CIRAK (University of Cambridge) -- Keynote Lecture: "Modeling and computation of patient-specific vascular fluid-structure interaction using Isogeometric Analysis" by Yuri BAZILEVS , Victor M. CALO, Thomas J. R. HUGHES (University of Texas at Austin), Yongie ZHANG (Carnegie Mellon University) -- Keynote Lecture: "Optimal shapes of mechanically motivated surfaces" by Kai-Uwe BLETZINGER , Matthias FIRL, Johannes LINHARD, Roland WUCHNER (TU Munich) -- "Subdivision shells for nonsmooth and branching geometries" by Quan LONG, Fehmi CIRAK (University of Cambridge) -- "Water landing analyses with explicit finite element method" by John T. WANG (NASA Langley Research Center) -- "On a geometrically exact contact description for shells: From linear approximations for shells to high-order FEM" by Alexander KONYUKHOV, Karl SCHWEIZERHOF (University of Karlsruhe

Generalized Closest Point Projection Procedures for Contact Analyses: On Existence and Uniqueness for Arbitrary Contact Surfaces

International Conference on Computational Plasticit

Geometrically exact theory for contact interactions

The intuitive understanding of contact bodies is based on the geometry and adjoining surfaces. A powerful approach to solve the contact problem is to take advantage of the geometry of an analyzed object and describe the problem in the best coordinate system. This book is a systematical analysis of geometrical situations leading to contact pairs: suface-to-surface, curve-to-surface, point-to-surface a.s.o. resultingin the corresponding computational algorithms to solve the contact problem