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1
Content available Model order reduction of Mikota’s vibration chain including damping effects by means of proper orthogonal decomposition
Weber W. E., Zastrau B. W.
Journal of Theoretical and Applied Mechanics
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2018
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Vol. 56 nr 2
511--521
EN
In engineering disciplines, both in scientific and practical applications, systems with a tremendous number of degrees of freedom occur. Hence, there is a need for reducing the computational effort in investigating these systems. If the system behaviour has to be calculated for many time instances and/or load scenarios, the need for efficient calculations further increases. Model order reduction is a common procedure in order to cope with such large systems. The aim of model order reduction is to reduce the (computational) effort in solving the given task while still keeping main features of the respective system. One approach of model order reduction uses the proper orthogonal decomposition. This approach is applied to Mikota’s vibration chain, a linear vibration chain with remarkable properties, where two cases of an undamped and a damped structure are investigated.
2
Content available Analytical description of frc subjected to transient loads
Weber W., Zastrau B. W.
Journal of Theoretical and Applied Mechanics
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2013
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Vol. 51 nr 1
183--194
EN
In many real-world applications, such as in civil engineering, non-periodic composite materials are used, whose dynamical behaviour is still not deeply understood, especially concerning its wave scattering properties. In this paper, the scattering of a transient non-plane elastic SH wave by an arbitrary arrangement of identical multi-layered and thus inhomogeneous obstacles is investigated. The obstacles are embedded in a homogeneous, isotropic, and linear elastic matrix of infinite extent. The solution procedure is analytical and will then be evaluated numerically for investigating a small material clipping of a real-world problem.
PL
W rzeczywistych obiektach, np. w inżynierii lądowej, zastosowanie znajdują materiały kompozytowe o strukturze nieperiodycznej. Dynamika takich elementów nadal pozostaje niedostatecznie rozpoznana, zwłaszcza w kontekście właściwości rozpraszania fal. W prezentowanej pracy omówiono problem rozpraszania przejściowych, niepłaskich fal sprężystości spolaryzowanych poziomo (typu SH) w dowolnym układzie identycznych, wielowarstwowych, i przez to niejednorodnych, ekranów tłumiących. Założono, że ekrany te zostały wbudowane w jednorodną, izotropową, liniowo-sprężystą osnowę o nieskończenie wielkich rozmiarach. Zaproponowano analityczne rozwiązanie problemu, które posłuży symulacjom numerycznym efektu słabego obcinania fali w materiale wybranego obiektu rzeczywistego.
3
Content available remote On the Characteristics of Non-Material Boundary Conditions Using the Example of a Vibrating String
Franze A., Zastrau B. W.
Machine Dynamics Research
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2011
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Vol. 35, No. 4
11-31
EN
In this paper the possibilities and limits of solving equations of motion with non-material boundary conditions are investigated. Therefore the system of equations for the nonstationary motion of a three-dimensional body is derived. To overcome the time dependency of the boundary conditions an Arbitrary Lagrangean Eulerian (ALE) kinematics is used. In combination with the introduced operator notation a very clear formulation of the system of the equations of motion is derived. The model of a perfect flexible and inextensible string is used as an illustration. In this case analytical solutions are given in a closed form for an example with one non-material boundary condition. This allows studying the characteristics of such boundary conditions.
4
Content available Non-plane wave scattering from a single eccentric circular inclusion - Part I: SH waves
Weber W., Zastrau B. W.
Journal of Theoretical and Applied Mechanics
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2011
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Vol. 49 nr 4
1183-1201
EN
In this contribution, an analytical formalism for investigating the scattering behaviour of a single multi-layered inclusion in a homogeneous isotropic matrix under the influence of non-plane elastic SH waves is derived. Herein, the inclusion is assumed to have a circular shape with its layers being eccentrically arranged. Numerical examples are performed with Textile Reinforced Concrete, a new building material in civil engineering. Within these investigations both shielding and amplification of SH waves is shown.
PL
W pracy przedstawiono analityczny formalizm zagadnienia rozpraszania fal na pojedynczym, wielowarstwowymwtrąceniu materiałowym w izotropowej, jednorodnej strukturze osnowy poddanej działaniu niepłaskich fal spolaryzowanych w płaszczyźnie poziomej (fale typu SH). Założono, że wtrącenie ma kołowy kształt, a jego warstwy są rozmieszczone mimośrodowo. Zamieszczono rezultaty symulacji numerycznych na przykładzie nowego materiału budowlanego, jakim jest beton wzmacniany tekstyliami. Pokazano efekt ekranowania i wzmacniania fal SH w takiej strukturze.
5
Content available remote On SH Wave Scattering in TRC. Pt. 1, Concentric Elliptical Inclusion
Weber W., Zastrau B. W.
Machine Dynamics Problems
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2009
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Vol. 33, No. 2
105-118
EN
An exact analytical solution for the scattering of antiplane elastic waves by a layered elastic elliptical cylinder is derived. The solution and its degenerate cases are compared with other models, e.g. the scattering due to circular cylindrical scatterers. The effects of the geometrical properties of the interphase are studied. The calculations are performed for material properties as they occur with textile reinforced concrete (TRC), a new building material in civil engineering which is therefore introduced first.
6
Content available remote Finite Element Modelling of Wheel and Rail in Rolling Contact
Damme S., Zastrau B. W.
Machine Dynamics Problems
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2004
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Vol. 28, No. 1
57-65
EN
The evaluation of the contact patch as well as the distribution of stress and strain in rolling contact requires a geometrically and materially nonlinear approach. The paper gives an overview over the theoretical background of the arbitrary Lagrangian-Eulerian formulation of the dynamics of rolling bodies. Contact formulations for dynamic contact conditions are developed using a velocity oriented approach. The transcription into the Finite Element Method, temporarily limited to an elastic material law, is given. Numerical examples for three dimensional simulations demonstrate the applicability of the developed program package.
7
Content available Plane contact problems with partial slip for rough half-space
Pauk V., Zastrau B. W.
Journal of Theoretical and Applied Mechanics
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2004
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Vol. 42 nr 1
107-124
EN
Plane contact problems with the partial slip in the contact area are considered in the paper. To make the problems more realistic, the deformation of roughness of the contacting boundary is involved. The Shatayerman model of roughness is generalized on the case of tangential problems. The problems are treated by the boundary integral method. Examples of the contact of a flat rigid punch and a rigid cylinder with an elastic half-space involving boundary imperfections are studied. The effects of roughness parameters on the distribution of normal and shearing tractions as well as on the stic-slip transition are investigated.
PL
Praca dotyczy zagadnień kontaktowych uwzględniających powstawanie poślizgów pomiędzy powierzchniami styku. Dodatkowo zakłada się, że te powierzchnie są chropowate. Rozważa się dwie podstawowe geometrie stempla: stempel o płaskiej podstawie oraz stempel walcowy. Do rozwiązania zagadnień kontaktowych stosuje się metodę równań całkowych. Ujawniono wpływ chropowatości na rozwiązania zagadnień kontaktowych.
8
Content available On surface-related shell theories for the numerical simulation of contact problems
Schlebusch R., Matheas J., Zastrau B. W.
Journal of Theoretical and Applied Mechanics
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2003
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Vol. 41 nr 3
623-642
EN
This paper deals with a surface-related shell theory and its conversion into the finite element method for the investigation of composites and contact problems. In particular, composites made of a textile reinforced concrete are examined for the strengthening of existing shell structures. The interaction between the existing structure and the strenghening layer is considered as a contact problem involving adhesion.
PL
W pracy omówiono problem powierzchniowej teorii powłok i jej konwersji do metody elementów skończonych w kontekście badań kompozytów i zagadnienia kontaktowego. W szczególności zajęto się kompozytami osnową cementową wzmacnianą materiałem tekstylnym jako komponentem nośnych konstrukcji powłokowych. Uwagę skoncentrowano na oddziaływaniu, jakie zachodzi pomiędzy strukturą nośną i wzmacniającą w takich powłokach. Przedstawiono analizę tego oddziaływania jako zagadnienia kontaktowego z włączaniem zjawiska adhezji.
9
Content available remote On the Avoidance of POISSON Thickness Locking in Surface-Related Shell Theories by an Extension of the EAS Method
Schlebusch R., Matheas J., Zastrau B. W.
Machine Dynamics Problems
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2002
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Vol. 26, No. 4
101-114
EN
The enhanced assumed strain (EAS) method as introduced by Simo and Rifai (1990), Buchter and Ramm (1992), Buchter et al. (1994) represents a very efficient concept for the prevention and reduction of locking phenomena. The utilization of the EAS method to prevent POISSON thickness locking in the context of a 6-parameter shell formulation without rotational degrees of freedom and the middle surface as reference surface is a well known procedure in literature, Bischoff (1999), Klinkel (2000). In this contribution the EAS method is applied in a shell theory that uses an outer surface as the reference surface and is therefore called a surface-related shell theory. In contrast to the middle surface shell theory the EAS concept to prevent POISSON thickness locking in connection with surface-related formulations evokes a coupling of the membrane force and moment tensor, if the orthogonality condition is evaluated. Two additional concepts against locking phenomena are introduced: the assumed natural strain (ANS) concept, cp. Simo and Hughes (1986), and the discrete shear gap (DSG) concept, cp Bletzinger et al. (1998). The combination of the aforementioned concepts leads to an efficient finite volume shell element that is demonstrated in numerical examples.
10
Content available remote General Aspects of Rolling Contact Mechanics for Tire-Road/Terrain and Wheel-Rail Application
Zastrau B. W., Damme S.
Machine Dynamics Problems
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2001
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Vol. 25, No. 3/4
153-167
EN
The development of contact theories and numerical formula for various applications is a field, which expands rapidly. This publication focuses on the rolling contact problem both for tire-road and wheel-rail contact. For the tire-road application a central problem is the modelling of the composite structure of the tire under internal pressure and axle load and the rolling on soft soil. In the wheel-rail case the contact area is much smaller and therefore much more emphasis is aid on the treatment of material changes, wear and creep phenomena. Several approaches are discussed in detail; ideas about damage mechanisms finish the article.
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