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  • 1
    Electronic Resource
    Electronic Resource
    Numerische Stabilitätsanalyse linear und nichtlinear, deformierbarer, parametererregter Schalentragwerke (1989)
    Springer
    Archive of applied mechanics 59 (1989), S. 345-356 
    Details
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Summary The present contribution derives a numerical concept for the stability analysis of linearly and nonlinearly responding shell structures under parametric excitation. Starting from a displacement discretization of the incremental principle of virtual displacements and using Ljapunow's stability definitions, handy stability bounds are presented, especially also for nonlinear fundamental motions. Two of many computed examples demonstrate their applicability; the correctness of the results is checked by properties of line-search evaluated neighbouring motions.
    Notes: Übersicht Im vorliegenden Beitrag wird ein numerisches Lösungskonzept für die Stabilitätsanalyse linear und nichtlinear antwortender Flächentragwerke unter periodischer Erregung vorgestellt. Ausgehend von einer Weggrößendiskretisierung des inkrementellen Prinzips der virtuellen Verschiebungen sowie den von Ljapunow angegebenen Stabilitätsdefinitionen werden einfach handhabbare, numerische Instabilitätsschranken angegeben, insbesondere auch für den Fall nichtlinearer Grundbewegungen. Die für je ein Beispiel ermittelten Lösungen werden durch charakteristische Eigenschaften einer Nachbarbewegung, berechnet mittels bewährter Zeitintegrationsverfahren, verifiziert.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00534064
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  • 2
    Electronic Resource
    Electronic Resource
    Bestmögliche innere Schalengleichungen für schubweiche Werkstoffe unter Berücksichtigung von Dickenänderungen (1993)
    Springer
    Archive of applied mechanics 64 (1993), S. 1-19 
    Details
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Summary Consistent shell theories can be derived in a particular correct manner by linear approximation of conservation laws of a three-dimensional continuum, described as a multi-director-body. In the present paper best interior shell equations-formulated in velocities—are developed, valid for arbitrarily large deformations and rather optional material laws, incorporating shear distorsions and thickness changes. The optimal character of the theory is guaranteed by the derivation process and proven by bounding techniques using tensor norms.
    Notes: Übersicht Konsistente Schalentheorien lassen sich in einer besonders anschaulichen Weise durch lineare Approximation der Erhaltungssätze eines als Multi-Direktor-Körper beschriebenen, dreidimensionalen Kontinuums herleiten. Im vorliegenden Beitrag entstchen auf diesem Wege bestmögliche, in Geschwindigkeiten formulierte innere Schalengleichungen für beliebig große Deformationen und willkürliche, in eine Leistungsaussage einpaßbare Materialgesetze. Dabei finden Schub- und Querdeformationen Berücksichtigung. Der optimale Charakter der Schalentheorie mit gleichen Unschärfen in allen Einzelbeziehungen wird durch den Herleitungsgang sichergestellt und durch Einschrankungen mittels lokaler Tensornormen bewiesen.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00792340
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  • 3
    Electronic Resource
    Electronic Resource
    Allgemeine Schalentheorie beliebiger Werkstoffe und Verformungen (1971)
    Springer
    Archive of applied mechanics 40 (1971), S. 311-326 
    Details
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Summary Using thermodynamic considerations the present paper derives basic equations of thick shells for arbitrary material and large deflections. Heat supply and heat flux is taken into consideration and the shell material owns velocity-damping properties. After several specific transformations a spatial invariance requirement leads to the equations of motion, the wellknown symmetry conditions and general constitutive equations. Finally all equations derived are specified to thin shells by a linear approximation.
    Notes: Übersicht Ausgehend von den beiden Hauptsätzen der Thermodynamik werden die Grundgleichungen eines dicken Schalenkontinuums abgeleitet, wobei beliebige Materialien, Bewegungen, Wärmeflüsse und -quellen Berücksichtigung finden. Der Schalenwerkstoff verfügt außerdem über geschwindigkeitsdämpfende Eigenschaften. Die Anwendung eines Invarianzprinzips führt auf Bewegungsgleichungen, Symmetriebedingungen und Stoffgesetze in bekannter Form, aus denen schließlich durch eine lineare Approximation die entsprechenden Beziehungen für dünne Schalen gewonnen werden.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00533148
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  • 4
    Electronic Resource
    Electronic Resource
    Tensor-orientierte Formulierung nichtlinearer, finiter Schalenelemente (1986)
    Springer
    Archive of applied mechanics 56 (1986), S. 114-129 
    Details
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Summary In accordance with the tensor formulation of geometrically nonlinear shell theories high precision finite displacement models will be developed. They can be applied to arbitrarily curved shell shapes and are especially able to simulate critical and supercritical mechanical responses. The paper describes the derivation of the elements and investigates their convergence behavior and efficiency.
    Notes: Übersicht In unmittelbarer Anlehnung an die Tensorformulierung geometrisch nichtlinearer Flächentrag-werkstheorien werden besonders genaue, finite Weggrößenmodelle hergeleitet. Sie sind für beliebige Schalen-formen einsetzbar und dienen insbesondere zur Simulation kritischer und überkritischer Systemantworten. Der vorliegende Aufsatz beschreibt die Herleitung der Elemente und überprüft deren Konvergenzverhalten und Leistungsfähigkeit.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00537241
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  • 5
    Electronic Resource
    Electronic Resource
    Finite-rotation shell elements via mixed formulation (1992)
    Springer
    Computational mechanics 10 (1992), S. 289-306 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Starting from a tensorial five-parametric finite-rotation shell theory a family of mixed finite elements is developed on the basis of a Reissner-Mindlin type functional. The family developed contains 4-node and 9-node quadrilateral shell elements. In each of them the displacement approximation is combined with various force variable interpolations in order to improve flexibility for numerical applications. The so-called difference vector occurring in the shell theory is expressed in terms of new rotational degrees of freedom which permit a unique determination of this variable in every deformed position. The corresponding constraints are then satisfied at the element level numerically. Due to the underlying theory the numerical models developed are able to predict the physical 2D force variables accurately. Their capability to deal with strongly nonlinear situations is demonstrated by several examples where numerical results due to Kirchhoff-Love type elements are also included for a systematical comparison.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00370095
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  • 6
    Electronic Resource
    Electronic Resource
    Finite element procedures for the nonlinear dynamic stability analysis of arbitrary shell structures (1990)
    Springer
    Computational mechanics 6 (1990), S. 157-166 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The objective is the development of numerical algorithms for the dynamic stability analysis of strongly nonlinear shell structures subjected, in particular, to parametric excitations. The finite-element discretization is achieved by displacement models of high accuracy. The basis for the stability analysis is Ljapunow's first approximation equation obtained from a finite-rotation shell theory by a variational method. The operator formulation used for this purpose shows the mathematical requirements imposed on consistent formulations. In close connection with Floquet's theory, a semi-analytical criterion is finally given for the stability analysis of parametric instability phenomena. The numerical results presented demonstrate the efficiency of the numerical algorithms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00350232
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  • 7
    Electronic Resource
    Electronic Resource
    On progressive damage phenomena of structures (2000)
    Springer
    Computational mechanics 25 (2000), S. 404-412 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract  For more than 50 years, the technology of linear damage processes has been known and mastered. Strong, progressive damage processes have recently been discovered on various types of structures, for which a uniform theory has been unavailable. A common feature of these processes is the wide-band excitation of the dominant forces (ocean waves, storm, traffic), a shift of the structural response spectrum into domains of higher excitation caused by degrading structural stiffness, as well as a damage-controlled self-adaptation phenomenon. Any numerical investigation of progressive damage phenomena should be based on the load- or time-evolution of the global stiffness matrix. The eigenvalues or natural frequencies of this stiffness matrix offer a decision basis regarding the damage-induced change of structural features.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004660050487
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  • 8
    Electronic Resource
    Electronic Resource
    Finite element procedures for parametric resonance phenomena of arbitrary elastic shell structures (1987)
    Springer
    Computational mechanics 2 (1987), S. 89-98 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A purely numerical method for the treatment of instability problems of parametric resonance is presented. The proposed way of solution, which is applicable to all types of structures, is based on the finite element discretization of an incremental variational principle. After the derivation of the theoretical background linear and quadratic eigenvalue problems for the critical excitation-frequencies of undamped and damped systems are presented and numerical procedures for the computation of the instability charts are established. Finally the efficiency of the developed algorithms is demonstrated by means of several shell responses.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00282131
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  • 9
    Electronic Resource
    Electronic Resource
    Dynamic instability analysis of elastic and inelastic shells (1998)
    Springer
    Computational mechanics 21 (1998), S. 48-59 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The present contribution is concerned with dynamic stability investigations of arbitrary structural responses, in particular shell responses. In order to trace such nonlinear fundamental processes, incremental/iterative path-following algorithms are employed to the tangential equation of motion which is derived under special regard of finite rotation shell theories, elasto-plastic material behaviour, and motion-dependent loading. Occuring instabilities can be detected with the help of Lyapunow exponents as generalized concept for the detection of quantitative stability properties. Well known investigation procedures are recognized as special cases of the Lyapunow-exponent-concept for stationary, transient, periodic, and arbitrary solution curves in the phase space. A new numerical procedure for the determination of one-dimensional Lyapunow exponents is introduced to identify critical directions in the solution space for large discretized structures by reduction to relevant manifolds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004660050282
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  • 10
    Electronic Resource
    Electronic Resource
    Stability conditions for non-conservative dynamical systems (1991)
    Springer
    Computational mechanics 8 (1991), S. 145-151 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The present paper treats dynamic instability problems of non-conservative elastic systems. Starting from general equations of motion, the equations of the perturbed motion are derived. The boundedness of the perturbed motions is studied and sufficient conditions for instability and a necessary condition for stability are deduced. These conditions may determine the instability of non-conservative systems and they are expressed in terms of the properties of generalized tangent damping and stiffness matrices of the systems. Thus, they can easily be incorporated with finite element computations of arbitrary structures.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00372684
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