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  • 1
    Electronic Resource
    Electronic Resource
    Stability of an explicit multi-time step integration algorithm for linear structural dynamics equations (1996)
    Springer
    Computational mechanics 18 (1996), S. 236-244 
    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 proof of stability is developed for an explicit multi-time step integration method of the second order differential equations which result from a semidiscretization of the equations of structural dynamics. The proof is applicable to an algorithm that partitions the mesh into subdomains according to nodal groups which are updated with different time steps. The stability of the algorithm is demonstrated by showing that the eigenvalues of the amplification matrices lie within the unit circle and that a pseudo-energy remains constant. Bounds on the stable time steps for the nodal partitions are developed in terms of element frequencies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00369941
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Stability of an explicit multi-time step integration algorithm for linear structural dynamics equations (1996)
    Springer
    Computational mechanics 18 (1996), S. 236-244 
    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 proof of stability is developed for an explicit multi-time step integration method of the second order differential equations which result from a semidiscretization of the equations of structural dynamics. The proof is applicable to an algorithm that partitions the mesh into subdomains according to nodal groups which are updated with different time steps. The stability of the algorithm is demonstrated by showing that the eigenvalues of the amplification matrices lie within the unit circle and that a pseudo-energy remains constant. Bounds on the stable time steps for the nodal partitions are developed in terms of element frequencies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00369941
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    An implicit multi-time step integration method for structural dynamics problems (1998)
    Springer
    Computational mechanics 22 (1998), S. 337-343 
    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 multi-time step integration algorithm is developed based on the trapezoidal rule time integration method for finite element equations of motion. This algorithm uses nodal groups to partition the mesh into subdomains that are updated with different time steps. A␣stability analysis of the method shows that the scheme retains the unconditionally stable behavior of the trapezoidal rule and conserves the same pseudo energy as the parent algorithm. Several numerical examples are used to verify the stability of the method and to investigate the accuracy of the scheme.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004660050365
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    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    Multi-time-step integration using nodal partitioning (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 349-359 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm is presented which integrates different groups of nodes of a finite element mesh with different time steps and different integrators. Since the nodal groups are updated independently no unsymmetric systems need be solved. Stability is demonstrated by showing that an energy norm of the solution decreases after every update if the time step is less than a given critical value. The element eigenvalue inequality theorem is used to give the critical time step in terms of element eigenvalues.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260205
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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