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  • Articles  (11)
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  • Solid mechanics  (11)
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  • Articles  (11)
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  • Springer  (11)
  • American Geophysical Union
  • American Institute of Physics (AIP)
  • American Physical Society
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  • 2000-2004
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  • 1
    Electronic Resource
    Electronic Resource
    Application of ‘Operational Quadrature Methods’ in Time Domain Boundary Element Methods (1997)
    Springer
    Meccanica 32 (1997), S. 179-186 
    Details
    ISSN: 1572-9648
    Keywords: BEM ; Time domain ; Multistep method ; Transform methods ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The usual time domain Boundary Element Method (BEM) contains fundamentalsolutions which are convoluted with time-dependent boundary data andintegrated over the boundary surface. Here, a new approach for theevaluation of the convolution integrals, the so-called ’OperationalQuadrature Methods‘ developed by Lubich, is presented. In thisformulation, the convolution integral is numerically approximated by aquadrature formula whose weights are determined using the Laplacetransform of the fundamental solution and a linear multisep method. Tostudy the behaviour of the method, the numerical convolution of afundamental solution with a unit step function is compared with theanalytical result. Then, a time domain Boundary Element formulationapplying the ’Operational Quadrature Methods‘ is derived. For thisformulation only the fundamental solutions in Laplace domain arenecessary. The properties of the new formulation are studied with anumerical example.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004258205435
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  • 2
    Electronic Resource
    Electronic Resource
    Boundary Element Calculation of Transient Response of Viscoelastic Solids Based on Inverse Transformation (1997)
    Springer
    Meccanica 32 (1997), S. 171-178 
    Details
    ISSN: 1572-9648
    Keywords: BEM ; Viscoelasticity ; Time domain ; Transform methods ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Mixed boundary value problems of solid mechanics are treated by numericalsolutions of Boundary Integral Equations (BIE) in time domain with theBoundary Element Method (BEM) thus reducing the spatial problem dimensionby one. Viscoelastic constitutive behaviour is implemented by means of aLaplace transform technique based on an elastic--viscoelasticcorrespondence principle. The concept of fractional differintegrationgeneralizes conventional constitutive equations and provides improvedcurve fitting of measured material response with fewer parameters. As theimplementation of viscoelasticity is provided in each time step in theLaplace domain, efficient algorithms for the inverse transformation intime domain are needed. This is why the performance of adapted algorithmsby Talbot, Durbin and Crump are compared. The impact responseof a base plate bonded on a viscoelastic soil halfspace is discussed as anumerical example. Viscous forces increase the velocities of surface wavepropagation and cause attenuation in addition to the so called geometricaldamping by radiation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004206221365
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  • 3
    Electronic Resource
    Electronic Resource
    Laplace Transform and New Mathematical Theory of Viscoelasticity (1997)
    Springer
    Meccanica 32 (1997), S. 187-195 
    Details
    ISSN: 1572-9648
    Keywords: Generalized variational principles ; Spectral theory ; Error estimates ; Transform methods ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract In this paper generalized variational principles in thesense of the Laplace transform for viscoelastic problems arederived. Then mathematical theory of viscoelasticity ingeneralized Hardy spaces and in weighted anisotropic Sobolevspaces and spectral theory of corresponding non-selfadjointoperators is elaborated. Finally the Laplace transform--FEMfor numerical analysis of time-dependent problems of themathematical physics is proposed and analysed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004210322274
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  • 4
    Electronic Resource
    Electronic Resource
    Linear Dynamical Identification: An Integral Transform seen as a Complex Wavelet Transform (1997)
    Springer
    Meccanica 32 (1997), S. 215-222 
    Details
    ISSN: 1572-9648
    Keywords: Identification ; Modal analysis ; Wavelets ; Transform methods ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract This paper presents a technique that allows the direct linearidentification of frequency response functions from the computation ofa weighted integral transform. This transform allows toemphasize the influence of the poles and zeros of the frequencyresponse functions its formation is based on the Cauchy--Weierstrass theorem. It isthen shown that this transform is directly linked to a complex wavelettransform. This representation with a wavelet transform provides abetter understanding of the amplification effects of the weightedintegral transform and allows the singularities analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004274709070
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  • 5
    Electronic Resource
    Electronic Resource
    Application of a Direct Stiffness Method to Wave Propagation in Multiphase Poroelastic Media (1997)
    Springer
    Meccanica 32 (1997), S. 205-214 
    Details
    ISSN: 1572-9648
    Keywords: Wave propagation ; Poroelasticity ; Unsaturated media ; Transform methods ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract In this paper, it is demonstrated how a direct stiffness method for wavepropagation in multilayered saturated poroelastic media, based on integraltransform techniques, can be modified to account for a small amount of gasin the pores. Unsaturated media with small gas fractions can be treatedusing Smeulders‘ extension of Biot‘s poroelastic theory. The effect of thepresence of gas bubbles on the fluid bulk modulus and the dispersioncharacteristics of a water-saturated sand of Mol is demonstrated. Thedirect stiffness method is illustrated with a numerical example wheretransient wave propagation in a dry, saturated and unsaturated halfspaceis considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004214523182
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  • 6
    Electronic Resource
    Electronic Resource
    Phase-Transition Fronts in Deformable Ferromagnets (1997)
    Springer
    Meccanica 32 (1997), S. 347-362 
    Details
    ISSN: 1572-9648
    Keywords: Magnetoelasticity ; Phase transition ; Ferromagnets ; Electromagneto-solid mechanics ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The notions of material inhomogeneity and balance of pseudomomentum are exploited to construct a thermodynamical framework for propagating coherent phase-transition fronts in ferromagnetic thermoelastic materials. This analysis results in the proposal of thermodynamically admissible criteria of progress for the fronts. Magnetoelastic domain walls may be viewed as special cases of such fronts.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004227307949
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  • 7
    Electronic Resource
    Electronic Resource
    Plane Sources of Waves in the Presence of Magnetic Field (1997)
    Springer
    Meccanica 32 (1997), S. 231-239 
    Details
    ISSN: 1572-9648
    Keywords: Magnetoelastic interaction ; Wave propagation ; Concentrated forces ; Transform method ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract In this paper the generation of harmonic waves in an elastic magneticmaterial, which is a perfect conductor of electricity, isconsidered. It has been assumed that an infinite body is subjected tothe action of an initially constant magnetic fieldH = (H,0,0) and in the plane ax+by=0 acts a source ofdistortion. It has been shown that this source may produce bothtransverse and longitudinal waves and each of them consists of two parts,which propagate with different speeds. The amplitudes and speeds in dependence on theangle between the direction of wave propagation and the magnetic fieldintensity H have been discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004226825908
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  • 8
    Electronic Resource
    Electronic Resource
    Fourier Transform in Bounded Domains (1997)
    Springer
    Meccanica 32 (1997), S. 197-204 
    Details
    ISSN: 1572-9648
    Keywords: Functional analysis ; Fourier transform ; Finite elements ; Transform methods ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The functional analysis, the concept of distributionsu ∈ $$\mathcal{D}\prime $$ in the sense of Schwartz [7] andtheir extension given by Gel‘fand and Shilov [5]to ultradistributions u ∈ $$\mathcal{Z}\prime $$ ,enables us to find by the means of the Fourier transform a second’language‘ to characterize physical behaviour. Almost any expressionwith physical meaning can be transformed, even if it isformulated in domains with complicated boundaries and evenif it is not integrable. Numerical procedures in the transformed space can bedeveloped in analogy to those well known in engineeringmechanics like the methods of Finite or BoundaryElements (FEM or BEM). Basis of the approaches presentedhere is the analytical representation of characteristicdistribution of a domain and the theorem of Parseval whichstates the invariance of energy in respect to thetransformation. In addition, the concept of thecharacteristic distribution leads to a very simplederivation of the Green-Gauss formulas fundamental for theBoundary or Finite Elements (e.g. [6]).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004262406344
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  • 9
    Electronic Resource
    Electronic Resource
    The Application of Special Transform Methods derived from the Laplace Transform (1997)
    Springer
    Meccanica 32 (1997), S. 241-249 
    Details
    ISSN: 1572-9648
    Keywords: Laplace transform ; Delta-transform ; Parameter identification ; Transform method ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The problem of realtime measurement, control and parameter identificationyields to numerical problems as processors with finite word length areused. The nature of these problems is caused in the mapping character of thez-transform which is normally applied. New transformmethods are introduced which have the feature of reduced sensitivityagainst inaccuracies of coefficients.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004278809978
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  • 10
    Electronic Resource
    Electronic Resource
    Unified Approach and Techniques to Performance of Mellin Convolution and Related Integral Transforms in Relaxation Experiments (1997)
    Springer
    Meccanica 32 (1997), S. 251-258 
    Details
    ISSN: 1572-9648
    Keywords: Logarithmic sampling ; Digital filters ; Relaxation measurements ; Transform method ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract A performance of direct and inverse integral transforms withkernels, depending on the division or product of arguments isconsidered for the study of linear viscoelastic behaviour ofsolid materials. An approach based on digital filteringlogarithmically sampled relaxation measurement data is developedfor carrying out the transforms. Examples of performingHeaviside-Carson sine transform and an inherently ill-conditionedinversion for determining relaxation spectrum are represented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004230926817
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  • 11
    Electronic Resource
    Electronic Resource
    Wavelet Analysis of Structures: Statics, Dynamics and Damage Identification (1997)
    Springer
    Meccanica 32 (1997), S. 223-230 
    Details
    ISSN: 1572-9648
    Keywords: Wavelet transform ; Adaptive methods ; Structural dynamics ; Transform methods ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Applications of the wavelet transform in solid mechanics are presented herein. The analysis problem is addressed first where the objective is to derive an adaptive wavelet-based method for the static and dynamic analysis of structures. This is done via a collocation scheme. The damage identification problem is investigated next making use of the space-localized properties of the wavelet transform: the regularity of the solution is detected by looking at the amplitude of the coefficients of the wavelet decomposition of the response. Open problems are finally outlined that will be the object of future work.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s11012-004-3200-5
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