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  • 1
    Electronic Resource
    Electronic Resource
    Homogenization of nonlinearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity (1993)
    Springer
    Archive for rational mechanics and analysis 122 (1993), S. 231-290 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00380256
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  • 2
    Electronic Resource
    Electronic Resource
    On the rigidity of certain surfaces with folds and applications to shell theory (1995)
    Springer
    Archive for rational mechanics and analysis 129 (1995), S. 11-45 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract In the asymptotic theory of thin elastic shells the rigidity of the mid-surface with kinematic boundary conditions plays an important role. Rigidity is understood in the sense of infinitesimal (linearized) rigidity, i.e., the displacements vanish provided the variation of the first fundamental form vanishes. In this case the surface is also called “stiff”, as it cannot undergo pure bendings. A stiff surface is imperfectly stiff or perfectly stiff when the origin respectively does or does not belong to the essential spectrum of the boundary-value problem. These questions are investigated in the framework of Douglis-Nirenberg elliptic systems, with boundary conditions and transmission conditions at the folds. The index properties ensures quasi-stiffness, i.e. stiffness up to a finite number of degrees of freedom. The concept of perfect stiffness is linked with estimates for the rigidity system at an appropriate level of regularity for the data and the solution. It is proved that surfaces with folds are never perfectly stiff. It is also shown that the transmission conditions at the folds contain more conditions than those satisfying the Shapiro-Lopatinskii property. This leads to certain rigidity properties of the folds. Some examples are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00375125
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  • 3
    Electronic Resource
    Electronic Resource
    On the vanishing viscosity limit for acoustic phenomena in a bounded region (1981)
    Springer
    Archive for rational mechanics and analysis 75 (1981), S. 257-268 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The problem of the linearized vibrations of a viscous, barotropic fluid in a bounded vessel is studied under various boundary conditions. It is shown that the essential spectrum is formed by one or two points that tend to infinity as the viscosity coefficients tend to zero. The asymptotics of solutions of the initialboundary value problem as the viscosity coefficients tend to zero is established. Some remarks about the physical properties of the associated sound waves are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00250785
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  • 4
    Electronic Resource
    Electronic Resource
    Post-buckling behavior of a non-linearly hyperelastic thin rod with cross-section invariant under the dihedral group Dn (1985)
    Springer
    Archive for rational mechanics and analysis 89 (1985), S. 307-388 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00250729
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  • 5
    Electronic Resource
    Electronic Resource
    Transport and propagation of a perturbation of a flow of a compressible fluid in a bounded region (1987)
    Springer
    Archive for rational mechanics and analysis 100 (1987), S. 53-81 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00281247
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  • 6
    Electronic Resource
    Electronic Resource
    The essential spectrum of elliptic systems of mixed order (1977)
    Springer
    Mathematische Annalen 227 (1977), S. 247-276 
    Details
    ISSN: 1432-1807
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01361859
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  • 7
    Electronic Resource
    Electronic Resource
    Sui problemi ai limiti per i sistemi lineari ellittici (1965)
    Springer
    Annali di matematica pura ed applicata 69 (1965), S. 207-284 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02414374
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  • 8
    Electronic Resource
    Electronic Resource
    Proprietà di alcuni spazi di funzioni indefinitamente derivabili a valori vettoriali (1967)
    Springer
    Annali di matematica pura ed applicata 76 (1967), S. 203-231 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02412235
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  • 9
    Electronic Resource
    Electronic Resource
    Il profilo alare ad arco di cerchio in flusso transonico continuo senza incidenza (1970)
    Springer
    Annali di matematica pura ed applicata 84 (1970), S. 341-373 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Summary In the present paper it is studied, with direct method on the hodograph plane, the aerodynamic field around thin circular arc aurfoils in asymptotically uniform flow with zero incidence and Mach number M∞〈1. The problem is, first of all, analitically formulated within the limits of small transonic perturbation with some assumption apt to make possible a first approximation treatment. Thus it is reduced to a particular boundary values problem with free boundary, for which an iteraction method for the solution is developed. In the iteraction process the solution of an other boundary values problem with fixed boudary occurs, for which it is given a variational formulation. The fixed boundary values problem is numerically treated by means of the finite differences method. Thus it is obtained a linear equations system which can be solved with the methods usually utilized on Computers.
    Notes: Sunto Nella presente ricerca viene studiato con metodo diretto sul piano odografico il campo aerodinamico attorno a profili alari sottili ad arco di cerchio investiti senza incidenza da una corrente asintoticamente uniforme con numero di Mach M∞〈1. Il problema viene anzitutto formulato in forma analitica nell'ambito delle piccole perturbazioni transoniche effettuando alcune assunzioni atte a renderne possibile una trattazione di prima approssimazione. Esso viene ricondotto ad un particolare problema di valori al contorno con frontiera mobile, di cui si indica un metodo iterativo per la risoluzione. In questo procedimento iterativo interviene in modo essenziale la risoluzione di un altro problema di valori al contorno con frontiera fissa, di cui viene anzitutto data una formulazione variazionale. Succesivamente tale problema con frontiera fissa viene affrontato mediante calcolo numerico col metodo delle differenze finite. Si ottiene così un sistema di equazioni lineari per il quale si adattano i metodi di risoluzione utilizzati usualmente sui calcolatori elettronici.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02413661
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  • 10
    Electronic Resource
    Electronic Resource
    Nonlinear Spherical Caps and Associated Plate and Membrane Problems (1999)
    Springer
    Journal of elasticity 57 (1999), S. 171-200 
    Details
    ISSN: 1573-2681
    Keywords: critical point ; membrane ; nonlinear elasticity ; path-following ; shell ; spherical caps
    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 deals with the existence and multiplicity problem of the equilibrium solutions of an elastic spherical cap within nonlinear strain theory. We pose the problem in the form of a three parameter bifurcation problem, one parameter being related to the load, the others to the geometry. When the geometrical parameters are different from zero, the so-called generic case, we revisit the nonuniqueness results, and explore the solutions in the parameter space. Then we analyze the formal limits as the geometrical parameters tend to zero. When the curvature tends to zero, we obtain from the nonlinear shell a von Kármán plate, a new, although natural, result. When the thickness parameter tends to zero, we get a nonlinear membrane problem. A study of the latter gives infinitely many solutions, and we discuss the construction, shapes, and stability in detail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007678528834
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