Examples of PDEs all whose points are characteristic

Let π : FM ! M be the bundle of linear frames of a manifold M. A basis Lijk , j < k, of diffeomorphism invariant Lagrangians on J1 (FM) was determined in [J. Muñoz Masqué, M. E. Rosado, Invariant variational problems on linear frame bundles, J. Phys. A35 (2002) 2013-2036]. The notion of a characteristic hypersurface for an arbitrary first-order PDE system on an ar- bitrary bred manifold π : P → M, is introduced and for the systems dened by the Euler-Lagrange equations of Lijk every hypersurface is shown to be characteristic. The Euler-Lagrange equations of the natural basis of Lagrangian densities Lijk on the bundle of linear frames of a manifold M which are invariant under diffeomorphisms, are shown to be an underdetermined PDEs systems such that every hypersurface of M is characteristic for such equations. This explains why these systems cannot be written in the Cauchy-Kowaleska form, although they are known to be formally integrable by using the tools of geometric theory of partial differential equations, see [J. Muñoz Masqué, M. E. Rosado, Integrability of the eld equations of invariant variational problems on linear frame bundles, J. Geom. Phys. 49 (2004), 119-155]

Elastoplastic consolidation at finite strain. Part 2: finite element implementation and numerical examples

A mathematical model for finite strain elastoplastic consolidation of fully saturated soil media is implemented into a finite element program. The algorithmic treatment of finite strain elastoplasticity for the solid phase is based on multiplicative decomposition and is coupled with the algorithm for fluid flow via the Kirchhoff pore water pressure. A two-field mixed finite element formulation is employed in which the nodal solid displacements and the nodal pore water pressures are coupled via the linear momentum and mass balance equations. The constitutive model for the solid phase is represented by modified Cam—Clay theory formulated in the Kirchhoff principal stress space, and return mapping is carried out in the strain space defined by the invariants of the elastic logarithmic principal stretches. The constitutive model for fluid flow is represented by a generalized Darcy's law formulated with respect to the current configuration. The finite element model is fully amenable to exact linearization. Numerical examples with and without finite deformation effects are presented to demonstrate the impact of geometric nonlinearity on the predicted responses. The paper concludes with an assessment of the performance of the finite element consolidation model with respect to accuracy and numerical stability.

Surface fitting in geomorphology - examples for regular-shaped volcanic landforms

In nature, several types of landforms have simple shapes: as they evolve they tend to take on an ideal, simple geometric form such as a cone, an ellipsoid or a paraboloid. Volcanic landforms are possibly the best examples of this ?ideal? geometry, since they develop as regular surface features due to the point-like (circular) or fissure-like (linear) manifestation of volcanic activity. In this paper, we present a geomorphometric method of fitting the ?ideal? surface onto the real surface of regular-shaped volcanoes through a number of case studies (Mt. Mayon, Mt. Somma, Mt. Semeru, and Mt. Cameroon). Volcanoes with circular, as well as elliptical, symmetry are addressed. For the best surface fit, we use the minimization library MINUIT which is made freely available by the CERN (European Organization for Nuclear Research). This library enables us to handle all the available surface data (every point of the digital elevation model) in a one-step, half-automated way regardless of the size of the dataset, and to consider simultaneously all the relevant parameters of the selected problem, such as the position of the center of the edifice, apex height, and cone slope, thanks to the highly performing adopted procedure. Fitting the geometric surface, along with calculating the related error, demonstrates the twofold advantage of the method. Firstly, we can determine quantitatively to what extent a given volcanic landform is regular, i.e. how much it follows an expected regular shape. Deviations from the ideal shape due to degradation (e.g. sector collapse and normal erosion) can be used in erosion rate calculations. Secondly, if we have a degraded volcanic landform, whose geometry is not clear, this method of surface fitting reconstructs the original shape with the maximum precision. Obviously, in addition to volcanic landforms, this method is also capable of constraining the shapes of other regular surface features such as aeolian, glacial or periglacial landforms.

Some examples of the simultaneous use of closed-form and numerical solutions in shell structural analysis

The computational advantages of the use of different approaches -numerical and analytical ones- to the analysis of different parts of the same shell structure are discussed. Examples of large size problems that can be reduced to those more suitable to be handled by a personal related axisyrometric finite elements, local unaxisymmetric shells, geometric quasi-regular shells, infinite elements and homogenization techniques are described