Fuzzy arithmetic provides a powerful tool to introduce uncertainty into mathematical models. With Zadeh's extension principle, one can obtain a fuzzy-valued extension of any real-valued objective function. An efficient and accurate approach to compute expensive multivariate functions of fuzzy numbers is given by fuzzy arithmetic based on sparse grids. In this paper, we illustrate the general applicability of this new method by computing two dynamic systems subjected to uncertain parameters as well as uncertain initial conditions. The first model consists of a system of delay differential equations simulating the periodic outbreak of a disease. In the second model, we consider a multibody mechanism described by an algebraic differential equation system.

The paper discusses ways of improving the accuracy of numerical calculations for vibrational levels of diatomic molecules close to the dissociation limit or for ultracold collisions, in the framework of a grid representation. In order to avoid the implementation of very large grids, Kokoouline et al. [J. Chem. Phys. 110, 9865 (1999)] have proposed a mapping procedure through introduction of an adaptive coordinate x subjected to the variation of the local de Broglie wavelength as a function of the internuclear distance R. Some unphysical levels ("ghosts") then appear in the vibrational series computed via a mapped Fourier grid representation. In the present work the choice of the basis set is reexamined, and two alternative expansions are discussed: Sine functions and Hardy functions. It is shown that use of a basis set with fixed nodes at both grid ends is efficient to eliminate "ghost" solutions. It is further shown that the Hamiltonian matrix in the sine basis can be calculated very accurately by using an auxiliary basis of cosine functions, overcoming the problems arising from numerical calculation of the Jacobian J(x) of the R-->x coordinate transformation.

The aim of this work is to compare different biaxial specimen geometries and loading conditions concerning their applicability as experimental database for an inverse finite element model updating procedure to identify the material parameters of sheet steel. Therefore, the deformation of the specimens is recorded with an optical, three‐dimensional full‐field deformation measurement system, and the utilised displacement data at the surface of the specimens are calculated via digital image correlation. The numerical material model for the simulations is based on a three‐dimensional, anisotropic elasto‐plastic ansatz and is implemented into a commercial finite element software code. The material parameters that are identified with the different specimen geometries are the hardening variables and the anisotropic plastic values. Based on the identification results, a selection criterion for the evaluation of specimen geometries for the inverse parameter identification is presented.

No abstract