Česká společnost pro mechaniku – odborná skupina Počítačová mechanika a Ústav termomechaniky AV ČR, v.v.i. pořádají cyklus přednášek při příležitosti návštěvy prof. M. Rashida, University of California, Davis, USA v Ústavu termomechaniky AV ČR, v.v.i. Přednášky se konají v Ústavu termomechaniky (posluchárna B), Dolejškova 5, Praha 8 (mapa) se začátkem vždy v 10 hodin.

Program přednášek

 
Finite Element Investigation of the Elastic-Plastic Response Underneath Various Indentors and its Application in Ni-based Alloys Indentation Processes

Zbyněk Hrubý

Stress and strain distribution underneath various types of indentors – spherical, conical, and Berkovich – can be provided by the finite element method. In the presented work, indentation of isotropic aluminium is introduced as a validation and verification benchmark problem, in which plasticity and contact algorithms and confronted with experimental results. The knowledge obtained in this way passes on to the real-life indentation processes involving orthotropic materials such as FCC metals (Ni-based alloys) in the context of nonlinear continuum and finite strain elasto-plasticity, including homogenization approach on the material microscale. The ABAQUS and an in-house FE-code were used in simulations.

Dispersion Error of Finite Element Discretizations in Elastic Wave Propagation

Radek Kolman

The spatial discretization of elastic continuum by finite element method (FEM) introduces dispersion errors to numerical solutions of stress wave propagation. When these propagating phenomena are modeled by FEM the speed of a single harmonic wave depends on its frequency and thus a wave packet is distorted. Moreover, the oscillations near the sharp wavefront in FE solution (called Gibb’s effect) appears. For higher order Lagrangian finite elements (FEs) there are the optical modes in the spectrum resulting in spurious oscillations of stress and velocity distributions near the theoretical sharp wavefront. Furthermore, the high mode behaviour of classical finite elements is divergent with order of approximation of a field of displacements.
In seismology the spectral finite elements appeared recently. Spectral finite elements are of h-type finite elements, where nodes have special positions along the elements corresponding to the numerical quadrature schemes, but the displacements along element are approximated by Lagrangian interpolation polynomials. The Legendre and Chebyshev higher order spectral elements are popular due to their small dispersion and anisotropy errors.
The modern approach to FEM presents isogeometric analysis (IGA). This numerical method uses spline basic functions as shape functions. For example, Bézier representation, B-spline, NURBS (non-uniform rational B-spline), T-spline and others are used for spatial discretization. IGA approach shows very good frequency and dispersion properties due to the smooth approximation of a displacement field. Therefore, the high mode behaviour of B-spline FEM is convergent with polynomial order of approximation. This approach has an advantage that the geometry and approximation of the field of unknown quantities is prescribed by the same technique. Another benefit is that the approximation is smooth with high order of continuity againts Lagrangian C0 FEs.
In this presentation, the classical Lagrangian FEs, Legendre and Chebyshev spectral FEs, hierarchical Legendre and hierarchical Fourier FEs and B-spline FEs will be tested in an one-dimensional elastic wave propagation with respect to the time and spatial dispersion properties. Further, results of the time and spatial dispersion analysis for bilinear and serendipity 8-node plane FEs will be presented in details.