Daniel Rypl

Triangulation of 3D surfaces

A simple generator of graded triangular meshes on spatial surfaces is introduced in this paper. The algorithm is based on the approximation of the surface by tensor product polynomial patches which are uniquely mappable on a planar parametric space. Each of the patches is triangulated separately in its parametric space, using modified advancing front technique allowing for generation of pre-stretched elements, and the obtained triangulation is mapped back onto the original surface. Large effort has been devoted to the treatment of singularities arising on surfaces approximated by degenerated patches.

Object-oriented, parallel finite element framework with dynamic load balancing

The present paper deals with the design and implementation of parallel load-balancing framework in an object-oriented finite element environment. The parallelization strategy is based on domain decomposition and message passing paradigms. The algorithmic and implementation aspects are discussed in detail. Paper also describes components of a complete adaptive strategy, i.e., the error estimator/indicator, projection operator and remeshing. The capabilities and performance of the developed framework are demonstrated on advanced engineering problems, showing the scalability of the implemented algorithm and advantages of dynamic load balancing when used in dedicated and nondedicated environments.

From the finite element analysis to the isogeometric analysis in an object oriented computing environment

During the last decades, the finite element method has become the most powerful tool for structural analysis massively used in practical engineering. However, recently the isogeometric analysis has been introduced as a viable alternative to the standard, polynomial-based finite element analysis. Moreover, it has been shown that it may outperform the classical finite element method in many aspects. This paper presents how the isogeometric analysis can be integrated within an object oriented finite element environment. The class hierarchy and corresponding methods are designed in such a way, that most of the existing functionality of the finite element code is reused. The missing data and algorithms are developed and implemented in such a way that the object oriented features, such as modularity, extensibility, maintainability, and robustness, are fully retained. The performance of the implemented isogeometric analysis methodology is presented on two- and three-dimensional examples.

Object oriented implementation of the T-spline based isogeometric analysis

Isogeometric analysis has been recently introduced as a viable alternative to the standard, polynomial-based finite element analysis. Initially, the isogeometric approach has been developed using the NURBS and although it has been shown that it can outperform the classical finite element method in many aspects, there are several drawbacks, namely related to the handling trimmed geometries and to the refinement of the adopted discretization. These may be overcome by extending the concept of isogeometric analysis to so-called T-splines which are a generalization of NURBS. This paper presents how the isogeometric analysis based on T-spline can be integrated within an object oriented finite element environment. The class hierarchy and corresponding methods are designed in such a way, that most of the existing functionality of the finite element code is reused. The missing data and algorithms are developed and implemented in such a way that the object oriented features are fully retained. The performance of the implemented T-spline based isogeometric analysis methodology is presented on a simple example.

Microplane models: computational aspects and proposed parallel algorithm

This paper discusses microplane models from the computational point of view. The basic introduction to microplane based models will be given. The computational aspects of these models will be discussed in details and an efficient parallel algorithm for explicit time integration will be proposed. The efficiency of the algorithm will be presented.

Parallel explicit finite element dynamics with nonlocal constitutive models

Abstract The present paper deals with the parallelization of an explicit time stepping algorithm in a general finite element environment. Particular attention has been paid to nonlocal constitutive models. A central difference method has been used to discretize the governing equations in time. Modifications of both node-cut and element-cut strategies have been developed to provide an efficient support for nonlocal constitutive models. Efficiency of the proposed approach is demonstrated on different hardware platforms.

Using the spherical harmonic analysis and the advancing front technique for the discretization of 3D aggregate particles

In this paper, an algorithm for the discretization of three-dimensional aggregate particles is presented. The initial description of the particle is assumed in the digital (voxel based) representation obtained (after appropriate processing) from computer tomography or magnetic resonance tomography. A smooth representation of the particle is derived from the digital description using the spherical harmonic analysis. The smooth surface of the aggregate particle is then subjected to the triangulation using the advancing front technique performed directly on the surface in the real space. This boundary mesh then serves as an input for the tetrahedrization, also based on the advancing front technique, of the particle itself and/or of the domain surrounding the particle.

MuPIF - A distributed multi-physics integration tool

This paper presents the design of a multi-physics integration tool with an object-oriented architecture that facilitates the implementation of multi-physics and multi-level simulations assembled from independently developed applications (components). The tool provides high-level support for mutual data exchange between codes, including support for different discretization techniques and specific field transfer operators, being aware of the underlying physical phenomena. Parallel and distributed applications and aspects of the applications are also addressed. Each application is required to implement application and data interfaces, which allow abstract access to solution domains and fields, and provide services for steering individual applications. The Python scripting language is extended by modules representing interfaces to existing codes. The high-level language serves as a glue to tie the modules or components together and to create a specialized application. The capabilities of the tool are demonstrated on two examples that illustrate staggered thermo-mechanical analysis and distributed field mapping.

Multiscale damage modeling of solid propellants: Theory and computational framework

The present work provides a theoretical and computational framework for modeling the macroscopic/microscopic behavior and interfacial decohesion of grains during propellant loading. The micro-scale is characterized by a unit cell, which contains micro-constituents (grains) dispersed in a polymeric blend. We have used a packing algorithm, treating the ammonium perchlorate (AP) as spheres or discs, which enables us to generate packs which match the size distribution and volume fraction of actual propellants. Then a novel technique to characterize the pack geometry suitable for meshing is described and a powerful mesh generator is employed to obtain high quality periodic meshes with refinement zones in the regions of interest. The proposed numerical multiscale framework, based on the mathematical theory of homogenization, is capable of predicting non-homogeneous microfields and damage nucleation and propagation along the particle matrix interface, as well as the macroscopic response and mechanical properties of the damaged continuum. Examples are considered involving simple unit cells in order to illustrate the multiscale algorithm and demonstrate the complexity of the underlying physical processes.

Using the recursive subdivision and the advancing front technique for the discretization of multi-phase microstructures

The present paper deals with the discretization of microstructure initially represented by a digital image obtained from computer tomography or any other similar scanning device. The boundary voxels in the digital representation are identified and then replaced by a boundary triangulation of the similar resolution as the original digital image. This triangulation is then subjected to recursive subdivision to recover a smooth surface of the microstructure which is then retriangulated according to a user specified resolution. Finally, the interior of the microstructure is discretized. The performance of the proposed approach is shown on an example.