The present paper deals with the volume preserving smoothing of triangular isotropic meshes over three-dimensional surfaces. The adopted approach is based on Laplacian smoothing combining in an alternating manner positive and negative weights in consecutive cycles of the smoothing. Since the aim is to improve the shape of individual elements of the mesh rather than to get rid of a noise, the weights are derived in a very simple way using a "do not harm" concept. The paper also extends the smoothing methodology from meshes on closed surfaces to meshes on open surfaces and discusses how the concept can be applied to meshes over surfaces with sharp features and curvature discontinuities. The performance and capabilities of the presented smoothing approach are demonstrated on several examples. (C) 2016 Civil-Comp Ltd. and Elsevier Ltd. All rights reserved.

This paper describes the application of the particle swarm optimization to the shape optimization of two-dimensional domains described by NURBS (non-uniform rational B-splines) and analyzed using the NURBS-based isogeometric analysis. The regularization of the optimization problem, preventing undesirable clustering of control points of the underlying geometry leading to invalid geometry or parametrization, is achieved by controlling the magnitude of perturbation of design variables within the PSO using a background mesh. This mesh, however, does not have to comply with requirements on a standard (e.g. finite element) computational mesh, as it does not have to follow the exact geometry. Thus construction of such a mesh (Matlab Distmesh tool is utilized) is simple and does not introduce a bottleneck to the whole process. The capabilities and performance of the developed optimization strategy are demonstrated on standard benchmark problems.

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.

Isogeometric analysis has been recently introduced as a viable alternative to the standard, polynomial-based finite element analysis. Similarly to the finite element method, isogeometric solution of complex engineering problems may lead to computationally very demanding analysis, demands of which can be alleviated by performing it in a parallel computing environment. This paper presents how the isogeometric analysis based on NURBS can be parallelized on memory distributed computing platforms. While the actual parallelization of the isogeometric computational code resembles methodologically very much the parallelization of the finite element code, the construction of the appropriate domain decomposition of the isogeometric mesh is rather complicated compared to the partitioning of the finite element mesh. The paper introduces a new methodology, how to construct a weighted dual graph of a two-dimensional NURBS-based isogeometric mesh that can be decomposed by standard graph-based partitioning approaches. The application of the proposed strategy is illustrated on a simple two-dimensional example.

Isogeometric analysis (IGA) has been recently introduced as a viable alternative to the standard, polynomial-based finite element analysis. One of the fundamental performance issues of the isogeometric analysis is the quadrature of individual components of the discretized governing differential equation. The capability of the isogeometric analysis to easily adopt basis functions of high degree together with the (generally) rational form of those basis functions implies that high order numerical quadrature schemes must be employed. This may become computationally prohibitive because the evaluation of the high degree basis functions and/or their derivatives at individual integration points is quite demanding. The situation tends to be critical in three-dimensional space where the total number of integration points can increase dramatically. The aim of this paper is to compare computational efficiency of several numerical quadrature concepts which are nowadays available in the isogeometric analysis. Their performance is assessed on the assembly of stiffness matrix of B-spline based problems with special geometrical arrangement allowing to determine minimum number of integration points leading to exact results.

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.

In the current digital age, it is befitting that complex heterogeneous materials, such as solid propellants, are characterized by digital computational and/or experimental techniques. Of those, microcomputer tomography (micro-CT) and advanced packing algorithms are the most popular for identifying the statistics of multimodal, random, particulate composites. In this work, we develop a procedure for the characterization and reconstruction of periodic unit cells of highly filled, multimodal, particulate composites from a packing algorithm. Rocpack, a particle packing software, is used to generate the solid propellant microstructures, and one-, two-, and three-point probability functions are used to describe their statistical morphology. However, both the experimentally scanned or computationally designed packs are usually nonoptimal in size and likely too big to be fully numerically resolved when complex nonlinear processes, such as combustion, decohesion, matrix tearing, etc., are modeled. Thus, domain reduction techniques, which can reconstruct the optimal periodic unit cell, are important to narrow the problem size while preserving the statistics. The three-dimensional reconstruction is carried out using a parallel augmented simulated annealing algorithm. Then, the resulting cell geometries are discretized, taking into consideration the periodic layout using our master/slave approach implemented into a sophisticated meshing generator T3D. Final discretized geometries show only a small loss of volume fraction. Particulate systems composed of 40 and 70% volume fractions are investigated, and the unit cells are reconstructed such that the statistical correspondence to the original packs is maintained.

This paper describes parallel adaptive framework with dynamic load balancing developed in the frame of the open source finite element method code OOFEM. The parallelization strategy is based on domain decomposition and message passing paradigms. The dynamic load balancing engine is designed to operate on distributed nondedicated parallel computing environments. The paper also briefly comments on other important components of a complete adaptive strategy, namely the error estimator/indicator, projection operator and remeshing. The performance of the proposed strategy is illustrated on the nonlinear fracture analysis of concrete specimen, using damage based material model with nonlocal integral formulation.

We present a theoretical and computational framework for modeling the multiscale constitutive behavior of highly filled elastomers, such as solid propellants and other energetic materials. Special emphasis is placed on the effect of the particle debonding or dewetting process taking place at the microscale and on the macroscopic constitutive response. The microscale is characterized by a periodic unit cell, which contains a set of hard particles (such as ammonium perchlorate for AP-based propellants) dispersed in an elastomeric binder. The unit cell is created using a packing algorithm that treats the particles as spheres or discs, enabling us to generate packs which match the size distribution and volume fraction of actual propellants. A novel technique is introduced to characterize the pack geometry in a way suitable for meshing, allowing for the creation of 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 the complex, heterogeneous stress and strain fields associated, at the microscale, with the nucleation and propagation of damage along the particle–matrix interface, as well as the macroscopic response and mechanical properties of the damaged continuum. Examples involving simple unit cells are presented to illustrate the multiscale algorithm and demonstrate the complexity of the underlying physical processes.

The stereolithography (STL) file format, developed for rapid prototyping industry, became an attractive alternative for surface representation in solid modeling. In this paper, an algorithm for the surface discretization of 3D models in STL format is presented. Initially, a boundary representation is reconstructed from the STL file format using feature recognition. Then a smooth surface is recovered over the original STL grid by adopting the interpolating subdivision procedure. And finally, the recovered surface is subjected to the triangulation accomplished using the advancing front technique operating directly on the surface.

An algorithm for the discretization of parametric 3D surfaces has been extended to the family of discrete surfaces represented by a triangular mesh of arbitrary topology. The limit surface is reconstructed from the mesh using the modified Butterfly scheme which is an interpolating subdivision technique yielding a C1 surface. The recovered surface is discretized directly in the physical space by the advancing front technique, thereby parameterization of the surface is not required. The mesh gradation is controlled by the octree data structure that simultaneously serves as a localization tool for the intersection investigation. Considering the discrete nature of the surface, special attention is paid to the proper implementation of the point-to-surface projection algorithm in order to achieve robustness and reasonable efficiency of the algorithm. The performance of the proposed strategy is presented on a few examples.

In the present paper, an algorithm for the discretization of parametric 3D surfaces has been extended to the family of discrete surfaces represented by stereolithography (STL) grids. The STL file format, developed for the rapid prototyping industry, is an attractive alternative to surface representation in solid modeling. Initially, a boundary representation is constructed from the STL file using feature recognition. Then a smooth surface is recovered over the original STL grid using an interpolating subdivision procedure. Finally, the reconstructed surface is subjected to the triangulation accomplished using the advancing front technique operating directly on the surface. The capability of the proposed methodology is illustrated on an example.

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.

An algorithm for discretization of parametric 3D surfaces has been extended to the family of discrete surfaces represented by a triangular mesh of arbitrary topology. The limit surface is reconstructed from the mesh using the modified Butterfly scheme which is an interpolation subdivision technique yielding a C1 surface. The recovered surface is discretized directly in the physical space by the advancing front technique, thereby parameterization of the surface is not required. The mesh gradation is controlled by the octree data structure that simultaneously serves as a localization tool for the intersection investigation. Considering the discrete nature of the surface, a special attention has to be paid to the proper implementation of the point-to-surface projection algorithm in order to achieve robustness and reasonable efficiency of the algorithm. The performance of the proposed strategy is presented on a few examples.