Bořek Patzák

Design of object oriented finite element code

Abstract In this paper, a general structure of a recently developed object oriented finite element code is presented. The main reasons which lead to the development of the new general environment for a complex finite element computations are discussed. The principal requirements for new FEM code are formulated. The attention in this paper is put on an overall description of the program design and, particularly, on the description of representations of the general material model–element frame and the analysis module. Finally, computational efficiency of developed environment is compared to existing codes.

Consistent tangent stiffness for nonlocal damage models

Abstract This paper deals with the computational analysis of strain localization problems using nonlocal continuum damage models of the integral type. The general framework for a consistent derivation of the “nonlocal” tangent stiffness is presented. The properties of the tangent stiffness matrix are discussed and the corresponding assembly procedure is described. The quadratic rate of convergence of the Newton–Raphson iteration procedure is demonstrated and the efficiency of the proposed technique is compared to the standard approach based on the secant or elastic stiffness matrices. In this context, performance of direct and iterative solvers for the linearized equilibrium equations is also examined.

Process zone resolution by extended finite elements

A new numerical technique for the computational resolution of highly localized strains in narrow damage process zones of quasibrittle materials is proposed. Objective description of localization due to softening is provided by a nonlocal damage model. The extended finite element method is exploited for an adaptive enrichment of the standard displacement approximation by regularized Heaviside functions that are close to the exact localization mode. An accurate closed-form expression for the width of the enriched zone is derived by localization analysis under uniaxial stress. Numerical examples show that satisfactory results can be obtained even on coarse basic meshes with only a few added degrees of freedom.

Effect of transversal reinforcement in normal and high strength concrete columns

This paper deals with an experimental investigation and numerical simulation of reinforced concrete columns. Behavior of normal and high strength columns is studied with special attention paid to the confinement effects of transversal reinforcement in columns with square cross section. Character of a failure, strengths, ductility and post-peak behavior of columns are observed in experiments and also in numerical solution. Three-dimensional computational model based on the microplane model for concrete was constructed and compared with experimental data. Results of numerical model showed good agreement in many aspects and proved capabilities of the used material model.RésuméCet article traite de la recherche expérimentale d’échantillons de colonnes en béton armé et de leur simulation numérique. Le comportement des colonnes à résistance normale et à haute résistance est étudié avec une attention particulière pour ce qui est des effets du confinement dû aux armatures transversales à section carrée. Le caractère de la rupture, les résistances, la ductilité et le comportement après-pic des colonnes sont observés de façon expérimentale et numérique. Le modèle mathématique tridimensionnel qui prend ses racines dans le modèle microplan pour le béton a été établi et comparé aux données expérimentales. Les résultats du modèle numérique sont en bon accord avec les expériences et témoignent de la grande capacité du modèle utilisé.

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.

Four-Node Quadrilateral Shell Element MITC4

Four-node quadrilateral element MITC4 applicable to both thick and thin shells is presented. The element formulation starts from three-dimensional continuum description degenerated to shell behavior. Shear locking, which is common problem in analysis of thin shells, is overcome by the use of MITC (Mixed Interpolation of Tensorial Components) approach. Element has been implemented into finite element code OOFEM and its performance is demonstrated on Scordelis-Lo shell, a benchmark problem frequently used in the evaluation of shell elements.

Construction of weighted dual graphs of NURBS-based isogeometric meshes

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. 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 aim of this paper is to introduce a new methodology for the construction of a weighted dual graph of a two-dimensional NURBS-based isogeometric mesh that can be decomposed by standard graph-based partitioning approaches.