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- Finite-Elemente-Methode (73) (remove)
Encapsulation-based self-healing concrete (SHC) is the most promising technique for providing a self-healing mechanism to concrete. This is due to its capacity to heal fractures effectively without human interventions, extending the operational life and lowering maintenance costs. The healing mechanism is created by embedding capsules containing the healing agent inside the concrete. The healing agent will be released once the capsules are fractured and the healing occurs in the vicinity of the damaged part. The healing efficiency of the SHC is still not clear and depends on several factors; in the case of microcapsules SHC the fracture of microcapsules is the most important aspect to release the healing agents and hence heal the cracks. This study contributes to verifying the healing efficiency of SHC and the fracture mechanism of the microcapsules. Extended finite element method (XFEM) is a flexible, and powerful discrete crack method that allows crack propagation without the requirement for re-meshing and has been shown high accuracy for modeling fracture in concrete. In this thesis, a computational fracture modeling approach of Encapsulation-based SHC is proposed based on the XFEM and cohesive surface technique (CS) to study the healing efficiency and the potential of fracture and debonding of the microcapsules or the solidified healing agents from the concrete matrix as well. The concrete matrix and a microcapsule shell both are modeled by the XFEM and combined together by CS. The effects of the healed-crack length, the interfacial fracture properties, and microcapsule size on the load carrying capability and fracture pattern of the SHC have been studied. The obtained results are compared to those obtained from the zero thickness cohesive element approach to demonstrate the significant accuracy and the validity of the proposed simulation. The present fracture simulation is developed to study the influence of the capsular clustering on the fracture mechanism by varying the contact surface area of the CS between the microcapsule shell and the concrete matrix. The proposed fracture simulation is expanded to 3D simulations to validate the 2D computational simulations and to estimate the accuracy difference ratio between 2D and 3D simulations. In addition, a proposed design method is developed to design the size of the microcapsules consideration of a sufficient volume of healing agent to heal the expected crack width. This method is based on the configuration of the unit cell (UC), Representative Volume Element (RVE), Periodic Boundary Conditions (PBC), and associated them to the volume fraction (Vf) and the crack width as variables. The proposed microcapsule design is verified through computational fracture simulations.
In this paper we present a theoretical background for a coupled analytical–numerical approach to model a crack propagation process in two-dimensional bounded domains. The goal of the coupled analytical–numerical approach is to obtain the correct solution behaviour near the crack tip by help of the analytical solution constructed by using tools of complex function theory and couple it continuously with the finite element solution in the region far from the singularity. In this way, crack propagation could be modelled without using remeshing. Possible directions of crack growth can be calculated through the minimization of the total energy composed of the potential energy and the dissipated energy based on the energy release rate. Within this setting, an analytical solution of a mixed boundary value problem based on complex analysis and conformal mapping techniques is presented in a circular region containing an arbitrary crack path. More precisely, the linear elastic problem is transformed into a Riemann–Hilbert problem in the unit disk for holomorphic functions. Utilising advantages of the analytical solution in the region near the crack tip, the total energy could be evaluated within short computation times for various crack kink angles and lengths leading to a potentially efficient way of computing the minimization procedure. To this end, the paper presents a general strategy of the new coupled approach for crack propagation modelling. Additionally, we also discuss obstacles in the way of practical realisation of this strategy.
The paper investigates accuracy of deflection predictions made by the finite element package ATENA and design code methods ACI and EC2. Deflections have been calculated for a large number of experimental reinforced concrete beams reported by three investigators. Statistical parameters have been established for each of the technique at different load levels, separately for the beams with small and moderate reinforcement ratio.
For modeling of singular fields of stresses and deformations in elasters with a crack is offered to use of three-dimesional a special finite element. Weak compessible of elasters is taken into account on the basis of threefold approximation of fields of displacements, deformations and function of volume change. At intensive cyclic loading of the elastomer constructions with a crack it is necessary to take into account warming and large deformations at the crack top. The stress-deformed state elasters with a crack is determined from the decision of a nonlinear problem by a modified method Newton-Kantorovich. Account stress intensity factors for a rectangular plate with a various arrangement of a through crack is executed. Process of development of a surface crack and dissipative warming in prismatic a element of shift is investigated.
Development and Analysis of Sparse Matrix Concepts for Finite Element Approximation on general Cells
(2004)
In engineering and computing, the finite element approximation is one of the most well-known computational solution techniques. It is a great tool to find solutions for mechanic, fluid mechanic and ecological problems. Whoever works with the finite element method will need to solve a large system of linear equations. There are different ways to find a solution. One way is to use a matrix decomposition technique such as LU or QR. The other possibility is to use an iterative solution algorithm like Conjugate Gradients, Gauß-Seidel, Multigrid Methods, etc. This paper will focus on iterative solvers and the needed storage techniques...
Die Eisenbahnbrücken des Lehrter Bahnhofs in Berlin - Ein ganzheitliches FE-Berechnungskonzept
(2000)
Der Komplexität moderner Brückenbauwerke scheinen die verwendeten Berechungsmodelle oft nicht angemessen. Tragwerksberechnungen basieren in vielen Fällen noch auf der Vorgehensweise, das Brückenbauwerk in Einzelbauteile zu zerlegen und mit unterschiedlichen Teilmodellen zu behandeln. Das erscheint, auch vor dem Hintergrund ständig wachsender Rechnerleistung, nicht mehr zeitgemäß. Dies gilt zum Beispiel auch für die gängige Praxis, flächenhafte Brückenüberbauten mit Balkenmodellen zu berechnen. Der vorliegende Beitrag stellt ein ganzheitliches Berech-nungskonzept vor, welches auf der Basis eines einzigen FE-Modells die Berechnung des Gesamtbauwerks erlaubt. Damit wird für alle Bauteile neben der Zustandsgrößenberechnung auch die Bemessung von Stahl- und Spannbetonbauteilen bis hin zu Nachweisen wie zur Beschränkung der Rissbreite geführt. Die Anwendung dieses Berechnungskonzeptes wird am Beispiel der Eisenbahnüberführung des neuen Lehrter Bahn-hofs in Berlin gezeigt. Das verwendete FE-Modell umfasst Baugrund, Fundamente, Stahl- bzw. Gußstahlunterkonstruktion sowie den Stahl- bzw. Spannbetonüberbau. Besonderheiten sind unter anderem die Modellierung des plattenbalkenartigen Überbaus durch exzentrische, vorspannbare Schalenelemente und das getrennte Vorhalten von tragwerks- und lastbezogenen Eingabefiles. Damit gelingt die sequentielle Erfassung unterschiedlicher Bettungsmoduli zur Simulation statischer und dynamischer Beanspruchungen, die Berücksichtigung des Anspannens und der Interaktion zwischen vorgespannten Stahlverbänden zur Aufnahme von Horizontallasten sowie die Berücksichtigung unterschiedlicher statischer Systeme bei der Herstellung des Spannbetonüberbaus.
Discrete-continual Finite Element Method of Analysis for Three-dimensional Curvilinear Structures
(2003)
This paper is devoted to discrete-continual finite element method (DCFEM) of analysis for three-dimensional curvilinear structures. Operational and variational formulations of the problem in the ring coordinate system are presented. The discrete-continual design model for structures with constant physical and geometrical parameters in longitudinal direction is offered on the basis of so-called curvilinear discrete-continual finite elements. Element coordinate system, approximation of nodal unknowns, construction of element nodal load vector are under consideration. Element system of differential equations is formulated with use of special generalized block-structured stiffness matrix of discrete-continual finite element. Local differential relations are formulated. Resultant multipoint boundary problem for system of ordinary differential equations is given. Method of analytical solution of multipoint boundary problems in structural analysis is offered as well. Its major peculiarities include universality, computer-oriented algorithm involving theory of distributions, computational stability, optimal conditionality of resultant systems, partial Jordan decomposition of matrix of coefficients, eliminating necessity of calculation of root vectors. Brief information concerning developed software is provided.
Bei komplexen Gründungskonstruktionen sind Planungsfehler durch eine konsistente Modellierung vermeidbar. Manuelle Berechnungsmethoden ermöglichen im allgemeinen ein dreidimensionales Vorgehen nicht. Numerische Berechnungsmethoden, wie z.B. die Finite-Element-Methode, sind ein optimales Werkzeug zur ganzheitlichen Simulation des Problems. Die für die Finite-Element-Analyse notwendige Diskretisierung komplexer Bau- grundstrukturen ist manuell nicht zu bewältigen. Der vorliegende Beitrag zeigt wie ein Finite-Element-Modell automatisch aus einem geotechnischen Modell unter Berücksichtigung der spezifischen Anforderungen der Baugrund-Tragwerk-Struktur und des Bauablaufes erzeugt werden kann. Hierbei wird die Berücksichtigung der geometrischen und der mechanischen Besonderheiten bei der Netzgenerierung dargestellt.
The paper deals with the simulation of the non-linear and time dependent behaviour of complex structures in engineering. Such simulations have to provide high accuracy in the prediction of deformations and stability, by taking into account the long term influences of the non-linear behaviour of the material as well as the large deformation and contact conditions. The limiting factors of the computer simulation are the computer run time and the memory requirement during solving large scale problems. To overcome these problems we use a dynamic-explicit time integration procedure for the solution of the semi-discrete equations of motion, which is very suited for parallel processing. In the paper at first we give a brief review of the theoretical background of the mechanical modelling and the dynamic-explicit technique for the solution of the semi-discrete equations of motion. Then the concept of parallel processing will be discussed . A test example concludes the paper.
Die vorliegende Arbeit beschäftigt sich mit der dynamischen Analyse der Sprottetalbrücke infolge aufgetretener Asphaltschäden. Sie beinhaltet die Erstellung eines FE-Modells, der Darstellung der theoretischen Grundlagen der Dynamik sowie die Auswertung von berechneten Eigenformen und Asphaltspannungen unter Berücksichtigung der derzeit gültigen Normen.