Object Oriented Finite Element Analysis for Structural Optimization using p-Elements

The optimization of continuous structures requires careful attention to discretization errors. Compared to ordinary low order formulation (h-elements) in conjunction with an adaptive mesh refinement in each optimization step, the use of high order finite elements (so called p-elements) has several advantages. However, compared to the h-method a higher order finite element analysis program poses higher demands from a software engineering point of view. In this article the basics of an object oriented higher order finite element system especially tailored to the use in structural optimization is presented. Besides the design of the system, aspects related to the employed implementation language Java are discussed

Free vibration analysis of curved Bernoulli-Euler beam using isogeometric approach

Isogeometric analysis (IGA) is based on a concept that uses the same base functions for representing both the model geometry and the solution space. The most common base functions used in the IGA are NURBS (Non-Uniform Rational B-Splines) functions for their capability to analytically represent various geometries. In this paper, the IGA is applied in the free vibration analysis of rotation-free plane curved Bernoulli-Euler beam. The stiffness and mass matrices have been developed using basic concepts of continuum mechanics and the principle of virtual work. Geometry of the undeformed and deformed beam is defined using convective coordinates and cross section basis vectors. Results of the free vibration analysis for beam with arbitrary curvature are compared with the results obtained from the conventional finite element method (FEM) software. The significant advantages of the IGA approach over the FEM are shown and discussed

A FRAMEWORK FOR THE INTERACTIVE VISUALIZATION OF ENGINEERING MODELS

Interactive visualization based on 3D computer graphics nowadays is an indispensable part of any simulation software used in engineering. Nevertheless, the implementation of such visualization software components is often avoided in research projects because it is a challenging and potentially time consuming task. In this contribution, a novel Java framework for the interactive visualization of engineering models is introduced. It supports the task of implementing engineering visualization software by providing adequate program logic as well as high level classes for the visual representation of entities typical for engineering models. The presented framework is built on top of the open source visualization toolkit VTK. In VTK, a visualization model is established by connecting several filter objects in a so called visualization pipeline. Although designing and implementing a good pipeline layout is demanding, VTK does not support the reuse of pipeline layouts directly. Our framework tailors VTK to engineering applications on two levels. On the first level it adds new – engineering model specific – filter classes to VTK. On the second level, ready made pipeline layouts for certain aspects of engineering models are provided. For instance there is a pipeline class for one-dimensional elements like trusses and beams that is capable of showing the elements along with deformations and member forces. In order to facilitate the implementation of a graphical user interface (GUI) for each pipeline class, there exists a reusable Java Swing GUI component that allows the user to configure the appearance of the visualization model. Because of the flexible structure, the framework can be easily adapted and extended to new problem domains. Currently it is used in (i) an object-oriented p-version finite element code for design optimization, (ii) an agent based monitoring system for dam structures and (iii) the simulation of destruction processes by controlled explosives based on multibody dynamics. Application examples from all three domains illustrates that the approach presented is powerful as well as versatile

Object Oriented Finite Element Analysis for Structural Optimization using p-Elements

The optimization of continuous structures requires careful attention to discretization errors. Compared to ordinary low order formulation (h-elements) in conjunction with an adaptive mesh refinement in each optimization step, the use of high order finite elements (so called p-elements) has several advantages. However, compared to the h-method a higher order finite element analysis program poses higher demands from a software engineering point of view. In this article the basics of an object oriented higher order finite element system especially tailored to the use in structural optimization is presented. Besides the design of the system, aspects related to the employed implementation language Java are discussed

Distributed computing of failure probabilities for structures in civil engineering

In this contribution the software design and implementation of an analysis server for the computation of failure probabilities in structural engineering is presented. The structures considered are described in terms of an equivalent Finite Element model, the stochastic properties, like e.g. the scatter of the material behavior or the incoming load, are represented using suitable random variables. Within the software framework, a Client-Server-Architecture has been implemented, employing the middleware CORBA for the communication between the distributed modules. The analysis server offers the possibility to compute failure probabilities for stochastically defined structures. Therefore, several different approximation (FORM, SORM) and simulation methods (Monte Carlo Simulation and Importance Sampling) have been implemented. This paper closes in showing several examples computed on the analysis server

LIFETIME-ORIENTED OPTIMIZATION OF BRIDGE TIE RODS EXPOSED TO VORTEX-INDUCED ACROSS-WIND VIBRATIONS

In recent years, damages in welded connections plates of vertical tie rods of several arched steel bridges have been reported. These damages are due to fatigue caused by wind-induced vibrations. In the present study, such phenomena are examined, and the corresponding lifetime of a reference bridge in Münster-Hiltrup, Germany, is estimated, based on the actual shape of the connection plate. Also, the results obtained are compared to the expected lifetime of a connection plate, whose geometry has been optimized separately. The structural optimization, focussing on the shape of the cut at the hanger ends, has been carried out using evolution strategies. The oscillation amplitudes have been computed by means of the Newmark-Wilson time-step method, using an appropriate load model, which has been validated by on-site experiments on the selected reference bridge. Corresponding stress-amplitudes are evaluated by multiplying the oscillation amplitudes with a stress concentration factor. This factor has been computed on the basis of a finite element model of the system "hanger-welding-connection plate", applying solid elements, according to the notch stress approach. The damage estimation takes into account the stochastics of the exciting wind process, as well as the stochastics of the material parameters (fatigue strength) given in terms of Woehler-curves. The shape optimization results in a substantial increase of the estimated hanger lifetime. The comparison of the lifetimes of the bulk plate and of the welding revealed that, in the optimized structure, the welding, being the most sensitive part in the original structure, shows much more resistance against potential damages than the bulk material

Optimierung druckbeanspruchter Stabtragwerke unter Berücksichtigung geometrischer Imperfektionen

Die vorliegende Arbeit befasst sich mit der Entwicklung eines Optimierungsmodells für druckbeanspruchte Stabtragwerke. Bei der Optimierung derartiger Strukturen ist die Berücksichtigung geometrischer Imperfektionen zur realitätsnahen Erfassung des Tragverhaltens zwingend notwendig. Im Optimierungsmodell wird das Tragsystem durch ein NURBS-basiertes Geometriemodell beschrieben. In dieses eingebunden ist ein Imperfektionsmodell, in dem die geometrischen Imperfektionen durch ein Zufallsfeld dargestellt werden. Die spektrale Zerlegung der Kovarianzmatrix des Zufallsfeldes ermöglicht es, die Imperfektionsform aus einer Linearkombination deterministischer Basisvektoren mit zufälligen Amplituden zu bestimmen. Die im Tragwerk vorhandenen Unsicherheiten werden mit einem konvexen Modell erfasst. Dieser Ansatz führt auf ein zweistufiges Optimierungsverfahren, bei dem in jedem Iterationsschritt die ungünstigste Imperfektionsform aus der Lösung eines Anti-Optimierungsproblems ermittelt wird

Seismic exploration in tunneling using full waveform inversion with a frequency domain model

With the knowledge of the geology in front of a tunnel, the excavation process can be optimized to avoid damage at the tunnel boring machine and settlements on the surface. Therefore, dwell times can be decreased and additional expenses can be avoided. Transmitted seismic waves will be spread, reflected and refracted due to geological changes. By utilizing geophones, the seismic waves will be captured and information about the geological structure in front of the tunnel can be extracted from the measured seismograms using e.g. the concept of full waveform inversion. A frequency domain model has been employed to demonstrate the potential of full waveform inversion for seismic reconnaissance in a tunnel environment. The success of the inversion procedure depends strongly on the positions of the utilized sender and receiver stations, the chosen initial material parameter distribution, and on the selected frequency groups for the inversion. Further challenges are an accurate representation of the reflecting surfaces and the application of absorbing borders to oppress reflections from the artificial boundaries, which delimit the analyzed domain. The results of the performed full waveform inversion for synthetic models of a 3D tunnel configuration with different disturbances ahead of the front tunnel face will be discussed. Additionally, the influence of different locations of the sender and receiver stations will be analyzed