Multi-scale Modelling for Structures and Composites

Numerous applications of rod structures in civil engineering, aircraft and spacecraft confirm the importance of the topic. On the other hand the majority of books on structural mechanics use some simplifying hypotheses; these hypotheses do not allow to consider some important effects, for instance the boundary layer effects near the points of junction of rods. So the question concerning the limits of applicability of structural mechanics hypotheses and the possibilities of their refinement arise. In this connection the asymptotic analysis of equations of mathematical physics, the equations of elasticity in rod structures (without these hypotheses and simplifying assumptions being imposed) is undertaken in the present book. Moreover, a lot of modern structures are made of composite materials and therefore the material of the rods is not homogeneous. This inhomogeneity of the material can generate some unexpected effects. These effects are analysed in this book. The methods of multi-scale modelling are presented by the homogenization, multi-level asymptotic analysis and the domain decomposition. These methods give an access to a new class of hybrid models combining macroscopic description with "microscopic zooms".

Content Level » Research

Related subjects » Dynamical Systems & Differential Equations - Mathematics - Mechanics

TABLE OF CONTENTS
From the contents

Introduction: Basic Notions and Methods.- Heterogeneous rods.- Heterogeneous Plate.- Finite Rod Structures.- Lattice Structures.- The Multi-Scale Domain Decomposition.- References. Subject Index.

Theory of Matrix Structural Analysis

Prediction of Ground Motion and Loss Scenarios for Selected Infrastructure Systems in European Urban Environments

The report is intended to make earthquake engineers familiar with the main methods and computational tools needed for developing scenarios of earthquake ground motions and of ensuing damage to representative urban Infrastructure Systems (IS), as well as with illustrative examples of application to cities in Europe and neighbouring countries. The material illustrated is the outcome of the work carried out in LESSLOSS Sub-Project SP11, devoted to the title subject. Of main concern are the water and natural gas distribution networks and the sewage networks, because these are, with the transportation network, by far the most extensive IS in cities and, especially the first one, often the most vulnerable. Also, emphasis is placed more on the tools for achieving a scenario and on their application, rather than on the economic loss evaluation. As a partial justification of the belated development and interest in seismic IS damage, it is recalled that destructive earthquakes of recent decades in Europe did not cause large scale damage to IS. In addition to describing tools for the practical construction of damage scenarios for IS, the report also highlights some innovative research trends in the field, especially the methods leading to the estimation of pipeline damage on the basis of the peak ground strains generated by the propagation of seismic waves, which in turn needs the support of advanced 2D or 3D wave propagation modelling.
The main sections of the report are devoted to:
- Calculation of seismic ground motions in an area, both of advanced and simplified engineering level, with applications for Thessaloniki and Düzce (Sect 2);
- Outline of the buried pipelines response during earthquakes, illustrating the chief elements at play on the side of the seismic loading effects and typical damage (Sect. 3);
- Vulnerability representations for IS components, mostly those consisting of buried pipelines (Sect. 4);
- Typical features of IS inventories, with examples (Sect 5);
- Damage evaluation tools at urban scenario and single pipeline level (Sect. 6);
- Damage scenario applications for Thessaloniki and Düzce (Sect 7);
- Conclusions.

Earthquake Disaster Scenario Predictions and Loss Modelling for Urban Areas

The overall aim of Sub-Project 10 (Earthquake disaster scenario predictions and loss modelling for urban areas) has been to create a tool, based on state-of-the-art loss modelling software, to provide strong, quantified statements about the benefits of a range of possible mitigation actions, in order to support decision-making by urban authorities for seismic risk mitigation strategies. A further larger aim has been to contribute to a seismic risk mitigation policy for future implementation at European level. Among the European cities for which loss estimation studies have been carried out are Istanbul, Lisbon and Thessaloniki, and tools, using GIS mapping, have been developed by research teams in each of these cities; these were made available for further development to examine mitigation strategies within SP10. Related research studies – on ground motion estimation, on the assessment of human casualties, and on the evaluation of uncertainty have been carried out by other research teams across Europe which includes INGV, UCAM and USUR respectively. In all three of the cities, a common general approach to loss modelling has been adopted which includes representing the earthquake hazard as a set of alternative ground motion scenarios (typically those with an expected recurrence periods of 50 and 500 years), and applying the ground motion over a target area of known population and building stock. Losses have then been estimated for this target area in terms of levels of building damage and human casualties expected both in the existing state of the target area, and after certain selected potential mitigation actions have been carried out. This has been done in each case using building stock classifications and vulnerability data specific to the particular city concerned. In each case the scope of the proposed mitigation action has been described, and its expected benefit in terms of reduced losses and human casualties has been determined with some preliminary assessment of uncertainty.

Probabilistic Methods for Seismic Assessment of Existing Structures

This self-contained document provides a presentation and illustration of two methods (one based on non-linear static analysis, the other on non-linear time-history analysis) for probabilistic seismic risk assessment of structures. The presented methods belong to a class which has been under development (mainly in the US) since more than a decade, and it is now firmly established and gaining wide international acceptance. The principal appeal of these methods is that they require only a limited background in probability and statistics. While they are presently directly usable for the assessment of existing structures, their extension for direct design purposes is currently under way. In order to facilitate the use of these methods the type and amount of information required for their application is also illustrated in this document. In particular, one chapter introduces the probabilistic representation, and evaluation, of the seismic hazard (PSHA) and the issue of selection and scaling of recorded ground motions for the purpose of dynamic analysis. A further chapter gives an overview of the most recent research aimed at developing models for the capacity (strength or deformability) of structural members and connections/joints in RC and steel structures. A detailed presentation of several case-studies illustrating the two approaches completes the document.

Guidelines for Displacement-based Design of Buildings and Bridges

Displacement-based seismic design has now come of age, especially for buildings. This report attempts to contribute to it, by focusing on special subjects which are crucial for its further advancement. It is divided in two Parts: one for buildings and another for bridges. Both parts have a chapter on the estimation of displacement and deformation demands and another on component force and deformation capacities.
For buildings, the part on analysis for displacement and deformation demands evaluates nonlinear analysis methods and the corresponding modelling at various degrees of sophistication, on the basis of experimental results (including identification of model parameters affecting reliability of deformation predictions) and compares nonlinear dynamic to linear analyses (static or modal) for irregular in plan buildings. It covers also soil- structure interaction in 3D, including uplift. It concludes with a description of the latest advances in adaptive pushover analysis for irregular buildings. Tools for the estimation of displacement and deformation demands are given, in the form of effective elastic stiffness of concrete members for use in linear analyses emulating nonlinear ones and of ductility-dependent equivalent damping. The chapter on component force and deformation capacities proposes acceptance and design criteria in terms of deformations at various performance levels, for concrete members in uni- or bi-directional cyclic loading.
The Part on bridges starts with an overview of displacement-based design methodologies for them, including evaluation of iterative procedures and proposals for the design of bridge piers directly on the basis of displacement and deformation demands, without analysis iterations. The chapter on estimation of displacement and deformation demands includes nonlinear analysis (static or dynamic), as well as the latest advances in adaptive pushover analysis for bridges. It also uses test results and numerical approaches to develop tools for the analysis, e.g., the secant-to-yield stiffness and the equivalent damping of concrete piers. The chapter on component force and deformation capacities focuses on concrete piers, developing simple rules for the estimation of their flexure- or shear-controlled cyclic ultimate deformation, on the basis of test results and numerical analyses. It also has a part devoted to seismic isolators, dealing with the evaluation of their displacement and re-centring capacity and the effect of exceedance of isolator displacement capacity on the bridge seismic response. The effect of the variation of the axial force of friction pendulum isolators on the response of the isolated bridge is also studied.

Pile Design and Installation Using Ultimate Design Methods

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