Discrete Computational Mechanics of Masonry Structures (CISM International Centre for Mechanical Sciences, 609)

Preface
Contents
1 Discrete Computational Mechanics of Masonry Structures
	1.1 Masonry as a Structural Material
	1.2 Discrete Computation Methods
		1.2.1 Limit State Analysis
		1.2.2 Graphic Statics and Computerised Graphic Statics
		1.2.3 Methods Based on Energy Principles
		1.2.4 The Discrete Element Method
		1.2.5 Block-By-Block Models Based on Stiffness Matrix
	References
2 Graphical Statics
	2.1 Fundaments of Graphical Statics
	2.2 Traditional Methods and Their Novel Versions for Masonry Arches and Domes
		2.2.1 Coulomb’s Method of “Maximis et Minimis”
		2.2.2 The Thrust Line Method for the Assessment of Masonry Arches
		2.2.3 A Focus on the Méry Method
		2.2.4 The True ‘Method of Méry’ and the So-Called ‘Method of Méry’
		2.2.5 Thrust Line Analysis and Graphical Methods for the Stability of Masonry Domes
		2.2.6 Modern Versions of Traditional Methods for the Equilibrium Analysis of Masonry Arches and Domes
	2.3 A Focus on Durand-Claye’s Method and its Modern Re-interpretation
		2.3.1 Introduction
		2.3.2 The Method of ‘Stability Areas’ as a Graphical Translation of Coulomb’s Method of Maxima and Minima
		2.3.3 The Influence of the Limited Compressive Strength According to Durand-Claye (1867)
		2.3.4 Durand-Claye’s treatment on the equilibrium of masonry domes
		2.3.5 A Modern Re-interpretation of Durand-Claye’s Method
		2.3.6 Some Applications of the Modern Computerized Version of Durand-Claye’s Method
	References
3 Discretised Continuum Approaches: From Continuum to Dis-Continuum
	3.1 Formulation of BVP: Basic Ingredients of Solid Mechanics
		3.1.1 Heyman’s Material
		3.1.2 The Equilibrium BVP for NRNT Materials
		3.1.3 Variational Formulation of the BVP
		3.1.4 Basic Partitions of Ω
		3.1.5 Stress–Strain Relation
		3.1.6 Compatibility of the Data
	3.2 Admissible Strain and Stress Fields
		3.2.1 Compatibility of the Data, Again
		3.2.2 Strain as a Measure for Fracture
		3.2.3 Regularity of Stress and Strain: Singularities
		3.2.4 Simple BVP Solutions: Examples
	3.3 Variational Formulations of the BVP
		3.3.1 Minimum of the Total Potential Energy
		3.3.2 Minimum of the Total Complementary Energy
	3.4 Numerical Approaches to the BVP Variational Formulation
		3.4.1 Displacement-Based Approaches: Discretisation of the Total Potential Energy
		3.4.2 Stress-Based Approaches: Discretisation of the Total Complementary Energy
	3.5 Application to a Practical Case Study
		3.5.1 Effects of the Settlement
		3.5.2 Load Bearing Capacity of the Masonry Structure
	References
4 Thrust Network Analysis for Masonry Assessment
	4.1 Introduction
	4.2 Thrust Network Analysis
		4.2.1 Main Elements
		4.2.2 Equilibrium Equations
		4.2.3 The Case of a Fixed Form Diagram
		4.2.4 Independent Edges in Form Diagrams
	4.3 Constrained Equilibrium
		4.3.1 Constraints from Limit Analysis
		4.3.2 Objective Functions
		4.3.3 Solving Strategies and Starting Points
	4.4 Applications
		4.4.1 Vault Geometry
		4.4.2 Computing the Extremes of Thrust
		4.4.3 Stability Domain
		4.4.4 Maximum Vertical Load Multiplier
		4.4.5 Maximum Horizontal Load Multiplier
		4.4.6 Internal State Under Support Displacements
		4.4.7 Towards the Application of TNA in Surveyed Buildings
	4.5 Conclusions
	References
5 Discrete Element Modeling
	5.1 Overview of DEM Models
		5.1.1 Introductory Remarks
		5.1.2 The Most Important Available Codes for Masonry Analysis
	5.2 Fundaments of the 3DEC Approach
		5.2.1 Cundall’s Distinct Element Method
		5.2.2 3DEC Modelling of Masonry Structures. Basic Assumptions and Features
		5.2.3 Formulation of a 3D DEM Block Model
	5.3 Application Topics and Examples
		5.3.1 Masonry Arches and Shells
		5.3.2 Walls and Panels
		5.3.3 Columns and Tall Structures
		5.3.4 Analysis of Natural Frequencies Using Rigid Block Models
		5.3.5 Simulation of Displacements Caused by Earthquakes
		5.3.6 Shaking Table Test of a Stone Masonry Building Model
		5.3.7 Modelling Structural Reinforcement
		5.3.8 Irregular Block Geometries
		5.3.9 Block Fracture
	5.4 Closing Remarks
	References