Finite Element Analysis for Building Assessment: Advanced Use and Practical Recommendations

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Foreword
Preface
Authors
1 Fundamentals of the finite element method
	1.1 Equilibrium of a three- dimensional body in elasticity
	1.2 Basics
		1.2.1 Weak form of governing equations in elasticity
		1.2.2 Example of an axially loaded column
	1.3 Generalization
		1.3.1 Convergence criteria on shape functions
		1.3.2 Matrix formulation
		1.3.3 Example of a beam subjected to bending
	1.4 Shape functions and numerical integration
		1.4.1 Hermitian beam elements
		1.4.2 Isoparametric elements
		1.4.3 Completeness of shape functions for quadrilateral elements
		1.4.4 Numerical integration, integration points and integration schemes
		1.4.5 Recovery process
	1.5 Commonly used finite elements
	Bibliography and further reading
2 Nonlinear structural analysis
	2.1 Potential sources of nonlinearities
	2.2 Geometrical nonlinearities and stability
		2.2.1 Introduction to finite displacements: the von Mises truss structure
		2.2.2 Geometric stiffness and linear buckling analysis
		2.2.3 Postbuckling analysis and geometrical imperfection
		2.2.4 Stability of compressed elements
	2.3 Computational strategies
		2.3.1 Incremental-iterative methods with material nonlinearities
			2.3.1.1 Forward Euler method
			2.3.1.2 Newton–Raphson method (regular, modified and linear)
			2.3.1.3 Quasi-Newton methods
		2.3.2 Advanced solution procedures
			2.3.2.1 Arc-length control
			2.3.2.2 Direct and indirect displacement control
			2.3.2.3 Line search
		2.3.3 Convergence criteria
		2.3.4 Example
	Bibliography and further reading
3 Constitutive models
	3.1 Material behaviour
		3.1.1 Main constitutive models
		3.1.2 Failure of concrete-like materials
		3.1.3 Simple nonlinear problems
	3.2 Elastoplasticity models
		3.2.1 Elastic domain and perfect elastoplasticity
		3.2.2 Yield functions for isotropic materials
		3.2.3 Constitutive law with associated plastic flow and perfect elastoplasticity
		3.2.4 Constitutive law with associated plastic flow and hardening
		3.2.5 Euler Forward and Euler Backward incremental methods with perfect elastoplasticity
	3.3 Damage models
		3.3.1 Uniaxial loading
		3.3.2 Isotropic and anisotropic damage models
		3.3.3 Damage deactivation
	3.4 Smeared crack models
		3.4.1 Main concept and strain decomposition
		3.4.2 Implementation of the fixed and rotating smeared crack model
	3.5 Strain localization and mesh sensitivity
	3.6 Examples of constitutive models in commercial software codes
		3.6.1 Smeared crack model (in tension) and plasticity in compression
		3.6.2 Plasticity models in tension and compression
		3.6.3 Total strain crack model
		3.6.4 Damaged plasticity
	Bibliography and further reading
4 Recommended properties for advanced numerical analysis
	4.1 Masonry
		4.1.1 Masonry morphologies
		4.1.2 Introduction to numerical modelling
		4.1.3 Mechanical properties of masonry components
			4.1.3.1 Unit
			4.1.3.2 Mortar
		4.1.4 Mechanical properties of interface
			4.1.4.1 Elastic parameters
			4.1.4.2 Mode I failure
			4.1.4.3 Mode II failure
			4.1.4.4 Shear–tension and shear– compression interaction
			4.1.4.5 Compressive failure
		4.1.5 Mechanical properties of masonry as a composite material
			4.1.5.1 Axial behaviour (compression)
			4.1.5.2 Axial behaviour (tension)
			4.1.5.3 Biaxial behaviour
		4.1.6 Structural behaviour of masonry as a composite
			4.1.6.1 Shear walls
			4.1.6.2 Masonry Quality Index
		4.1.7 Synthesis of the mechanical properties
			4.1.7.1 Individual masonry components
			4.1.7.2 Masonry as a composite material
			4.1.7.3 Data from Italian code
			4.1.7.4 Data from American code
	4.2 Timber
		4.2.1 Strength grading
		4.2.2 Mechanical properties
	4.3 Reinforced concrete
		4.3.1 Mechanical properties of concrete and reinforcement
			4.3.1.1 Elastic parameters
			4.3.1.2 Compressive behaviour
			4.3.1.3 Tensile behaviour and tension stiffening
			4.3.1.4 Biaxial behaviour
			4.3.1.5 Reinforcement behaviour and modelling
		4.3.2 Nonlinear models of frame elements
	4.4 Steel and iron
		4.4.1 General behaviour and material properties
			4.4.1.1 Tensile strength
			4.4.1.2 Ductility
			4.4.1.3 Code properties
		4.4.2 Mechanical properties of various types of iron and steel
	4.5 Safety assessment
		4.5.1 Eurocode 8 and Italian code
			4.5.1.1 Knowledge levels KL and confidence factors CF
			4.5.1.2 Masonry
			4.5.1.3 Timber
			4.5.1.4 Concrete and steel
		4.5.2 Italian guidelines for built heritage
		4.5.3 Safety formats for nonlinear analysis according to model code 2010
			4.5.3.1 Basic principles
			4.5.3.2 Probabilistic method
			4.5.3.3 Global resistance factor method (GRF)
			4.5.3.4 Method of estimation of a coefficient of variation of resistance (ECOV)
			4.5.3.5 Partial safety factor method (PSF)
	Bibliography and further reading
5 Guidelines for practical use of nonlinear finite element analysis
	5.1 Overview
	5.2 Preprocessing
		5.2.1 Type and main aspects of analysis
		5.2.2 Geometry
		5.2.3 Type of element
		5.2.4 Mesh
			5.2.4.1 Mesh refinement
			5.2.4.2 Mesh quality and controls
		5.2.5 Examples of element types and mesh refinement
		5.2.6 Material properties
		5.2.7 Constraints and loads
	5.3 Solution process
	5.4 Postprocessing
	5.5 Structural analysis report
	5.6 Examples
		5.6.1 Steel plate
		5.6.2 Concrete beam
		5.6.3 Masonry shear wall
			5.6.3.1 Macro-modelling
			5.6.3.2 Micro-modelling
	Bibliography and further reading
Index