Direct Methods for Limit State of Materials and Structures: Advanced Computational Algorithms and Material Modelling (Lecture Notes in Applied and Computational Mechanics, 101)

Foreword
Preface
Contents
Contributors
Direct Methods: History, Present and Future
	Abstract
	1 Milestones and the Scientists Behind
		1.1 Early Developments
		1.2 The Next Generation; Theoretical Advances and Development of Numerical Methods
	2 Illustrative Examples of Applications
	3 Perspectives
	References
A Unified Shakedown Limit Equation for Pavements and Railways Under Repeated Traffic Loads
	1 Introduction
	2 Key Factors for Pavement and Railway Shakedown Solutions
	3 Terzaghi’s Bearing Capacity Equation and Correction Factors
	4 A Unified Shakedown Limit Equation
	5 Coefficients for a Rolling Contact Problem
		5.1 A Rolling Contact Problem
		5.2 Lower-Bound Shakedown Analysis
		5.3 Coefficients Ncsd and Nγsd
		5.4 Effect of At-Rest Lateral Earth Pressure Coefficient
	6 Conclusion
	References
Elastic–Plastic Optimisation of a Cable–Rib Satellite Antenna
	1 Introduction
	2 Structural Modelling and Analysis of a Space Antenna
		2.1 Finite Element Modelling of the Antenna
		2.2 Evolutive Algorithm for Elastic–Plastic Analyses
	3 Structural Optimisations of the Space Antenna
		3.1 Elastic–Plastic Optimisation Strategy
		3.2 Combined Dynamic Modal Analysis and Elastic–Plastic Optimisation Strategy
	4 Conclusions
	References
An Introduction to the Probabilistic Linear Matching Method Framework for Structural Integrity Assessment Under Uncertain Design Conditions
	1 Introduction
	2 Probabilistic Shakedown Analysis Under the pLMM Framework
		2.1 Probabilistic Shakedown Boundary and the Implementation of Reliability-Based Shakedown Analysis
	3 Probabilistic Low Cycle Fatigue and Ratcheting Analysis Under pLMM Framework
		3.1 Linear Matching Method-Driven Neural Network (LDNN) for LCF Life and Ratchet Limit Predictions
		3.2 Benchmark of Probabilistic Low Cycle Fatigue Analysis
		3.3 Benchmark of Probabilistic Ratcheting Analysis
		3.4 Reliability-Based LCF and Ratchet Analyses for the Elbow Pipe Bend
	4 Probabilistic Creep-Fatigue Analysis Under pLMM Framework
		4.1 Linear Matching Method-Driven Neural Network (LDNN) for Creep-Fatigue Life Prediction
		4.2 Benchmark of Probabilistic Creep-Fatigue Analysis
	5 Conclusions
	References
Peak Load Prediction of Human Bone Proximal Femur: Sensitivity to Tissues Strength and Geometry
	1 Introduction
	2 Simplified Mechanical Model of Human Proximal Femur
	3 Constitutive Assumptions: Tsai-Wu-Type Yield Surface
	4 Limit Load Prediction of Human Proximal Femur
		4.1 The Elastic Compensation Method for the Evaluation of a PLB
	5 Sensitivity Analysis
	6 Discussion
	7 Concluding Remarks
	References
Graded Damage Solutions in One Dimension
	1 Introduction
	2 The Damageable Rod
	3 The Block with Cohesive Interface
	4 Closure
	References
Fatigue Strength Prediction of Nodular Cast Iron by Shakedown Analysis
	1 Introduction
	2 Material
	3 Methods
		3.1 Generation of Finite Element Representative Volume Elements
		3.2 Implementation of Melan\'s Static Shakedown Theorem
		3.3 Model Calibration and Validation
	4 Results
		4.1 Influence of the RVE Size and the Mesh on the Shakedown Limit
		4.2 Shakedown Limits of Synthetic RVEs
		4.3 Comparison of Shakedown Limits with Fatigue Experiments
	5 Discussion
	6 Conclusions
	References
A Macroscopic Fatigue Criterion for Ductile Porous Materials with Drucker-Prager Matrix
	1 Introduction
	2 Problem Formulations
	3 Macroscopic Fatigue Criterion for Ductile Porous Materials with Drucker-Prager Dilatant Matrix
		3.1 Asymptotic Behavior Under Repeated Pure Hydrostatic Loading
		3.2 Macroscopic Shakedown Criterion Under General Cyclic Loadings
	4 Numerical Verification of the Established Criterion
		4.1 Step-by-Step FEM Numerical Procedure
		4.2 Comparison Between Analytical Solutions and Numerical Results
	5 Conclusion
	References
A Direct Method for Cyclic Crystal Plasticity with Application to High-Cycle Fatigue
	1 Introduction
	2 Constitutive Laws
		2.1 Single Crystal
		2.2 Polycrystal
	3 Incremental Energy Minimization
	4 Simplified Problem
		4.1 Piecewise-Constant Plastic Slips
		4.2 Critical Grains
	5 Illustration
		5.1 Mesoscopic Model Construction
		5.2 Finite Element Model Construction
	6 Direct Approach for Cyclic Loadings
	7 Mesoscopic Fatigue Criterion
		7.1 Influence of the Grain Shape
		7.2 Influence of the Crystalline Orientation
	8 Probabilistic Aspects
		8.1 Survival Function for a Critical Grain of Random Orientation
		8.2 Survival Function for a RVE with M Critical Grains
	9 Concluding Remarks
	References
Masonry Domes Under Complex Loading Conditions: A Shell-Based Static Limit Analysis Approach
	1 Introduction
	2 Shell-based Static Limit Analysis
		2.1 Equilibrium
		2.2 Static Admissibility
		2.3 Collapse and Minimum-Thrust Analysis Problems
	3 Problem Discretization
		3.1 Finite Difference Method
		3.2 Finite Volume Method
		3.3 Discrete Collapse and Minimum-Thrust Analysis Problems
	4 Numerical Results
		4.1 Pseudo-static Seismic Analysis
		4.2 Minimum-Thrust Analysis Under Differential Settlements
	5 Conclusions
	References
Robust Optimization Applied to Uncertain Limit Analysis
	1 Introduction
	2 Robust Limit Analysis with Strength Uncertainties
		2.1 Nominal and Uncertain Limit Analysis Problem
		2.2 Adjustable Robust Optimization
		2.3 Static Robust Optimization
		2.4 Affinely Adjustable Robust Optimization
		2.5 Comparison Between the Different Approaches
	3 Robust Strength Conditions
		3.1 Uncertain Strength Conditions and a Tractable Approximation
		3.2 Illustrative Application on a Robust Mohr-Coulomb Criterion
	4 Solving Robust Limit Analysis Problems
		4.1 Strength Uncertainty with Static Formulation
		4.2 Loading Uncertainties
		4.3 Robust Counterpart
	5 Conclusions
	References
Advances of the RSDM-S: Robustness and Fast Convergence Issues
	1 Introduction
	2 Theoretical Background
	3 Examples of Application
		3.1 The Simple Frame
		3.2 The Slab with the Hole
		3.3 90ο Pipe Elbow
	4 Convergence Issues
	5 Concluding Remarks
	References
Mixed Fiber Elements and Incremental-Iterative Algorithm for Shakedown and Limit Fire Analysis of 3D Frames
	1 Introduction
	2 Modeling of 3D Frame Structures
		2.1 The 3D Beam Model
		2.2 Discretization in Mixed Finite Elements
		2.3 Fiber Analysis
		2.4 Linear Elastic Solution
		2.5 Elasto-plastic Solution
	3 Shakedown Analysis
		3.1 Load Domain
		3.2 Melan\'s Shakedown Theorem and Admissibility Condition
		3.3 Elastic Stress Envelope
		3.4 Shakedown Yield Function
		3.5 Shakedown Safety Factor According to the Lower Bound Theorem
		3.6 Elastic Limit and Non-empty Limit
		3.7 Incremental Strategy for Fiber-Based Shakedown Analysis
	4 Limit Fire Analysis
		4.1 Model of the RC Frames in Fire
		4.2 Time-Dependent Admissibility Condition
		4.3 Safety Condition in Case of Fire
		4.4 Lower Bound Theorem of Limit Fire Analysis
		4.5 Incremental Strategy for Limit Fire Analysis
	5 Incremental Algorithm: Strain-Driven Implementation
		5.1 Section State Determination
		5.2 Element State Determination
		5.3 Incremental-Iterative Global Solution
	6 Numerical Tests on Shakedown Analysis
		6.1 A Continuous Beam Supported on Four Points
		6.2 A Large Building
	7 Numerical Tests on Limit Fire Analysis
	8 Conclusions
	References