Mathematical applications in continuum and structural mechanics / Francesco Marmo [and three others].

Format:

Book

Author/Creator:

Marmo, Francesco, author.

Series:

Advanced Structured Materials

Advanced Structured Materials ; v.127

Language:

English

Subjects (All):

Continuum mechanics--Mathematical models.

Continuum mechanics.

Structural analysis (Engineering)--Mathematical models.

Structural analysis (Engineering).

Physical Description:

1 online resource (275 pages)

Place of Publication:

Cham, Switzerland : Springer International Publishing, [2021]

Summary:

This book presents a range of research projects focusing on innovative numerical and modeling strategies for the nonlinear analysis of structures and metamaterials. The topics covered concern various analysis approaches based on classical finite element solutions, structural optimization, and analytical solutions in order to present a comprehensive overview of the latest scientific advances. Although based on pioneering research, the contributions are focused on immediate and direct application in practice, providing valuable tools for researchers and practicing professionals alike.

Contents:

Intro

Contents

Contributors

1 Usage of Guided Wave Resonance Phenomena for Defect Detection in Laminate Elastic Structures

1.1 Introduction

1.2 Computational Models

1.3 Experimental Evaluation of Resonance Frequencies

1.4 Estimation of the Defect Size

1.5 Conclusion

References

2 Modelling of Piezocomposites with Mechanical Interface Effects

2.1 Introduction

2.2 Effective Moduli Method for Homogenization of Two-Phase Piezoelectric Nanocomposite

2.3 Dimensionless Homogenization Problem

2.4 Finite Element Modelling

2.5 Modelling of Representative Volume Elements

2.6 Results and Discussion

2.7 Conclusion

3 A Mathematical Model for Bone Cell Population Dynamics of Fracture Healing Considering the Effect of Energy Dissipation

3.1 Introduction

3.2 The Model

3.2.1 The Main Assumptions

3.2.2 The Governing Equations

3.2.3 The Stimulus

3.2.4 The Function κ()

3.2.5 The Mechanical Framework

3.2.6 Numerical Data

3.2.7 Healing of Bone

3.2.8 Dissipation

3.3 Results and Discussion

3.4 Conclusion

4 Second Gradient Linear and Nonlinear Constitutive Models of Architectured Materials: Static and Dynamic Behaviors

4.1 Introduction

4.2 First- and Second-Order Effective Moduli of Periodic Networks

4.2.1 Analytical Method

4.2.2 Homogenized Viscoelastic Behavior

4.2.3 Incremental Scheme

4.3 Wave Propagation Analysis Based on Nonlinear Models

4.3.1 Strain Energy Density

4.4 Conclusion

5 An Application of Coulomb-Friction Model to Predict Internal Dissipation in Concrete

5.1 Introduction

5.2 A Brief Synopsis of the Employed Model

5.2.1 3D Formulation of a Micromorphic Concrete-Based Material

5.2.2 Simplified Formulation for the Case of a Pure Compression

5.3 Numerical Simulations and Discussions.

5.4 Conclusion

6 From the Swarm Robotics to Material Deformations

6.1 Introduction

6.2 Other Models in Literature

6.2.1 Position-Based Dynamics (PBD)

6.2.2 Swarm Robotics

6.3 The Model Here Proposed

6.3.1 A Recall About Graph Theory

6.3.2 Constructing the Model

6.3.3 Relationship with Other Models

6.3.4 Meaning of Neighbors

6.4 Numerical Simulations

6.4.1 Standard Simulations

6.4.2 Second Neighborhoods and Exotic Simulations

6.5 Conclusion

7 A Review of the Class of Bouc-Wen Differential Models for Simulating Mechanical Hysteresis Phenomena

7.1 Introduction

7.2 Modeling of Symmetric Hysteresis Loops

7.2.1 Bouc Model and Its Modified Versions

7.2.2 Sensitivity Analysis

7.3 Modeling of Asymmetric Hysteresis Loops

7.3.1 Asymmetric Bouc-Wen Models

7.3.2 Sensitivity Analysis

7.4 Modeling of Pinched Hysteresis Loops

7.4.1 Pinching Bouc-Wen Models

7.4.2 Sensitivity Analysis

7.5 Modeling of Degrading Hysteresis Loops

7.5.1 Degrading Bouc-Wen Models

7.5.2 Sensitivity Analysis

7.6 Conclusion

8 A Generalized Formulation of Time Integration Methods for Nonlinear Dynamic Analysis of Hysteretic Mechanical Systems

8.1 Introduction

8.2 Families of Time Integration Methods

8.2.1 Nonlinear Equilibrium Equations

8.2.2 Generalized Formulation of Time Integration Methods

8.3 Conventional Time Integration Methods

8.3.1 Newmark's Family of Methods

8.3.2 Some Instances of the NFMs

8.3.3 Implementation Scheme of the NFMs

8.4 Structure-Dependent Time Integration Methods

8.4.1 Chang's Family of Explicit Methods

8.4.2 Some Instances of the CFEMs

8.4.3 Implementation Scheme of the CFEMs

8.5 Numerical Experiments

8.5.1 Mechanical System Properties

8.5.2 Applied Generalized External Force.

8.5.3 Hysteretic Model Parameters

8.5.4 Results of the Nonlinear Time History Analyses

8.6 Conclusion

9 Quasi-Harmonic Solutions for Transversely Isotropic Magneto-Electro-Thermo-Elasticity: A Symbolic Mathematics Approach

9.1 Introduction

9.2 Field Equations

9.3 A General Solution to the Field Equations in Terms of Quasi-Harmonic Potentials

9.3.1 Inversion of the Differential Operator mathcalL

9.3.2 Factorization of the Differential Equation |mathcalL|= 0

9.4 Automatic Evaluation of |mathcalL| and mathcalL* and Relevant Coefficients

9.4.1 Evaluation of |mathcalL|

9.4.2 Evaluation of mathcalL*

9.5 Conclusion

10 Mathematical Tools for the Seismic Analysis of Reinforced Concrete Structures: A Selected Review

10.1 Introduction

10.2 Review of Strategies Accounting for Global Torsion in Buildings

10.2.1 Review of the Dynamic Equivalent Rotational Spectrum

10.3 Computation of Multicomponent Actions by Seismic Envelopes

10.4 Capacity Checks of Reinforced Concrete Beams

10.4.1 A General Algorithm to Perform Capacity Checks by the Supreme Envelope

10.5 Conclusions

11 Form Finding of Shell Structures by Using Membrane Theory

11.1 Introduction

11.2 The Membrane Theory of Shells

11.2.1 Global and Local Reference Frames

11.2.2 Transformation Formulas for Lengths and Areas

11.2.3 Distributed Loads and Stress Components

11.2.4 Equilibrium

11.3 Form-Finding Algorithm

11.3.1 Discretization of the Equilibrium Equations by the Finite Difference Method

11.3.2 Assigning the Distribution of Projected Membrane Stresses

11.3.3 Evaluation of the Shell Mid-Surface Height

11.3.4 Iterative Procedure for Assigning Projected Loads

11.4 Numerical Examples

11.4.1 Shell with One Free Side

11.4.2 Shell Supported at Corners.

11.5 Conclusion

12 Influence of Non-structural Components on Equivalent Linearization of Buildings

12.1 Introduction

12.2 Brief Review of Tail-Equivalent Linearization

12.3 Influence of Secondary Devices on TELS

12.3.1 Frequency Content Comparison

12.3.2 First Excursion Probability Comparison

12.4 Conclusion

13 Do We Really Need Pantographic Structures?

13.1 Introduction

13.2 Metamaterials Are (Natural) Materials on Demand

13.3 Second Gradient Theories

13.4 Microstructure in Continuum Mechanics

13.4.1 The Synthesis Problem

13.5 Why We Really Need Pantographic Structures

13.5.1 The Existence of Pantographic Metamaterial Motivates the Need of Second Gradient Theories

13.5.2 A Mechanical Diode

13.5.3 An Iterative Algorithm for Synthesising Metamaterials

13.6 Conclusion

References.

Notes:

Description based on print version record.

Other Format:

Print version: Marmo, Francesco Mathematical Applications in Continuum and Structural Mechanics

ISBN:

3-030-42707-2

OCLC:

1287129363