Modern Experimental Stress Analysis

All structures suffer from stresses and strains caused by factors such as wind loading and vibrations. Stress analysis and measurement is an integral part of the design and management of structures, and is used in a wide range of engineering areas.

There are two main types of stress analyses – the first is conceptual where the structure does not yet exist and the analyst has more freedom to define geometry, materials, loads etc – generally such analysis is undertaken using numerical methods such as the finite element method. The second is where the structure (or a prototype) exists, and so some parameters are known. Others though, such as wind loading or environmental conditions will not be completely known and yet may profoundly affect the structure. These problems are generally handled by an ad hoc combination of experimental and analytical methods.

This book therefore tackles one of the most common challenges facing engineers – how to solve a stress analysis problem when all of the required information is not available. Its central concern is to establish formal methods for including measurements as part of the complete analysis of such problems by presenting a new approach to the processing of experimental data and thus to experimentation itself. In addition, engineers using finite element methods will be able to extend the range of problems they can solve (and thereby the range of applications they can address) using the methods developed here.

Modern Experimental Stress Analysis:

• Presents a comprehensive and modern reformulation of the approach to processing experimental data
• Offers a large collection of problems ranging from static to dynamic, linear to non-linear
• Covers stress analysis with the finite element method
• Includes a wealth of documented experimental examples
• Provides new ideas for researchers in computational mechanics

Preface.

Notation.

Introduction.

1 Finite Element Methods.

1.1 Deformation and Strain.

1.2 Tractions and Stresses.

1.3 Governing Equations of Motion.

1.4 Material Behavior.

1.5 The Finite Element Method.

1.6 Some Finite Element Discretizations.

1.7 Dynamic Considerations.

1.8 Geometrically Nonlinear Problems.

1.9 Nonlinear Materials.

2 Experimental Methods.

2.1 Electrical Filter Circuits.

2.2 Digital Recording and Manipulation of Signals.

2.3 Electrical Resistance Strain Gages.

2.4 Strain Gage Circuits.

2.5 Motion and Force Transducers.

2.6 Digital Recording and Analysis of Images.

2.7 Moiré Analysis of Displacement.

2.8 Holographic Interferometry.

2.9 Photoelasticity.

3 Inverse Methods 171

3.1 Analysis of Experimental Data.

3.2 Parametric Modeling of Data.

3.3 Parameter Identification with Extrapolation.

3.4 Identification of Implicit Parameters.

3.5 Inverse Theory for Ill-Conditioned Problems.

3.6 Some Regularization Forms.

3.7 Relocation of Data onto a Grid Pattern.

3.8 Discussion.

4 Static Problems 219

4.1 Force Identification Problems.

4.2 Whole-Field Displacement Data.

4.3 Strain Gages.

4.4 Traction Distributions.

4.5 Nonlinear Data Relations.

4.6 Parameter Identification Problems.

4.7 Choosing the Parameterization.

4.8 Discussion.

5 Transient Problems with Time Data.

5.1 The Essential Difficulty.

5.2 Deconvolution using Sensitivity Responses.

5.3 Experimental Studies.

5.4 Scalability Issues: Recursive Formulation.

5.5 The One-Sided Hopkinson Bar.

5.6 Identifying Localized Stiffness and Mass.

5.7 Implicit Parameter Identification.

5.8 Force Location Problems.

5.9 Discussion.

6 Transient Problems with Space Data.

6.1 Space–Time Deconvolution.

6.2 Preliminary Metrics.

6.3 Traction Distributions.

6.4 Dynamic Photoelasticity.

6.5 Identification Problems.

6.6 Force Location for a Shell Segment.

6.7 Discussion.

7 Nonlinear Problems.

7.1 Static Inverse Method.

7.2 Nonlinear Structural Dynamics.

7.3 Nonlinear Elastic Behavior.

7.4 Elastic-Plastic Materials.

7.5 Nonlinear Parameter Identification.

7.6 Dynamics of Cracks.

7.7 Highly Instrumented Structures.

7.8 Discussion.

Afterword.

References.

Index.

James F. Doyle is the author of Modern Experimental Stress Analysis: Completing the Solution of Partially Specified Problems, published by Wiley. All structures suffer from stresses and strains caused by operating loads and extraneous factors such as wind loading and vibrations; typically, these problems are solved using the finite element method. The most common challenge facing engineers is how to solve a stress analysis problem of real structures when all of the required information is not available. Addressing such stress analysis problems, Modern Experimental Stress Analysis presents a comprehensive and modern approach to combining experimental methods with finite element methods to effect solutions. Focusing on establishing formal methods and algorithms, this book helps in the completion of the construction of analytical models for problems. This book also:

• Applies to a variety of structures and components.
• Provides new ideas to researchers in computational mechanics.
• Discusses complex models.
• Offers solutions to a large collection of problems ranging from static to dynamic, linear to non-linear.
• Includes a wealth of documented experimental examples.
• Enables stress analysts to extend the range of problems and applications they can address.

Offering practical examples, this book is an essential tool for all senior undergraduate and postgraduate students in experimental mechanics and engineering analysis. Practising civil, mechanical and aerospace engineers involved in the stress analysis of structures and components will also find this book a very useful reference.