Content in this book
Introduction to Inverse Problems ........................ 3
1.1 Premise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 General Rules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.2 Rules for Inverse Problems . . . . . . . . . . . . . . . . . . . 4
1.2 Forward and Inverse Problems for Elastic
Discretized Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 Quality Indicators of Inverse Solutions . . . . . . . . . . . 13
1.2.2 Inverse Solution for Systems in Matrix Form . . . . . . . 14
1.3 Systems in Functional Form . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.3.1 Regularization Method of Tikhonov-Phillips. . . . . . . . 18
1.3.2 Regularization Using Regularization Matrix . . . . . . . . 19
1.3.3 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2 Introduction to the Application of Strain Gages . . . . . . . . . . . . . . 23
2.1 Properties of Strain Gages . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1.1 Relationship Between Strain and Resistance
Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.1.2 Materials for Metal Strain Gages . . . . . . . . . . . . . . . 26
2.1.3 Resistance Values . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.1.4 Transverse Sensitivity and Strain Gage Factor . . . . . . 32
2.1.5 Influence of a Temperature Variation . . . . . . . . . . . . 34
2.1.6 Compensation for Thermal Output . . . . . . . . . . . . . . 36
2.2 Strain Gage Rosettes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.2.1 Three-Gage Rectangular
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