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Appendix A: Matrix Algebra
Intro to Matrix Algebra [PDF]
Adding Two Matrices [YOUTUBE 4:53]
Subtracting Two Matrices [YOUTUBE 5:34]
Multiplying Two Matrices [YOUTUBE 10:06]
Determinant of a matrix using
minors Theory [YOUTUBE 4:41]
Determinant of a matrix using
cofactors Theory [YOUTUBE 3:26]
Determinant of a matrix using minors
Example [YOUTUBE 6:26]
Determinant of a matrix using
cofactors Example [YOUTUBE 5:31]
A real life problem of setting up
simultaneous linear equations [YOUTUBE 5:23]
Writing simultaneous linear
equations in matrix form [YOUTUBE 5:25]
Can we divide two matrices? [YOUTUBE 5:39]
Some statements about the inverse
of matrices [YOUTUBE 2:53]
Inverse of matrices Example [YOUTUBE 3:40]
Using concept of inverse to solve a set of
equations [YOUTUBE 2:27]
Finding the inverse of a matrix
Theory [YOUTUBE 4:32]
Finding the inverse of a matrix Example [YOUTUBE 7:03]
Finding the inverse of a matrix by
adjoints Theory [YOUTUBE 2:15]
Finding the inverse of a matrix by adjoints
Example [YOUTUBE 7:19]
Appendix B: Transformation of Stresses and
Strains
Transformation of Stresses [LIVESCRIBE 13:55]
2.1 Introduction
Deformations of unidirectional lamina under load [ PDF]
[PPT]
2.2 Review of Definitions
Review of definitions [PDF] [PPT]
2.3 Hooke's Law for Different Types of
Materials
3D stiffness and compliance matrices [PDF] [PPT]
2.4 Hooke's Law for a Two Dimensional
Unidirectional Lamina
Stiffness and compliance matrices for a unidirectional lamina [PDF] [PPT]
2.5 Hooke's Law for a Two Dimensional Angle
Lamina
Stress-strain relationship for an angle lamina [PDF] [PPT]
2.6 Engineering Constants of an Angle Lamina
Engineering constants of an angle lamina [PDF] [PPT]
Problem 2.27 [PDF]
Problem 2.28 [PDF]
Problem 2.29 [PDF]
Problem 2.32 [LIVESCRIBE 9:03]
Background to #2.32: Linear
Regression With Zero Intercept: Derivation [YOUTUBE 9:32]
Test problem#3 [problem
statement] [LIVESCRIBE Parta
1:34] [LIVESCRIBE Part
b 3:08] [LIVESCRIBE Partc
3:46]
2.7 Invariant Form of Stiffness and
Compliance Matrices for an Angle Lamina
Invariant form of transformation matrices [PDF] [PPT]
2.8 Strength Failure Theories of an Angle
Lamina.
Maximum stress failure theory [PDF] [PPT]
Maximum strain failure theory [PDF] [PPT]
Tsai-Hill failure theory [PDF] [PPT]
Tsai-Wu failure theory [PDF] [PPT]
Comparison of failure theories [PDF] [PPT]
Test problem#4 [problem
statement] [LIVESCRIBE 6:53
]
2.9 Hygrothermal Stresses and Strains in a
Lamina
Hygrothermal stresses and strains [PDF] [PPT]
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