Vector Operations
Inputs
A =
B =
Unit Vectors
u
A
=
u
B
=
Magnitudes
A =
B =
Angle =
degrees
Cross Product
A x B =
unit =
Dot Product
A
.
B =
Simultaneous Equations
A
*
x
=
B
*
=
Matrix Inverse & Transpose
Input
Inverse
Transpose
Determinant =
Matrix Operations
Mat A
Mat B
Result
Double Dot Product A:B =
Eigenvalues & Eigenvectors
Input Tensor
Principal Values
Eigenvectors
RU Polar Decomposition
Deformation Gradient, F
Rotation Matrix, R
Stretch Tensor, U
VR Polar Decomposition
Deformation Gradient, F
Stretch Tensor, V
Rotation Matrix, R
Strain Tensors
Def Gradient, F
Small Strain
Almansi Strain
Green Strain
Rotations
Psi =
Theta =
Phi =
Rotation Matrix, R
Angle =
Vector =
Invariants
Input
Invariants
I
1
=
I
2
=
I
3
=
Tensor Transforms
Tensor
Transform Matrix
Rotate
1 - 2
degrees
following
2 - 3
plane...
3 - 1
Stress = Stiffness : Strain
Iso Stiffness
E
ν
Ortho Stiffness
C11
C12
C44
Strain
Stress
Dynamic Eigenmodes
Mass
Stiffness
Eigenvectors
Eigenvalues
Lambda =
Omega =