Page 28 - Using ANSYS for Finite Element Analysis A Tutorial for Engineers

IntroductIon to FInIte element AnAlysIs • 15
• Automobile engineering
• Electrical engineering
• Chemical engineering
• Geomechanics
• Biomechanics

1.2 review toPiCs

1.2.1 Matrix oPerations

Matrix Algebra
• A matrix is an m × n array of numbers arranged in m rows and n
columns.
• m = n A square matrix.
• m = 1 A row matrix.
• n = 1 A column matrix.
• a Element of matrix a row i, column j
ij
Multiplication of a matrix by a scalar:

[a] = k [c] a = k c
ij
ij
Addition of matrices: Matrices must be of the same order (m × n). Add
them term by term:

[c] = [a] + [b] c = a + b ij
ij
ij
Multiplication of two matrices: If [a] is m × n, then [b] must have n rows:

[c] = [a] [b]

n
ij ∑
�
c = a b
ie ie
e=1
Transpose of a matrix: Interchange of rows and columns:

[a ] = [a ] T
ij
ji
• If [a] is m × n, then [a] is n × m
T
• If [a] = [a] , then [a] is symmetric. [a] must be a square matrix
T