Adding Matrix in sympy from a 2x2 to a 3x3

user_18521717 0
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So im trying to add two matrixes together in sympy from a 2x2 matrix to a 3x3 matrix and im not really sure how to do it! What i want to achieve is this: Wanted Result

By adding together: K1 and K2. Beacuse they have different places in the total matrix. What i have done:

    import sympy as sy
E,t = sy.symbols("E,t")
K1 = sy.Matrix([[17.5*E*t,-17.5*E*t],[-17.5*E*t,17.5*E*t]])
K2 = sy.Matrix([[12.5*E*t,-12.5*E*t],[-12.5*E*t,12.5*E*t]])

K_Total_Rad_1 = []
K_Total_Rad_2_1 = []
K_Total_Rad_2_2 = []
K_Total_Rad_3 = []
for i in range(len(K1)-2):
    K_Total_Rad_1.append(K1[i])

for i in range(len(K2)-2):
    K_Total_Rad_2_1.append(K1[i+2])    
    
for i in range(len(K2)-2):
    K_Total_Rad_2_2.append(K2[i])

for i in range(len(K2)-2):
    K_Total_Rad_3.append(K2[i-2])

K_Total = sy.Matrix([K_Total_Rad_1, K_Total_Rad_2_2, K_Total_Rad_3])

K_Total

I Obviosly know that the error here is with defining the Matrix dimentions but i dont know how to do this here in python. Hope someone can help

sympy numeric symbolic-math math python
2 Answers

If I'm not mistaken, this is "standard" notation for FEM-like stiffness matrices.

This is how I would do it:

import sympy as sy
E, t = sy.symbols("E, t")
K1 = sy.Matrix([[17.5*E*t,-17.5*E*t],[-17.5*E*t,17.5*E*t]])
K2 = sy.Matrix([[12.5*E*t,-12.5*E*t],[-12.5*E*t,12.5*E*t]])
K = sy.zeros(3)
K[:2, :2] = K1
K[1:, 1:] += K2
K
user_23299680

Maybe a bit less pythonic but more mathematical:

import sympy as sy

E, t = sy.symbols( "E, t" )

K1 = sy.Matrix(
    [
        [ +17.5 * E * t, -17.5 * E * t ],
        [ -17.5 * E * t, +17.5 * E * t ]
    ]
)

K2 = sy.Matrix(
    [
        [ +12.5 * E * t, -12.5 * E * t ],
        [ -12.5 * E * t, +12.5 * E * t ]
    ]
)

A = sy.diag( 1, sy.Matrix( [ 1, 0 ] ) )
B = sy.diag( sy.Matrix( [ 0, 1 ] ), 1 )

K = A * K1 * A.T + B * K2 * B.T
user_8033590
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