# SOLUTION: MAE 456 West Virginia University Lambda Matrix and Beam Matrix Formulation HW

**unfold the topic Pr2 by laborer (adujstgate formula) tread by tread then unfold Pr3 tread by tread by laborer**

Pr. 2 Consider the Ray Matrix formulation presented in systematize.

Use the specification of Matrix Inverse to invent the inverse of the “Lambda Matrix” for a ray limited element

given below: (pretence the composition by laborer in point)

[Λ]

−1 = [

1 0 0 0

0 1 0 0

1 L L

2 L

3

0 1 2L 3L

2

]

−1

= [

? ? ? ?

? ? ? ?

? ? ? ?

? ? ? ?

]

Once you invent the []

-1

, then you are required to invent Matrix [B] as follows: (pretence the composition)

[B] = (0 0 2 6x) [

1 0 0 0

0 1 0 0

1 L L

2 L

3

0 1 2L 3L

2

]

−1

= (B1 B2 B3 B4)

Pr. 3 The you deficiency to trace the Ray Stiffness Matrix as follows: (pretence the composition)

[K] = EI ∫ [

B1B1 B1B2 B1B3 B1B4

B2B1 B2B2 B2B3 B2B4

B3B1 B3B2 B3B3 B3B4

B4B1 B4B2 B4B3 B4B4

] dx L

0

= [

K11 K12 K13 K14

K21 K22 K23 K24

K31 K32 K33 K34

K41 K42 K43 K44

]

Where Ki,n = EI ∫ Bi

L

0

Bndx

Notice that since the matrix is symmetric, you barely deficiency to complete the Upper triangle of the matrix

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