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Cheatsheet for FEA course, Summaries of Mechanical Engineering

San José State University (SJSU)Mechanical Engineering

Cheatsheet for the class for mditerm & final

Typology: Summaries

2023/2024

Uploaded on 01/11/2025

eduardo-chan-7
eduardo-chan-7 🇺🇸

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bg1
𝑁𝑁3(𝑥𝑥) = 1
𝐿𝐿3−2𝑥𝑥3+ 3𝑥𝑥2𝐿𝐿
𝑁𝑁4(𝑥𝑥) = 1
𝐿𝐿3𝑥𝑥3𝐿𝐿 − 𝑥𝑥2𝐿𝐿2
𝑣𝑣(𝑥𝑥) = 𝑁𝑁1(𝑥𝑥)𝑣𝑣1+𝑁𝑁2(𝑥𝑥)𝜙𝜙1+𝑁𝑁3(𝑥𝑥)𝑣𝑣2+𝑁𝑁4(𝑥𝑥)𝜙𝜙2
𝑁𝑁1(𝑥𝑥) = 1
𝐿𝐿32𝑥𝑥3−3𝑥𝑥2𝐿𝐿+𝐿𝐿3
𝑁𝑁2(𝑥𝑥) = 1
𝐿𝐿3𝑥𝑥3𝐿𝐿 − 2𝑥𝑥2𝐿𝐿2+𝑥𝑥𝐿𝐿3
[]
−
−
−−
−
−
−−
=
θθθθ
θθ
θθθθθθ
θθ
θθθθ
θθθθθθ
22
22
22
22
sin
sincossin
sincos
sincoscossincoscos
sin
sincossinsincos
sincos
cossincoscos
L
AE
k
[ ]
=
θθ
θθ
sincos00
00sincos
T
𝑓𝑓
1𝑦𝑦
𝑚𝑚1
𝑓𝑓
2𝑦𝑦
𝑚𝑚2
=𝐸𝐸𝐸𝐸
𝐿𝐿3
12 6𝐿𝐿 −12 6𝐿𝐿
6𝐿𝐿 4𝐿𝐿2−6𝐿𝐿 2𝐿𝐿2
−12 −6𝐿𝐿 12 −6𝐿𝐿
6𝐿𝐿 2𝐿𝐿2−6𝐿𝐿 4𝐿𝐿2
𝑣𝑣1
𝜙𝜙1
𝑣𝑣2
𝜙𝜙2
𝑓𝑓
1𝑥𝑥
𝑓𝑓
2𝑥𝑥
=𝑘𝑘 −𝑘𝑘
−𝑘𝑘 𝑘𝑘
𝑢𝑢1
𝑢𝑢2
[ ]
{}
d
L
E
θ
θθθσ
sincossincos −−
=
𝑓𝑓
1𝑥𝑥
′
𝑓𝑓
2𝑥𝑥
′=𝐴𝐴𝐸𝐸
𝐿𝐿
1−1
−1 1
𝑢𝑢1
′
𝑢𝑢2
′

Partial preview of the text

Download Cheatsheet for FEA course and more Summaries Mechanical Engineering in PDF only on Docsity!

𝑁𝑁 3 (𝑥𝑥) =

1

𝐿𝐿^3

− 2 𝑥𝑥 3

  • 3𝑥𝑥 2 𝐿𝐿

𝑁𝑁 4 (𝑥𝑥) =

1

𝐿𝐿^3

𝑥𝑥 3 𝐿𝐿 − 𝑥𝑥 2 𝐿𝐿 2

𝑣𝑣(𝑥𝑥) = 𝑁𝑁 1 (𝑥𝑥) 𝑣𝑣 1 + 𝑁𝑁 2 (𝑥𝑥) 𝜙𝜙 1 + 𝑁𝑁 3 (𝑥𝑥) 𝑣𝑣 2 + 𝑁𝑁 4 (𝑥𝑥) 𝜙𝜙 2

𝑁𝑁 1 (𝑥𝑥) =

1

𝐿𝐿^3

2 𝑥𝑥 3 − 3 𝑥𝑥 2 𝐿𝐿 + 𝐿𝐿 3

𝑁𝑁 2 (𝑥𝑥) =

1

𝐿𝐿^3

𝑥𝑥 3 𝐿𝐿 − 2 𝑥𝑥 2 𝐿𝐿 2

  • 𝑥𝑥𝐿𝐿 3

[ ]

θ θ θ θ θ θ

θ θ θ θ θ θ

θ θ θ θ θ θ

θ θ θ θ θ θ

2 2

2 2

2 2

2 2

cos sin sin cos sin sin

cos cos sin cos cos sin

cos sin sin cos sin sin

cos cos sin cos cos sin

L

AE

k

[ ] 

0 0 cos sin

cos sin 0 0 T

3

2 −6𝐿𝐿 2 𝐿𝐿

2

2 −6𝐿𝐿 4 𝐿𝐿

2

[ ]{ d }

L

E

σ = −cosθ −sinθ cosθ sin θ

′

2𝑥𝑥

′

′

2

′