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Finite Element Method - I HW #3

The document outlines a homework assignment focused on the Finite Element Method for analyzing two higher order beam elements in civil engineering. It includes tasks such as determining shape functions, stiffness matrices, equivalent nodal force vectors, and vertical deformation variations for different element configurations under uniform loading. The assignment emphasizes practical applications with specific parameters like loading intensity and beam length.

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hamid dehnavipour
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24 views1 page

Finite Element Method - I HW #3

The document outlines a homework assignment focused on the Finite Element Method for analyzing two higher order beam elements in civil engineering. It includes tasks such as determining shape functions, stiffness matrices, equivalent nodal force vectors, and vertical deformation variations for different element configurations under uniform loading. The assignment emphasizes practical applications with specific parameters like loading intensity and beam length.

Uploaded by

hamid dehnavipour
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Finite Element Method – I Amir R.

Khoei
HW #3. Civil Engineering Department
Sharif University of Technology

Consider two higher order beam elements of length ℓ and flexural rigidity EI , as shown in Figure.
Model (a) is 2-noded element with three-degrees of freedom (υ, θ, κ) at each node. Model (b) is 3-
noded element with two-degrees of freedom (υ, θ) at each node.

1 κ1 κ2 2 1 2 3

θ1 θ2 θ1 θ2 θ3
υ1 υ2 υ1 υ2 υ3

ℓ ℓ
model (a) model (b)

1. Determine the shape functions of elements (a) and (b).


2. Determine the stiffness matrix of elements (a) and (b).
3. Consider that the elements are subjected to the uniform distributed loading with intensity q
per unit length, determine the vector of equivalent nodal force for each element.
4. Consider the cantilever beam shown in figure, determine the variations of vertical
deformation along the beam in the following cases;
a. Using four-elements of type (a).
b. Using four-elements of type (b).
c. Using four-simple-beam-elements of 2-nodal points with (υ, θ) at each node.

q = 5000 Kg/m

ℓ= 8 m

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