Example Problem
using the
One-Dimensional Spring Element

Three linear springs are assembled in series with spring constants as shown below. An external static force is applied at node #2.

 

Problem Statement: 3 Springs in Parallel

 

 

 

Comments:

  1. Three linear springs in series.

  2. The problem is statically indeterminate since there are two unknown reactions and only one horizontal force equilibrium equation.

  3. Method is independent of node and element numbering.

    1. Node or element does affect computer storage requirements.

    2. It is not necessary to be concerned with node and element numbering since it is optimized transparent to the user of commercial finite element codes.

     

  4. Mesh Summary:

    1. 3 1-D longitudinal linear spring elements.

    2. 4 Nodes

    3. 1 DOF/Node

    4. 4 DOF in Mesh

    5. 2 constrained DOF in mesh (nodes 1 and 4)

    6. 2 unconstrained DOF in mesh (nodes 2 and 3)

     

  5. Note that the units of spring constants and external force are consistent.

    1. Force - [Newtons]

    2. k - [N/m]

    3. Displacement - [m]

 

Finite Element Analysis:


 

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