for a typical sub-region or element. The simplest form is a 2-node system 

 with a straight line connecting the nodes. The simplest displacement field 

 is also linear in form. This field assumes that the displacement of any 

 point on the line segment is obtained by simple linear interpolation form 

 the displacements of the nodes. This is known as the 1-D simplex element. It 

 also assumes there is no bending or torsional resistance so that only the 

 spatial positions of the nodes are used. Thus the element has 3 degrees of 

 freedom per node in a 3-D problem. The equations of motion for this element are 

 obtained by an application of kinematic, material constitutive and energy 

 relations. Since the assiuned functions are defined only on the single element, 

 the entire structure and its dynamic equations are obtained by summing the 

 individual element contributions under the obvious assumption that the elements 

 are joined at the nodes. 



Element forms of higher order that the 1-D simplex can be used. The most 

 readily defined forms are based on polynomials, and the next logical element 

 form is one which uses a parabola for the geometry and the displacement fields. 

 Such an element uses one more node along the line between the two end nodes, 

 and the functional form is obtained using Lagrangian interpolation on the 

 three nodes. The process could be extended to cubics and higher orders, but 

 there appears to be no justification for doing so. Even though the higher 

 order fields are more capable of modeling complicated geometries and responses 

 with fewer elements , the number of nodes required does not change much while the 

 complexity of the equations and the cost of their calculation increase 

 considerably. 



The very regular and orderly form of the stiffness method makes it very 

 attractive for coding on a digital computer. The method also makes it very 



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