I want to derive the theory of finite element using my own understanding. With this derivation i want to understand the fea theory of rod element(adsbygoogle = window.adsbygoogle || []).push({});

I call the nodes as "points" in a structure.

This scenario is for a simple one dimensional displacement of points(that is the single degree of freedom nodes)

i have 4 points names 1,2,3,4 consecutively along a line and the displacement of each point is named as u1,u2,u3,u4. and force at each point as f1,f2,f3,f4. The displacements will occur only along a line.

There are elements between the nodes signifying the stiffness. The elements have stiffness named,K1,K2,K3.

here K1 is the element between point 1 and 2 K2 between point 2 and 3 and K3 between point 3 and 4.

Now i am writing an equation for displacement of point 1

u1=f1/stiffness. How can i derive the stiffness.

I can say the stiffness is equal to K1 and say u=f1/K1 if and only if u2=0. But u2 may have a definite displacement in this scenario.

so what is the equation of u1

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# Deriving stiffness of a node in finite element theory

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