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- Are partial differential equations involved in transient, structural FEA?

I am a mechanical an engineer with a few years of experience. Most of the work I do is transient, structural finite element analysis. I have gotten reasonably competent at building models and pumping out results, but I regularly come across gaps in my fundamental knowledge. I have been doing some reading on the basics of finite element analysis because I want to understand more of its mathematical foundations.

My understanding is that the finite element method is often (primarily?) used to solve partial differential equations, which get pretty hairy. In structural analysis, the fundamental equation I am solving is the Equation of Motion:

[tex]F=m\ddot{x}+c\dot{x}+kx[/tex]

This is an ordinary differential equation, not a PDE. Are PDE’s involved in structural analysis?

My understanding is that the finite element method is often (primarily?) used to solve partial differential equations, which get pretty hairy. In structural analysis, the fundamental equation I am solving is the Equation of Motion:

[tex]F=m\ddot{x}+c\dot{x}+kx[/tex]

This is an ordinary differential equation, not a PDE. Are PDE’s involved in structural analysis?