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Finite Element allows one to divide a continuous medium into a mesh and compute structural properties of it. Instead of discretizing the continuous, why not start with a discrete method to begin with? Could we not see the entire structure as a space grid, whose equations are known and test the structure accordingly?

I ask because I saw research that implements fracture mechanics through a plane frame (2D), remove links that are too stressed and re-runs, and obtains realistic fracture results with it. In 3D could we not do the same with space frames?

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  • $\begingroup$ The description of solids and fluids happens through the equations of continuum mechanics. There is no other universally accepted description of media "as a space grid, whose equations are known". $\endgroup$ Feb 1 at 18:20
  • $\begingroup$ Even the continuous formulation is an approximation.. and it gets discretized later. For aerodynamics there is no way to accurately compute turbulence. So, if a bottom approach that is mathematically accurate enough why not use it? The research group I mentioned used it where continuous FEA models failed. $\endgroup$
    – BBSysDyn
    Feb 1 at 19:05
  • $\begingroup$ Every model is an approximation. But I don't see the point you're making: "if a bottom approach that is mathematically accurate enough". There is no such other approach. All other approaches are discretizations of some sort -- but so is the finite element method. $\endgroup$ Feb 1 at 22:26
  • $\begingroup$ "...as a space grid, whose equations are known..." I suspect these equations are derived using many of the same assumptions used in deriving the continuum formulation. If you truly want to get at the discrete mechanics underlying continuum mechanics, you would have to simulate the quantum mechanical interactions of trillions upon trillions of particles. I don't know of any way to discretize spacetime above a Planck scale that doesn't presuppose some degree of homogeneity and continuity in the same way that continuum mechanics does., $\endgroup$
    – whpowell96
    Feb 2 at 15:56

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