Let’s try to figure out something from the history. I won’t go deep, but atleast one should know that matrix method came in existence somewhere around 1940s-50s. Whereas, the finite elements got its inspiration from the matrix method around 1960s.
Although, the matrix method was an analytical approach, still there were lot of problems which was accounted by the finite elements.
As a matter of fact, the stiffness matrix method was developed from the method of consistent deformation which was applicable only to solids.
Basically, in matrix method, the stiffness method deals with a unit displacement and the flexibility deals with a unit force.
On the other hand, the finite elements deals with the governing differential equation, be it solid, fluid, or any phenomenon.
The matrix method can’t be applied to non-linear and plastic deformation, because they involve unsymmetrical stiffness matrices, which is out of scope for the matrix method.
It is very complicated to develop the matrix method for triangular elements or something like that ( I haven’t tried it, but I suppose that it needs some rocket science). Therefore, the analysis of 2D elements is going to be a challenge in matrix method.
You can’t plot the SFD, BMD and similar curves because you don’t have any shape functions in matrix method. Well offcourse, one can use a huge number of elements but that is rubbish for a big structure.
These are the main disadvantages of the matrix method which can be easily overcome by using the finite elements and hence it is used in coding for the structural analysis packages.
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