Finite element method for frames/beams

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To implement internal hinges in a finite element method program, the stiffness matrix of the beam must be adjusted. A challenge arises when two interconnected beams share a hinge location, leading to singularity in the stiffness matrix. To address this issue, treating the hinged joint as fixed in terms of rotation can resolve the singularity problem. This approach effectively eliminates the rotational degree of freedom at the joint. The solution allows for accurate modeling of hinged joints in beam structures.
mohamadh95
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I would like to know how to implement internal hinges in a program I'm developing. A hinge is created by changing the stiffness matrix of the beam. The problem is when two interconnected beams have a hinge at the same location, so basically we have a hinged joint, in this scenario I will obtain singularity in the stiffness matrix.
I'm mainly interested in hinged joint so is there another way to do it? Thank you
 
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I actually managed to find the solution. Consider the hinged joint as fixed in terms of rotation since the rotational degree of freedom of that joint is not free anymore.
 

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