[Erikhfp]

I've always wondered how point loads are handled in FEAs. Theoretically, a point load will have infinite strain but when a point load is applied the strain is not infinite, why is this? How does the software prevent the strain solution for the node to which the load is applied from going to infinity?

Another question I have is how reliable will the displacements be when a 1D element is fixed to a 3D element and a purely axial load is applied to the 1D element?

[karachun]

Software calculates stiffness matrix for all DOF`s - degrees of freedom of nodes, then loads applied and displacements of nodes calculated. Stress/strains calculated at some points of integration from displacement of nodes. All loads can be applied only to nodes, loads applied to element faces are translated to nodes by solver. So, stress/strains is more like postprocessing and it is calculated for some part of element (4 nodes tetra element have only one point of integration so after calculation it will have one value of stress for whole volume).
But you are right - applying load only at one node in model lead to singularity - if you refine mesh you get larger stress and it will tend to infinite stress if mesh size tends to zero.
For second question - nodes of solid elements have only 3 translational dof`s. So, to constrain solid model you should constrain at least 3 nodes than don’t lying on line. To get rotational dos you can add coincident plate elements or use rigid elements like RBE2.