please see the attached image from this source: Element Library Reference.
1) What is the elastic axis? If it is the same as the neutral axis, I will not need an explanation.
2) But then, do neutral axis and gravity axis not coincide all the time? If not, do you have an example of a cross-section?
3) If the elastic axis is different from the neutral axis, please explain it + example of a cross-section.
The elastic neutral axis is at the area centre. For pure bending the longitudinal stress at that point is zero by definition. To answer your question I think the "elastic axis" is short for "elastic neutral axis".
The plastic neutral axis is generally offset from the area centre for non-symmetrical sections. Note also that the term "neutral axis" sometimes also is used to define the point with zero longitudinal stress when having combined bending and axial force. Care should therefore be paid when using the "neutral axis" term.
The gravity axis definition is used for the CBEAM element, allowing you to to define non structural mass offset from the area centre. This additional axis definition is not possible for the CBAR element.
This is my understanding. Please correct me if I am wrong.
Geir Olav Guddal