What happens to resultant displacement URES if force "F" is increased to 2xF with an unchanged mesh?

The correct answer focuses on the relationship between force and displacement in a linear analysis scenario. When the force acting on a structure is doubled and the mesh remains unchanged, the resultant displacement, or URES, will also double if the analysis is linear and there are no sources of nonlinearity present in the system.

In linear elastic materials, Hooke's Law applies, which states that the displacement is directly proportional to the applied force. Therefore, under these conditions, if the force is increased to 2xF and there are no changes in material behavior or structural interactions that would introduce nonlinearity, the resultant displacement will indeed be doubled.

However, if nonlinearity is introduced due to factors like large deformations or complex contact interactions, this direct proportionality may not hold true, potentially affecting resultant displacements in unpredictable ways. Since option D explicitly states the conditions necessary for doubling URES, it is deemed the most accurate choice in this context.