Holding one end of a rod and pulling on the other end with a load P results in a change in length of the rod. This is a tensile stress which acts along the entire rod. Think of the complicated shape as a much simpler shape and solve the problem for the simpler shape. Solve some very messy partial differential equations from theory of elasticity. Use finite element analysis.
Finite elements are really neat.
They are used to approximate the real-world structure. It is important to realize that finite elements, no matter how good, are only approximations. For example, the equations for elastic displacement are of the 4th order. This simply means that there are basic assumptions about how the displacements change across an element from one node to another. In finite element analysis, the displacements are generally computed first.