**2.1 Dynamic and static loading**

An important definition to establish is the difference between static and dynamic loading. In theory, a load is static when time is not considered at its application and, therefore, inertial reaction of bodies is not part of the calculation. In practice, pure static load does not exist, since the load will require an amount of time to be applied at a body. In physical environment, a load can be considered static when not producing relevant inertial effects to the system.

**Figure 1** shows two beams with the same length and section. The beams are constrained at the left extremity and have an actuator applying force at the right extremity. The actuators are applying the same F force in both beams; however, the actuator on the left is applying the F force in a large amount of time, which is not enough to produce any relevant inertial effect to the system and therefore can be considered static. The actuator on the right is applying the F force but in a small amount of time, which creates relevant inertial effects to the system and therefore can be considered dynamic.

### **2.2 The chosen structures and the method for analysis**

The structure-mechanism chosen for our study in this chapter is a torsion axle and the pure structure a sub-frame. Both are structures of the same system, a commercial vehicle. The system "vehicle" was chosen here for a reason, to submit the two structures to the same loading condition. The geometries in this chapter are simplified

**Figure 1.**

*Comparison between two beams under a force with the same magnitude but different duration of application.*

**Figure 2.**

*Torsion axle—High displacement structure. The geometry was conceived using a topology optimization algorithm just for this study.*

#### **Figure 3.**

*Sub-frame—Pure structure. The geometry was also conceived using a topology optimization algorithm just for this study.*

models created only for academic purposes, based on the same characteristics of the original models. They have the same mass, stiffness, and normal modes of the real torsion axle and sub-frame. The geometries were developed using topology optimization algorithms in order to maintain the same mentioned physical and mechanical properties. The models are conceived in finite element shell based (CQUAD4 elements) on structural analysis required in this chapter (stress/strain for fatigue and modal). The material considered for the structures is common steel, both with the same fatigue properties in order to make the comparisons of this study consistent (**Figure 2**).

The torsion axle is a common component present in commercial vehicles, used to support the entire suspension system (usually the rear suspension), since all suspension parts are attached to it, such as springs, shocks, and wheels. It performs also as a stabilizer beam, linking the left side to the right.

The sub-frame (**Figure 3**), also known as cradle, is a part of the vehicle used to attach the entire front suspension framework. It transmits all forces that came from the road from suspension to the body of the vehicle, and it has no relative movement between its points of interface. Uniquely in contrast to the torsion axle, it does not act as a stabilizer bar; in fact, in many vehicle designs, the sub-frame supports a stabilizer bar.
