Inertia relief in a pick-up truck

A 1994 Chevrolet C1500 pick-up truck (see Figure 1) is modeled using approximately 55,000 elements. The model was obtained from the Public Finite Element Model Archive of the National Crash Analysis Center at George Washington University. The finite element model was converted into an Abaqus/Standard input file, and several missing constraints were added to carry out the analyses. The model consists of various parts—such as cabin, truck bed, doors, etc.—which are meshed with shell elements, three-dimensional beam elements, and three-dimensional solid elements. The parts are attached with connector elements, coupling elements, and multi-point constraints.

The materials used in the truck model are idealized as elastic or elastic-plastic. Suitable adjustments are made to the material properties to account for unmodeled features of various parts such as the internal details of the engine, gearbox, etc. A summary of the material properties and the parts for which they are used is given in Table 1 and Table 2.

Rigid body definitions are used for brakes and brake assemblies to take advantage of the high stiffness of these parts relative to other parts. Connector elements are used to model kinematic constraints governing relative motions between various parts (see Substructure analysis of a pick-up truck model for details).

The finite element model of the truck is oriented such that the positive 1-direction goes from the rear to the front of the truck, the positive 2-direction goes from the passenger (right-hand) side to the driver (left-hand) side, and the positive 3-direction is upward. In this system the braking loads are applied at the respective wheel spindles as concentrated forces in the negative 1-direction.

To simplify the analysis, normal contact between the tires and the road surface is modeled through spring elements that have one node connected to the wheel spindle and the other node fixed against displacement in the 3-direction and kinematically constrained to the wheel spindle in the other directions. Friction between the tires and the road surface is assumed to be nonexistent. This allows the truck to translate freely in the 1- and 2-directions and rotate freely about the 3-direction; the constraints on the spring nodes prevent translation in the 3-direction and rotation about the 1- and 2-directions.

A separate static analysis is performed to obtain the correct initial configuration and stress distribution under the applied gravity load. The details of this analysis are explained in Substructure analysis of a pick-up truck model. This gives us the base state for the analysis of interest.

The total braking load for the truck moving at 13.89 m/s is computed by assuming the truck to be a rigid body that comes to rest over a distance of 20 m after the brakes are applied. This gives a deceleration of 4.82 m/s² in the 1-direction for the truck. The total mass of the truck as computed from the finite element analysis is 1.72 × 10³ kg, which gives the total inertial force resisted by the brakes (or braking load) as 8.30 kN. Assuming that the front brakes provide 75% of the total resistance and the rear brakes provide the remaining 25%, the braking load for each of the front wheels is 3.11 kN and the braking load for each of the rear wheels is 1.04 kN. The four braking loads applied to the truck are balanced in a static analysis with an inertia relief load. The inertia relief load represents the dynamic effects (not modeled otherwise in a static analysis) of a constant deceleration from the truck's travel velocity to a complete stop.

Since the truck is free to translate in the 1- and 2-directions and rotate about the 3-direction, inertia relief is performed in these three directions. The other directions are constrained by boundary conditions as explained in the previous section.

For comparison purposes a transient dynamic analysis is also performed (after the initial static equilibrium under gravity load) in which the truck is accelerated from zero velocity to the final uniform velocity of 13.89 m/s. This dynamic analysis step is followed by another dynamic analysis step in which the braking loads are applied to bring the truck to a complete stop. The braking loads are ramped up smoothly from zero to the maximum value over 0.5 seconds and then kept constant for 2.88 seconds—the time required to bring the truck to rest from the initial velocity of 13.89 m/s with an average deceleration of 4.82 m/s². To minimize the analysis time, substructures are used in the dynamic analysis for all deformable parts except the chassis and suspension components, which are modeled as fully deformable since they are the parts that show significant stresses.