**8.1. Symbols and descriptions**

c Acoustic wave speed through the material of which the element is made


[*K*] Global stiffness matrix lc Element characteristic length [M] Lumped-mass matrix n Indicates step n *x* Displacement *x*˙ Velocity *x* ¨ Acceleration t Time ∆t Timestep size

site of "DynaLook" [28]. For a better representation of an explicit dynamics simulation, **Figure**

Whole crash-worthiness studies are remarkable starting with the elementary functions of the profound methods of NCAP tests considering despite the costs of the experiments are

For a robust vehicle, the engineers should design a structure that can able to absorb some of the energy by collapsing itself or deforming to an adequate level to protect the human beings. If the structure is too rigid, there is an amplification occurs and affect everything in a poor way that is transferring the accelerations to the occupants causing worse situation. Therefore, even

Nevertheless, for diminishing the costs of the studies of FEM and explicit dynamics methods, which are proceeding under the supervision of the computers and codes verified by the longterm researches and applications, are competent to handle the complicated algorithms yielding with satisfactory results. The incidents dealing with the short duration of time are appropriate for the explicit dynamics solution technique enclosed with superior nonlinear behaviors and

Take into account the results of the experiments, analytic solutions and computerized methods are mentioned as FEM codes are robust approximations to understand the behavior of the vehicle and occupants in the course of statics, dynamics, and collisions. Consequently, the finite element method and explicit dynamics solutions have been proven to validate the

It should be clearly stated that the autonomous vehicles decreasing the risks of the collisions

for the safety and reliability, optimum way is better to protect lives against accidents.

loading velocities demanding small timesteps for more precision sequels.

experiments and real life experiences in the range between 80 and 100%.

c Acoustic wave speed through the material of which the element is made

when it is compared to the human driver controlled vehicle.

**7** demonstrates the full vehicle crash scenario [29].

enormous, contribution of the test results is challenging.

**7. Conclusion**

76 Autonomous Vehicle

**8. Nomenclature**

[C] Damping matrix

{*Fext*} External forces {*Fint*} Internal forces

**8.1. Symbols and descriptions**

{D} Nodal displacement vector

{*F*} Nodal force vector or External load vector
