Newmark nonlinear analysis efficiently captures energy decay and exhibits a satisfactory long-term performance after being tested [15].To reduce the dynamic effects, dynamic relaxation is used in the explicit scheme. A diagonal damping matrix proportional to the mass matrix http://www.selleckchem.com/products/mek162.html is added to the dynamic equation[C]=2��T[M],(4)where �� is the relaxation value and T is the period to be damped. Thus, a viscous stress tensor is added to the stress tensor. In an explicit code, the application of the dashpot force modifies the velocity equation without relaxationVt+��t/2=Vt?��t/2+��t��t(5)to velocity equation with relaxationVt+��t/2=(1?2��)Vt?��t/2+(1??)��t��t,(6)where��=�¦�tt.(7)When this option is activated, the running time of the whole simulation is increased.

However, the damping period for the system is controlled within acceptable limits.3. Contacts and Load CasesThree different parabolic leaf spring designs were analyzed in this study. Each design was simulated with different loading cases. Therefore, different simulation boundary condition setups for the vertical push, wind-up, and roll suitable to the load case were conducted accordingly. First, the boundary conditions for the vertical push were performed with free rotation around the y-axis for the front eye, whereas the rear eye was constrained in the Y, Z translation and the X, Z rotation. The boundary conditions are complied with [21]. The center of the spring was allowed only in the X-Z translation and the Y rotation. The vertical push boundary condition setup is shown in Figure 2(a).

For the wind-up load case setup, the applied boundary conditions for the eye were similar to the vertical push with free rotation around the y axis for the front eye, whereas the rear eye was constrained in the Y-Z translation and the X-Z rotation. After maximum vertical loading is applied, a longitudinal force was created and applied at the center of the parabolic leaf springs [22]. The wind-up establishment of the parabolic leaf springs is illustrated in Figure 2(b).Figure 2Boundary conditions and loads applied: (a) vertical push, (b) wind-up.For the suspension roll study, loads are applied to push the suspension to a curb position. A moment is subsequently applied to the suspension by increasing the vertical load on the left side and decreasing the load on the right side [8].

The leaf spring is expected to hit the jounce stopper after a 40mm displacement is imposed. In this case, the load is applied at the tire patch that represents the contacts of tire to the ground. The boundary condition of the parabolic leaf spring can freely rotate around the Y axis for the front eye, whereas the rear eye is attached to the shackle, and the shackle can rotate in the y-axis Cilengitide only. The front module of conventional buses considered in this study employed an antiroll bar to enhance the roll stiffness of the vehicle.