Optimization in a Class of Relaxation Moduli for Linearly Viscoelastic Materials.
CALIFORNIA UNIV SAN DIEGO LA JOLLA DEPT OF THE AEROSPACE AND MECHANICAL ENGINEERING SCIENCES
Pagination or Media Count:
Optimization of relaxation functions E for linearly viscoelastic materials is considered for a one-dimensional problem which is suggested by desirable performance of a lap-seat belt in automobiles. An optimum relaxation modulus E bar of the belt is sought which would permit the speed v sub 0 of the vehicle prior to an abrupt impact to have maximum value v bar sub 0 under certain constraints imposed for the safety of the user of the belt. A class c star of costfunctions is defined on the deceleration u that is imposed by the belt on the user. For given c belongs to c star, the post-impact constraints imposed are 1 the maximum displacement of the body must not exceed a critical displacement, 2 the forward speed of the body, if and when at the critical displacement, should not exceed a prescribed maximal value v sub f, and 3 the values of c during the motion of the body must not exceed an allowed maximal value cmax. Optimization of E is sought in a defined class of relaxation moduli, constructed so as to limit the rubbery moduli to values not exceeding a specified, relatively low value, thus contributing to the comfort of the passenger during non-crash conditions. It is shown in the paper, for each c belongs to c star, that constraints 1 and 2 are both active if the E bar material is employed at the maximal speed v bar sub 0. In addition, it is shown that constraint 3 is active for any c of a certain subset of c star. Author
- Surface Transportation and Equipment
- Safety Engineering
- Solid State Physics