Optimization in a Class of Relaxation Moduli for Linearly Viscoelastic Materials.
Abstract
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1971
- Accession Number
- AD0731114
Entities
People
- J. B. Schipmoelder
- W. Nachbar
Organizations
- University of California, San Diego