Development of simplified models for automotive crashworthiness simulation and design using optimization

A review of the literature showed that very little had been done for identification and development of simplified models for automotive crash problems. Development of such models is desirable for use at the conceptual design stage of automotive structures for passenger safety during crash. Using these simplified models, it is possible to perform a rapid analysis and redesign for the structure. An objective of this research is to propose and develop various formulations for simplified models. General parametric and nonparametric formulations for identification of simplified models for automotive frontal crash simulation have been developed. Constraints on dynamic response of the system as well as the resistance force of the elements are included in the formulations. This had not been done before in the literature. Among the investigated cost functions, L₂, L₁ and L_∞ it is concluded that the L₂ cost function works quite well with all the proposed formulations. The proposed formulations are evaluated using single and three degree of freedom lumped mass models. The front horn of an automotive structure is simplified to a single degree of freedom model. The frontal automotive crash event is simplified to a three degree of freedom model. Although various shape functions to represent the quantities to be identified can be used, it is concluded that the Hat shape functions are quite efficient and simple to use. The representation of the resistance force of elements is more appropriate in the time domain than in the displacement domain. Force-deformation histories for nonlinear systems are not functions and so they cannot be represented with shape functions in the displacement domain. When the force-deformation histories are specified, they need to be converted to force-time histories using a simulation algorithm. The elastoplastic-collapse concept introduced for crushed tubes allows physical interpretation of the force-deformation or force-time curves. These curves are interpreted as several springs that become active at different times in a sequential manner. Using the developed formulations several redesign problems for single and three degree of freedom systems are also solved to meet the new design requirements. These force histories represent new concepts for design of structural components for automotive crash problems.