SUMMARYContact-impact algorithms, which are sometimes called slideline algorithms, are a computationally timeconsuming part of many explicit simulations of non-linear problems because they involve many branches, so they are not amenable to vectorization, which is essential for speed on supercomputers. The pinball algorithm is a simplified slideline algorithm which is readily vectorized. Its major idea is to embed pinballs in surface elements and to enforce the impenetrability condition only to pinballs. It can be implemented in either a Lagrange multiplier or penalty method. It is shown that, in any Lagrange multiplier method, no iterations are needed to define the contact surface. Examples of solutions and running times are given. 1NTRODUCTIONThe interaction of bodies in impact-penetration is treated by special algorithms, often called slideline algorithms, which enforce the constraint that the two bodies cannot occupy the same space at the same time. Lagrange multiplier,'. penalty' and p r~j e c t i o n~.~ techniques have all been proposed to enforce this constraint. Usually the interpenetration condition is imposed on the piecewise linear or quadratic approximation to the surfaces by the finite element mesh. For problems which include large relative motions between the two bodies and erosion of elements, it becomes difficult and time consuming to keep track of which elements should be involved in the impact calculations. This computational expense is magnified by the fact that these slideline algorithms have many branches, and hence are difficult to vectorize. In dynamic finite element programs with explicit time integration, many of the element and nodal calculations can be vectorized; therefore, if the slideline calculations are not vectorized they can consume a considerable percentage of the total computation time.In this paper, a new contact-impact procedure called the pinball algorithm is described; a short description was previously given by Belytschko and Neal.' The thrust of the pinball algorithm is to allow vectorization of as much of the slideline calculations as possible. This is accomplished by greatly simplifying both the search for the elements involved in the impact and in the enforcement of impenetrability with the use of spheres, or pinballs, embedded in the elements in the slideline calculations. The search then requires only a simple check on the distances between pinballs to determine interpenetration. A similar idea has also been used in the two-dimensional NABOR algorithm,6 but the NABOR method used an ad hoc method based on spheres for the determination of stresses in the continua and did not use a surface normal. In the pinball algorithm the Present address: Engineering

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SUMMARYAn algorithm is presented which integrates different groups of nodes of a finite element mesh with different time steps and different integrators. Since the nodal groups are updated independently no unsymmetric systems need be solved. Stability is demonstrated by showing that an energy norm of the solution decreases after every update if the time step is less than a given critical value. The element eigenvalue inequality theorem is used to give the critical time step in terms of element eigenvalues.

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Objective: Analyses of crash data have shown that older, obese, and/or female occupants have a higher risk of injury in frontal crashes compared to the rest of the population. The objective of this study was to use parametric finite element (FE) human models to assess the increased injury risks and identify safety concerns for these vulnerable populations. Methods: We sampled 100 occupants based on age, sex, stature, and body mass index (BMI) to span a wide range of the U.S. adult population. The target anatomical geometry for each of the 100 models was predicted by the statistical geometry models for the rib cage, pelvis, femur, tibia, and external body surface developed previously. A regional landmark-based mesh morphing method was used to morph the Global Human Body Models Consortium (GHBMC) M50-OS model into the target geometries. The morphed human models were then positioned in a validated generic vehicle driver compartment model using a statistical driving posture model. Frontal crash simulations based on U.S. New Car Assessment Program (U.S. NCAP) were conducted. Body region injury risks were calculated based on the risk curves used in the US NCAP, except that scaling was used for the neck, chest, and knee-thigh-hip injury risk curves based on the sizes of the bony structures in the corresponding body regions. Age effects were also considered for predicting chest injury risk. Results: The simulations demonstrated that driver stature and body shape affect occupant interactions with the restraints and consequently affect occupant kinematics and injury risks in severe frontal crashes. U-shaped relations between occupant stature/weight and head injury risk were observed. Chest injury risk was strongly affected by age and sex, with older female occupants having the highest risk. A strong correlation was also observed between BMI and knee-thigh-hip injury risk, whereas none of the occupant parameters meaningfully affected neck injury risks.Conclusions: This study is the first to use a large set of diverse FE human models to investigate the combined effects of age, sex, stature, and BMI on injury risks in frontal crashes. The study demonstrated that parametric human models can effectively predict the injury trends for the population and may now be used to optimize restraint systems for people who are not similar in size and shape to the available anthropomorphic test devices (ATDs). New restraints that adapt to occupant age, sex, stature, and body shape may improve crash safety for all occupants. ARTICLE HISTORY