Cohesive Elements for Shells

A cohesive element for shell analysis is presented. The element can be used to simulate the initiation and growth of delaminations between stacked, non-coincident layers of shell elements. The procedure to construct the element accounts for the thickness offset by applying the kinematic relations of shell deformation to transform the stiffness and internal force of a zero-thickness cohesive element such that interfacial continuity between the layers is enforced. The procedure is demonstrated by simulating the response and failure of the Mixed Mode Bending test and a skin-stiffener debond specimen. In addition, it is shown that stacks of shell elements can be used to create effective models to predict the inplane and delamination failure modes of thick components. The results indicate that simple shell models can retain many of the necessary predictive attributes of much more complex 3D models while providing the computational efficiency that is necessary for design

Effects of punishment in a mobile population playing the prisoner’s dilemma game

We deal with a system of prisoner’s dilemma players undergoing continuous motion in a two-dimensional plane. In contrast to previous work, we introduce altruistic punishment after the game. We find punishing only a few of the cooperator-defector interactions is enough to lead the system to a cooperative state in environments where otherwise defection would take over the population. This happens even with soft nonsocial punishment (where both cooperators and defectors punish other players, a behavior observed in many human populations). For high enough mobilities or temptations to defect, low rates of social punishment can no longer avoid the breakdown of cooperation

On the structure of cooperative and competitive solutions for a generalized assignment game

We study cooperative and competitive solutions for a many- to-many generalization of Shapley and Shubik (1972)'s assignment game. We consider the Core, three other notions of group stability and two al- ternative definitions of competitive equilibrium. We show that (i) each group stable set is closely related with the Core of certain games defined using a proper notion of blocking and (ii) each group stable set contains the set of payoff vectors associated to the two definitions of competitive equilibrium. We also show that all six solutions maintain a strictly nested structure. Moreover, each solution can be identified with a set of ma- trices of (discriminated) prices which indicate how gains from trade are distributed among buyers and sellers. In all cases such matrices arise as solutions of a system of linear inequalities. Hence, all six solutions have the same properties from a structural and computational point of view.