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This work addresses the determination of yield surfaces for geometrically exact elastoplastic rods. Use is made of a formulation where the rod is subjected to an uniform strain field along its arc length, thereby reducing the elastoplastic problem of the full rod to just its cross-section. By integrating the plastic work and the stresses over the rod’s cross-section, one then obtains discrete points of the yield surface in terms of stress resultants. Eventually, Lamé curves in their most general form are fitted to the discrete points by an appropriate optimisation method. The resulting continuous yield surfaces are examined for their scalability with respect to cross-section dimensions and also compared with existing analytical forms of yield surfaces.

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Abstract. We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget" remaining to satisfy each constraint; the augmented Hamilton-Jacobi-Bellman PDE is then solved numerically. The efficiency of our approach hinges on the causality in that PDE, i.e., the monotonicity of characteristic curves in one of the newly added dimensions. A semi-Lagrangian "marching" method is used to approximate the discontinuous viscosity solution efficiently. We compare this to a recently introduced "weighted sum" based algorithm for the same problem [25]. We illustrate our method using examples from flight path planning and robotic navigation in the presence of friendly and adversarial observers. Section 1. Introduction.In the continuous setting, deterministic optimal control problems are often studied from the point of view of dynamic programming; see, e.g., [1], [8]. A choice of the particular control a(t) determines the trajectory y(t) in the space of system-states Ω ⊂ R n . A running cost K is integrated along that trajectory and the terminal cost q is added, yielding the total cost associated with this control. A value function u, describing the minimum cost to pay starting from each system state, is shown to be the unique viscosity solution of the corresponding Hamilton-Jacobi PDE. Once the value function has been computed, it can be used to approximate optimal feedback control. We provide an overview of this classic approach in section 2.However, in realistic applications practitioners usually need to optimize by many different criteria simultaneously. For example, given a vehicle starting at x ∈ Ω and trying to "optimally" reach some target T , the above framework allows to find the most fuel efficient trajectories and the fastest

A finite element (FE) formulation is presented for a direct approach to model elastoplastic deformation in slender bodies using the special Cosserat rod theory. The direct theory has additional plastic strain and hardening variables, which are functions of just the rod's arc-length, to account for plastic deformation of the rod. Furthermore, the theory assumes the existence of an effective yield function in terms of stress resultants, that is, force and moment in the cross-section and cross-section averaged hardening parameters. Accordingly, one does not have to resort to the three-dimensional theory of elastoplasticity during any step of the finite element formulation. A return map algorithm is presented in order to update the plastic variables, stress resultants and also to obtain the consistent elastoplastic moduli of the rod. The presented FE formulation is used to study snap-through buckling in a semicircular arch subjected to an in-plane transverse load at its midsection. The effect of various elastoplastic parameters as well as pretwisting of the arch on its load-displacement curve are presented.

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