An augmented Lagrangian optimization method for inflatable structures analysis problems

1. Abstract This paper describes the development of an augmented Lagrangian optimization method for the numerical simulation of the inflation process in the design of inflated space structures. Although the Newton-Raphson scheme has proved to be efficient for solving many non linear problems, it can lead to lacks of convergence when it is applied to the simulation of the inflation process. As a result, it is recommended in the literature to use an optimization algorithm in order to find the minimum energy configuration that satisfies the equilibrium equations characterizing the final shape of the inflated structure subject to an internal pressure. Besides, given that some degrees of freedom may be linked, the optimum may be constrained. The paper presents the formulation and the augmented Lagrangian method (ALM) developed in SAMCEF Mecano for inflatable structures analysis problems. The related quasiunconstrained optimization problem is solved with a non linear conjugate gradients method. The Wolfe conditions are used in conjunction with a cubic interpolation for the line search. Equality constraints are considered and can be easily treated by the ALM formulation. Numerical applications present simulations of unconstrained as well as constrained inflation processes (i.e. where some nodes’ motion is ruled by a rigid body element restriction, and/or problems including contact conditions). 2.