Autoclave cure simulation of composite structures applying implicit and explicit FE techniques

Simulation of the autoclave manufacturing technique of composites can yield a preliminary estimation of induced residual thermal stresses and deformations that affect component fatigue life, and required tolerances for assembly. In this paper, an approach is proposed to simulate the autoclave manufacturing technique for unidirectional composites. The proposed approach consists of three modules. The first module is a Thermo-chemical model to estimate the temperature and the degree of cure distributions in the composite part during the cure cycle. The second and third modules are a sequential stress analysis using FE-Implicit and FE-Explicit respectively. User-material subroutine is used to model the Viscoelastic properties of the material based on theory of micromechanics

The genesis and early developments of Aitken\u2019s process, Shanks\u2019 transformation, the \u3b5\u2013algorithm, and related fixed point methods

In this paper, we trace back the genesis of Aitken\u2019s \u3942 process and Shanks\u2019 sequence transformation. These methods, which are extrapolation methods, are used for accelerating the convergence of sequences of scalars, vectors, matrices, and tensors. They had, and still have, many important applications in numerical analysis and in applied mathematics. They are related to continued fractions and Pad\ue9 approximants. We go back to the roots of these methods and analyze the original contributions. New and detailed explanations on the building and properties of Shanks\u2019 transformation and its kernel are provided. We then review their historical algebraic and algorithmic developments. We also analyze how they were involved in the solution of systems of linear and nonlinear equations, in particular in the methods of Steffensen, Pulay, and Anderson. Testimonies by various actors of the domain are given. The paper can also serve as an introduction to this domain of numerical analysis