Abstract
After discussing possible sources of non-linearities, the subject is discussed for the case of non-linear constitutive equations and spatially one-dimensional problems. Developing FEM for non-linear boundary value problems leads eventually to systems of non-linear algebraic equations and the use of Newton’s method for solving such systems is demonstrated. The commonly applied approach for controlling convergence of Newton’s method by employing a time or pseudo time incrementation procedure, respectively, with nested iteration loop is laid out. Numerical integration employing Gauss integration is discussed together with its benefits regarding the separation of spatial discretisation and material routines.
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Mühlich, U. (2023). Non-linear Boundary Value Problems. In: Enhanced Introduction to Finite Elements for Engineers. Solid Mechanics and Its Applications, vol 268. Springer, Cham. https://doi.org/10.1007/978-3-031-30422-4_4
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DOI: https://doi.org/10.1007/978-3-031-30422-4_4
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