Local Parameterization and the Asymptotic Numerical Method

The Asymptotic Numerical Method (ANM) is a family of algorithms, based on computation of truncated vectorial series, for path following problems [2]. In this paper, we present and discuss some techniques to define local parameterization [4, 6, 7] in the ANM. We give some numerical comparisons of pseudo arc-length parameterization and local parameterization on non-linear elastic shells problem

Buckling and lateral buckling interaction in thin-walled beam-column elements with mono-symmetric cross sections

International audienceEffects of axial forces on beam lateral buckling strength are investigated here in the case of elements with mono-symmetric cross sections. A unique compact closed-form is established for the interaction of lateral buckling moment with axial forces. This new equation is derived from a non-linear stability model. It includes first order bending distribution, load height level and effect of mono-symmetry terms (Wagner's coefficient and shear point position). Compared to the so-called three-factors (C-1-C-3) formula commonly employed in beam lateral buckling stability, another factor C-4 is added in presence of axial loads. Pre-buckling deflection effects are considered in the study and the case of doubly-symmetric cross sections is easily recovered. The proposed solutions are validated and compared to finite element simulations where 3D beam elements including warping are used. The agreement of the proposed solutions with bifurcations observed on the non-linear equilibrium paths is good. Dimensionless interaction curves are dressed for the beam lateral buckling strength and the applied axial load, where the flexural-torsional buckling axial force is a taken as reference

A mesh-free approach for the simulation of incompressible flows

In this work, we propose to investigate numerically the incompressible flows by the Asymptotic Numerical Method (ANM) with the Moving Least Square (MLS). The mathematical formulation is based on theNavier-Stokes equations written in a strongly formulation to avoid all difficulties of the numerical integration. The used algorithm is developed to investigate the effective of the ANM with the MLS in the strongly formulation

Variational Problems for Föppl--von Kármán Plates

Some variational problems for a Föppl--von Kármán plate subject to general equilibrated loads are studied. The existence of global minimizers is proved under the assumption that the out-of-plane displacement fulfils homogeneous Dirichlet condition on the whole boundary while the in-plane displacement fulfils nonhomogeneous Neumann condition. If the Dirichlet condition is prescribed only on a subset of the boundary, then the energy may be unbounded from below over the set of admissible configurations, as shown by several explicit conterexamples: in these cases the analysis of critical points is addressed through an asymptotic development of the energy functional in a neighborhood of the flat configuration. By a Gamma-convergence approach we show that critical points of the Föppl--von Kármán energy can be strongly approximated by uniform Palais--Smale sequences of suitable functionals: this property leads to identifying relevant features for critical points of approximating functionals, e.g., buckled configurations of the plate. The analysis for rescaled thickness is performed by assuming that the plate-like structure is initially prestressed, so that the energy functional depends only on the out-of-plane displacement and exhibits asymptotic oscillating minimizers as a mechanism to relax compressive states

Vibration of composite thin-walled beams with variable open cross section by a high order implicit algorithm

In this work, we study the forced nonlinear vibrations with large amplitude and large torsion of composite thinwalled beams with open variable cross sections under external dynamic loads using a high order implicit algorithm. The used algorithm is based on the temporal and spatial discretizations, the homtopoy transformation, Taylor series expansion and the continuation technique. A 3D beam element with two nodes and seven degrees of freedom per node is adopted. The obtained results are compared with those computed by the industriel Abaqus code