Dynamics of structures

https://hal.archives-ouvertes.fr/hal-00315288/document

A high order purely frequency-based harmonic balance formulation for continuation of periodic solutions

Mechanical mismatches between implanted electronics and biological tissues can lead to inaccurate readings and long-term tissue damage. Here, we show that functionalized multi-walled carbon nanotubes twisted into helical fibre bundles that mimic the hierarchical structure of muscle can monitor multiple disease biomarkers in vivo. The flexible fibre bundles are injectable, have a low bending stiffness and display ultralow stress under compression. As proof-of-concept evidence of the sensing capabilities of these fibre bundles, we show that the fibre bundles enable the spatially resolved and real-time monitoring of H2O2 when implanted in tumours in mice, and that they can be integrated with a wireless transmission system on an adhesive skin patch to monitor calcium ions and glucose in the venous blood of cats for 28 d. The versatility of the helical fibre bundles as chemically functionalized electrochemical sensors makes them suitable for multiple sensing applications in biomedicine and healthcare. Functionalized multi-walled carbon nanotubes twisted into helical fibre bundles that mimic the hierarchical structure of muscle can be used for the long-term monitoring of multiple disease biomarkers in vivo.

Functionalized helical fibre bundles of carbon nanotubes as electrochemical sensors for long-term in vivo monitoring of multiple disease biomarkers

The Local Point Interpolation Method (LPIM) is a newly developed truly meshless method, based on the idea of Meshless Local Petrov-Galerkin (MLPG) approach. In this paper, a new LPIM formulation is proposed to deal with 4th order boundary-value and initial-value problems for static and dynamic analysis (stability, free vibration and forced vibration) of beams. Local weak forms are developed using weighted residual method locally. In order to introduce the derivatives of the field variable into the interpolation scheme, a technique is proposed to construct polynomial interpolation with Kronecker delta function property, based only on a group of arbitrarily distributed points. Because the shape functions so-obtained possess delta function property, the essential boundary conditions can be implemented with ease as in the conventional Finite Element Method (FEM). The validity and efficiency of the present LPIM formulation are demonstrated through numerical examples of beams under various loads and boundary conditions.

A local point interpolation method (LPIM) for static and dynamic analysis of thin beams

Cellular Structures in Instabilities

Discussion about parameterization in the asymptotic numerical method: Application to nonlinear elastic shells

Resume Nous proposons quelques techniques de regularisation permettant d'adapter les methodes asymptotiques numeriques (developpement en series couple avec une discretisation par elements finis) a des problemes fortement non lineaires. Des applications seront presentees pour un probleme d'elasticite avec contact, en dynamique des fluides visqueux et pour le gonflement hydraulique d'une plaque viscoplastique.

Traitement des fortes non-linéarités par la méthode asymptotique numérique

In the present work, a high order implicit technique is associated with a meshless method to model material mixing observed in friction stir welding (FSW) process. This new algorithm combines the following mathematical procedures: a time discretization, a space discretization, a homotopy transformation, a perturbation technique and a continuation method. The perturbation technique, after a time discretization, a space discretization, a homotopy transformation, transforms the nonlinear problem into a sequence of linear ones at each time. By comparison to the classical iterative algorithms, the proposed one allows obtaining very large time steps and reducing computation time by minimizing the number of tangent matrix decompositions. The strong formulation is considered to avoid the drawback of numerical integration. The resulting algorithm is well adapted to large deformations in the mixing zone nearly the welding tool. We limit ourselves to bidimensional visco-plastic problems to show the performance of the proposed algorithm by comparison to the classical incremental iterative methods.

A new algorithm based on Moving Least Square method to simulate material mixing in friction stir welding

A numerical mesh-free model applied to a strong formulation for simulating elasto-plastic structures with contact is developed in the context of large deformation. This numerical mesh-free model is based on the Asymptotic Numerical Method (ANM) which is used in the meshless collocation framework to extend its application field to elasto-plastic problems with contact. The efficiency of this model is to take into account of large deformations and to avoid the meshing distortion problem. According to (ANM) techniques, the development in Taylor series is performed to obtain a sequence of linear systems to be solved. These linear systems are then discretized by a collocation meshless approach by using the Moving Least Squares (MLS) functions and a continuation method is adopted to evaluate the solution. The unilateral contact problem is identified to boundary conditions which are replaced by force-displacement relations through a regularization technique. The performance of the proposed approach is tested on several elasto-plastic bi-dimensional examples without and with contact. The obtained results are compared to those computed by the Newton–Raphson method.

A numerical mesh-free model for elasto-plastic contact problems

In this paper a high order implicit algorithm is developed for solving instationary non-linear problems. This generic numerical method combines four mathematical techniques: a time discretization, a homotopy transformation, a perturbation technique and a space discretization. The time integration is performed by classical implicit schemes (Euler implicit for problems with a first order time derivative and Newmark for second order). The time-discretization leads to non-linear equations. In this paper a new technique is proposed to solve iteratively the latter equations. The key points in this approach are, first a high order solver based on perturbation techniques, second the possibility of choosing the iteration operator, which limits the number of matrices to be triangulated. To illustrate the performance of the proposed algorithm two examples are considered: the Korteweg-de Vries equation (KdV) and the non-linear oscillations of a 2D elastic pendulum.

Bouazza Braikat

Papers

Discussion about parameterization in the asymptotic numerical method: Application to nonlinear elastic shells

Traitement des fortes non-linéarités par la méthode asymptotique numérique

A new algorithm based on Moving Least Square method to simulate material mixing in friction stir welding

A numerical mesh-free model for elasto-plastic contact problems

A high order implicit algorithm for solving instationary non-linear problems