Vol 3 - Issue 2

Uncertainties and Reliability of Multiphysical Systems

List of Articles

Fluid mechanics describes the physical phenomena of fluids which are often governed by partial derivative equations namely the continuity equation and the Navier-Stokes equation. The resolution of these equations using conventional methods encounters certain difficulties when it comes to dealing with problems where the geometry of the medium is complex or when there are several phases of a fluid or several fluids [TAO 16]. The current trend is towards a new approach to simulation research [CFD], which has gained a lot of popularity in recent years, it is called in English
"Lattice Boltzmann Method" (LBM), which is a relatively new development in the Computational fluid dynamics [CFD]. The lattice Boltzmann method is a method of fluid dynamics (CFD). Instead of the Navier-Stokes equations, the Boltzmann discrete equation is solved to simulate the behavior of fluids using a collision-propagation scheme. In this work, the LBM was integrated in a python code in order to simulate in 2D the behavior of a pipe flow against an obstacle, which will be used later to determine in the pipes the most solicited zones (maximum velocity and maximum pressure) to better size both the pipe and its accessories (valve, etc.) and prevent their rapid degradation.

Review of the capabilities of multibody simulation models and their short comings are discussed in this article. Finally an attempt was made to evolve a methodology which leads to dynamically efficient robust design of mechanical systems like gear box.

Austin-Moore hemiarthroplasty had been critically utilized for aged patients with femoral neck fractures. However, this implant became no longer favorable when increasing life activity. A multiobjective shape optimization has been integrated to improve its performance. The resulting configuration is called Improved Austin-Moore (IAM) model. Probabilistic analysis is very important when the input data are random, that leads to stochastic results. In this paper, a probabilistic analysis is applied to solid and IAM stems implanted in a proximal femur in order to show their advantages. This way it is possible to control the biomechanical effects of the implanted femur to determine its performance. The applied loads are generated randomly using Monte Carlo Simulations (MCS). MSC sampling technique is applied and the different von-Mises stresses of the layers (bone and metal) are selected as performance indicators. Two simple 2D implant-bone models of the solid and IAM designs are studied with a target reliability index
equals to  3 t , which corresponds to a high level of confidence (reliability) 99.87%. The major finding of this article is that the skewness values of all output parameters of the IAM stem are positive which means that the majority of the maximum von-Mises stress values are closer to their minimum values than those associated with the solid stem. In addition, the sensitivity analysis shows that the input parameters for the IAM stem are more effective on the output
parameters relative to those associated with the solid stem. The IAM stem shows a high interdependence (correlation) between the input and output parameters when comparing with the solid stem. Since this study is carried out considering loading uncertainty, the geometry can affect the load transfer. Therefore, a correlation study between the input parameters is carried out and showed significant coefficient values for the IAM stem relative to the solid one. The results show that the IAM stem is much more advantageous than the solid stem.

The reliability analysis is used to in order to measure the stability of the mini-plate fixation system used in the human fractured mandibles after the chirurgical operation. The failure is assumed to take place when the Most Probable failure Point (MPP) is found. In this work, two studied cases of 3-dimensional finite element models are considered for the same fracture situation. A successful fracture healing requires that a number of constraints which are influenced by the loading conditions are fulfilled, and since muscle activity is difficult to evaluate, there is a strong need to introduce loading uncertainties in order to obtain a reliable design. Several categories of critical failure scenarios are considered in this study: The first category of failure scenarios is that of the relative displacement between two fracture surfaces should not exceed a critical threshold to ensure rapid healing. The second category is failure of the mini-plates which in this work is interpreted as when the yield stress within the mini-plates is reached, and the third category of failure scenarios is that of the yield stress in the mandible bone tissues should not be exceeded. Two fractured mandibles are studied under the convalescence period: Case I (a single isotropic bone tissue) and Case II (composite anisotropic bone tissues). During the fixation of the mini-plates, the drilling positions in the two cases can vary when considering a composite bone tissue mandible relative to a homogeneous bone tissue one. To show the effect of the bone anisotropy, an analytical formulation is developed as a helpful technique to analyze the effect of the mini-plate position changes. The bone properties used in the anisotropic case (Case II) are orthotropic. The results show that the reliability indices are very affected when considering the bone anisotropy.