Predicting the onset of shear localization is among the most challenging problems in machining. This phenomenon affects the process outputs, such as machining forces, surface quality, and machined part tolerances. To predict this phenomenon, analytical, experimental, and numerical methods (especially finite element analysis) are widely used. However, the limitations of each method hinder their industrial applications, demanding a reliable and time-saving approach to predict shear localization onset. Additionally, since this phenomenon largely depends on the type and parameters of the constitutive material model, any change in these parameters requires a new set of simulations, which puts further restrictions on the application of finite element modeling. This study aims to overcome the computational efficiency of the finite element method to predict the onset of shear localization when machining Ti6Al4V using machine learning methods. The obtained results demonstrate that the FCM (fuzzy c-means) clustering ANFIS (adaptive network-based fuzzy inference system) has given better results in both training and testing when it is compared to the ANN (artificial neural network) architecture with an R2 of 0.9981. Regarding this, the FCM-ANFIS is a good candidate to calculate the critical cutting speed. To the best of the authors’ knowledge, this is the first study in the literature that uses a machine learning tool to predict shear localization.

Losses induced by tip clearance limit decisive improvements in the system efficiency and aerodynamic operational stability of aero-engine axial compressors. The tendency towards even lower blade heights to compensate for higher fluid densities aggravates their influence. Generally, it is emphasised that the tip clearance should be minimised but remain large enough to prevent collisions between the blade tip and the casing throughout the entire mission. The present work concentrates on the development of a preliminary aero-engine axial compressor casing design methodology involving meta-modelling techniques. Previous research work at the Institute for Turbomachinery and Flight Propulsion resulted in a Two-Dimensional (2D) axisymmetric finite element model for a generic multi-stage high-pressure axial compressor casing. Subsequent sensitivity studies led to the identification of significant parameters that are important for fine-tuning the tip clearance via specific flange design. This work is devoted to an exploration of the potential of surrogate modelling in preliminary compressor casing design with respect to rapid tip clearance assessments and its corresponding precision in comparison with finite element results. Reputed as data-driven mathematical approximation models and conceived for inexpensive numerical simulation result reproduction, surrogate models show even greater capacity when linked with extensive design space exploration and optimisation algorithms.

Compared with high-fidelity finite element simulations, the reductions obtained in computational time when using surrogate models amount to 99.9%. Validated via statistical methods and dependent on the size of the training database, the precision of surrogate models can reach down to the range of manufacturing tolerances. Subsequent inclusion of such surrogate models in a parametric optimisation process for tip clearance minimisation rapidly returned adaptions of the geometric design variables.

To reveal the thermal shock resistance of double-layer thermal barrier coatings (TBCs), two types of TBCs were prepared via atmospheric plasma spraying, i.e., Gd2Zr2O7/yttria-stabilized zirconia (GZ/YSZ) TBCs and La2Zr2O7 (LZ)/YSZ TBCs, respectively. Subsequently, thermal cycling tests of the two TBCs were conducted at 1100 °C and their thermal shock resistance and failure mechanism were comparatively investigated through experiments and the finite element method. The results showed that the thermal shock failure of the two TBCs occurred inside the top ceramic coating. However, the GZ/YSZ TBCs had longer thermal cycling life. It was the mechanical properties of the top ceramic coating, and the thermal stresses arising from the thermal mismatch between the top ceramic coating and the substrate that determined the thermal cycling life of the two TBCs together. Compared with the LZ layer in the LZ/YSZ TBCs, the GZ layer in the GZ/YSZ TBCs had smaller elastic modulus, larger fracture toughness, and smaller thermal stresses, which led to the higher crack propagation resistance and less spallation tendency of the GZ/YSZ TBCs. Therefore, the GZ/YSZ TBCs exhibited superior thermal shock resistance to the LZ/YSZ TBCs.

Precise bone cut is fundamental in total knee arthroplasty. However, notching of anterior femoral is not uncommon in clinical practice. Reviewing the article, notching and its complication may reach up to 30% and 2.5%, and there is scanty study of notching on the femoral strength. We therefore conduct the finite element analysis to elucidate the effect of notching on femoral mechanical strength. The computerized tomography images were used as the basis to develop the knee model, which was assumed mainly to consist of cortical and cancellous bones. For the implant joint, Zimmer data was considered partly as the basis to develop the model. This study investigated the femoral improper cut effect on the surgery with a static standing condition. The results show that the anterior femoral cut should be undercut 2 mm to overcut 1 mm during the surgery, in order to prevent bone materials from yielding. The exposure of the cancellous bone may cause bone materials to yield when the femur overcut was 2 mm; the cancellous bone may load too much and result in a fracture when the undercut was 3 mm. The effect of undercut, which was rarely discussed, was particularly addressed in our study. Precise femoral cut is crucial for the longevity of total knee arthroplasty.

The crystal plastic theory was used to examine the effect of film-cooling hole arrangements on mechanical properties of cooled turbine blade. The finite element method was used to analyze the maximum von Mises stress and resolved shear stress of an octahedral slip system considering the number of rows, diameter, spacing, and tangential-to-longitudinal hole spacing (h/l) ratio. The different arrangements were found to have a significant influence on the maximum von Mises stress and resolved shear stress. For the triangular arrangement, the von Mises stress and resolved shear stress were highest with double rows, followed by a single row and then triple rows. For the quadrilateral arrangement, the stresses were highest with double rows, followed by triple rows and then a single row. Increasing the spacing or decreasing the diameter reduced the maximum von Mises stress and weakened the multi-hole interference effect. Both the maximum von Mises stress and resolved shear stress decreased with the h/l ratio.

In this study, continuous contact problem in the functionally graded (FG) layer loaded with two rigid flat blocks resting on the elastic semi-infinite plane was analyzed by the finite element method. The two-dimensional numerical model of the FG layer was made with the software added to the ANSYS program. This software can be adapted to all contact problem types by making minor changes. The accuracy check of the program was performed by comparing with the analytical solution of the problem by homogeneous layer and its solution by the finite element method. So, fast and practical solutions can be obtained by the developed finite element method on many applications such as; automotive, aviation and space industry applications. The comparisons made showed that the proposed solution gave good results at acceptable levels. In the problem, it was thought that all surfaces were frictionless. The external loads P and Q were transmitted to the FG layer via two flat rigid blocks. Normal stresses between the FG layer and the elastic plane, initial separation loads, initial separation distances and contact stresses under the blocks were investigated for various dimensionless quantities.

This paper describes a method to analyze open or closed elliptical structures with constant axial ratio by a Body-of-Revolution (BoR) Finite Element Method (FEM). The method is based on Transformation Optics, a coordinate transformation that maps the elliptical shape to a circular shape, for which BoR-FEM represents a greatly efficient tool for the analysis.

Surface exfoliation was observed on single-crystal silicon surface under the action of compressed plasma flow (CPF). This phenomenon is mainly attributed to the strong transient thermal stress impact induced by CPF. To gain a better understanding of the mechanism, a micro scale model combined with thermal conduction and linear elastic fracture mechanics was built to analyze the thermal stress distribution after energy deposition. After computation with finite element method, J integral parameter was applied as the criterion for fracture initiation evaluation. It was demonstrated that the formation of surface exfoliation calls for specific material, crack depth, and CPF parameter. The results are potentially valuable for plasma/matter interaction understanding and CPF parameter optimization.

This paper is devoted to the American option pricing problem governed by the Black-Scholes equation. The existence of an optimal exercise policy makes the problem a free boundary value problem of a parabolic equation on an unbounded domain. The optimal exercise boundary satisfies a nonlinear Volterra integral equation and is solved by a high-order collocation method based on graded meshes. This free boundary is then deformed to a fixed boundary by the front-fixing transformation. The boundary condition at infinity (due to the fact that the underlying asset's price could be arbitrarily large in theory), is treated by the perfectly matched layer technique. Finally, the resulting initial-boundary value problems for the option price and some of the Greeks on a bounded rectangular space-time domain are solved by a finite element method. In particular, for Delta, one of the Greeks, we propose a discontinuous Galerkin method to treat the discontinuity in its initial condition. Convergence results for these two methods are analyzed and several numerical simulations are provided to verify these theoretical results.

Anisotropic mesh adaptation is studied for linear finite element solution of 3D anisotropic diffusion problems. The 𝕄-uniform mesh approach is used, where an anisotropic adaptive mesh is generated as a uniform one in the metric specified by a tensor. In addition to mesh adaptation, preservation of the maximum principle is also studied. Some new sufficient conditions for maximum principle preservation are developed, and a mesh quality measure is defined to server as a good indicator. Four different metric tensors are investigated: one is the identity matrix, one focuses on minimizing an error bound, another one on preservation of the maximum principle, while the fourth combines both. Numerical examples show that these metric tensors serve their purposes. Particularly, the fourth leads to meshes that improve the satisfaction of the maximum principle by the finite element solution while concentrating elements in regions where the error is large. Application of the anisotropic mesh adaptation to fractured reservoir simulation in petroleum engineering is also investigated, where unphysical solutions can occur and mesh adaptation can help improving the satisfaction of the maximum principle.