A numerical method is proposed for a class of one-dimensional stochastic control problems with unbounded state space. This method solves an infinite-dimensional linear program, equivalent to the original formulation based on a stochastic differential equation, using a finite element approximation. The discretization scheme itself and the necessary assumptions are discussed, and a convergence argument for the method is presented. Its performance is illustrated by examples featuring long-term average and infinite horizon discounted costs, and additional optimization constraints.

Large truss structures have many potential applications in space, such as antennas, telescopes and space solar power plants. In this scenario, a natural concern is the susceptibility of these lightweight structures to be damaged during their operational life, due to impacts, transient thermal states and fatigue phenomena. The inclusion of active elements, equipped with sensor/actuator systems capable of modulating their shape and strength, makes it possible to transform the truss into a smart structure capable of remedying the damage, once it is detected. In this paper, a procedure is described that is capable of restoring at least the basic functionality of a composite truss for space applications, starting with the observation that damage has occurred, regardless of its specific location. The system eigenstructure is used as a benchmark for damage detection, as well as a target characteristic for the subsequent restoration activity. The observer/Kalman filter identification algorithm (OKID), in cascade with the eigensystem realization algorithm (ERA), is adopted to reconstruct, from sensor recordings, the dynamic response of the truss in terms of system state-space representation and eigen-characteristics. Finally, a static output feedback control is developed to recover the low-frequency dynamic behaviour of the truss. The entire procedure is tested using finite element analysis. All activities are coordinated in an innovative procedure that, within a unique Python language code, automatically generates finite element (FE) models, launches finite element analysis (FEA), extracts output data, implements OKID-ERA, processes the control law and applies it to the final FE simulation.

The finite element method (FEM) is widely used to simulate a variety of physics phenomena. Approaches that integrate FEM with neural networks (NNs) are typically leveraged as an alternative to conducting expensive FEM simulations in order to reduce the computational cost without significantly sacrificing accuracy. However, these methods can produce biased predictions that deviate from those obtained with FEM, since these hybrid FEM-NN approaches rely on approximations trained using physically relevant quantities. In this work, an uncertainty estimation framework is introduced that leverages ensembles of Bayesian neural networks to produce diverse sets of predictions using a hybrid FEM-NN approach that approximates internal forces on a deforming solid body. The uncertainty estimator developed herein reliably infers upper bounds of bias/variance in the predictions for a wide range of interpolation and extrapolation cases using a three-element FEM-NN model of a bar undergoing plastic deformation. This proposed framework offers a powerful tool for assessing the reliability of physics-based surrogate models by establishing uncertainty estimates for predictions spanning a wide range of possible load cases.

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.