The multigroup neutron diffusion equations are often used to model the neutron density at the nuclear reactor core scale. Classically, these equations can be recast in a mixed variational form. This chapter presents an adaptive mesh refinement approach based on a posteriori estimators. We focus on refinement strategies on Cartesian meshes, since such structures are common for nuclear reactor core applications.
Variational-hemivariational inequalities are an important mathematical framework for nonsmooth problems. The framework can be used to study application problems from physical sciences and engineering that involve non-smooth and even set-valued relations, monotone or non-monotone, among physical quantities. Since no analytic solution formulas are expected for variational-hemivariational inequalities from applications, numerical methods are needed to solve the problems. This paper focuses on numerical analysis of variational-hemivariational inequalities, reporting new results as well as surveying some recent published results in the area. A general convergence result is presented for Galerkin solutions of the inequalities under minimal solution regularity conditions available from the well-posedness theory, and Céa's inequalities are derived for error estimation of numerical solutions. The finite element method and the virtual element method are taken as examples of numerical methods, optimal order error estimates for the linear element solutions are derived when the methods are applied to solve three representative contact problems under certain solution regularity assumptions. Numerical results are presented to show the performance of both the finite element method and the virtual element method, including numerical convergence orders of the numerical solutions that match the theoretical predictions.
Molecular dynamics simulation methodology is widely used to explore numerous properties of engineering materials. This methodology is very economical and provides in-depth atomic information of materials properties like mechanical, thermal, electrical, corrosion properties, etc. In this study, a method called large-scale molecular dynamics simulation was used to look at the tensile and creep properties of a single-crystal Fe-Cr-Ni alloy. Many elements of physical metallurgy such as atomistic structural changes and dislocation activity during tensile and creep deformation have been explored. The adaptive common neighbor analysis (aCNA) and potential energy (PE) evolution have all been used to describe the atomistic placement of the Fe-Cr-Ni alloy during tensile deformation. The main results of this study could help us fully understand the atomic mechanical properties of different types of steel and similar alloys. This has helped improve the performance of engineering metals.
In this study, analysis of the variation in the stiffness of Thenar muscle for dominant and non-dominant hands is carried out using myotonometry. For this purpose, 22 young healthy right-dominant volunteers are recruited, and myotonometry signal has been bilaterally acquired from the Thenar muscle belly. The myotonometric parameters, Dynamic Stiffness (DS) and Logarithmic Decrement (LoD) has been extracted to be compared between the two hands. Bilateral association is investigated using Linear Regression analysis. The myotonometric parameters is found to be reliable with the ICC > 0.8 for DS. The stiffness is found to be higher on the dominant side when compared to the non-dominant side while there is no definitive pattern observed for LoD. The viscoelastic properties are found to be significantly different between the male and female sub groups. The results can be clinically relevant characterizing APB muscle properties in healthy condition.
The current work deals with the fundamental frequencies of porous FGM sandwich folded plates using the finite element analysis. The FEM formulation is based on First-order shear deformation theory (FSDT). The lower and the upper layers of the plate made of FGM are composed of pure metal and pure ceramic and the FGM is used for core. The present formulation is modeled using an 8-noded element along with five degrees of freedom. The output of the current analysis matches well with the benchmark methods.
The basic goal of dynamic analysis of simple structures is to forecast how a structure will respond to external excitation. One of the most crucial elements in engineering design is the material choice. Advanced composites known as functionally graded materials (FGM) is idealized using the power law to account for the continuously varying characteristics from one surface to another. The present study provides a detailed dynamic characteristic analysis of functionally graded beams (FGB) employing a unique finite element approach. A convergence analysis is conducted for the first six natural frequencies. Dynamic characteristics such as mode shapes and frequency response functions (FRF) for varying boundary conditions are reported.
The estimation of leakage in elastomeric seals has been an ill-developed area due to a lack of research that attempts to model leakage through the seal and its interface. Some recent works, however, propose methods and models such as interface crack propagation analysis and porous media-based leakage models. In this work, we compare the performance of one such model, viz. the interface crack propagation technique, in describing leakage through O-rings. Leakage data from already conducted O-ring leakage experiments are used to verify the model’s performance. It is observed that the interface crack propagation analysis is able to make reasonably agreeable predictions about the threshold pressure, which are close to the experimental results.
In recent years, quadcopters have become popular. Due to many advantages of the quadcopter, it is used widely in military and commercial applications. It consists of four propellers to produce thrust and achieve flight. In this study, an attempt is made to obtain the response characteristics of a quadcopter for different propeller configurations. A series of thrust produced by each propeller configuration is obtained using CFD analysis in Ansys workbench. The obtained thrust coefficient is given as an input to the Simulink model and the response characteristics results are drawn.
The basic purpose of an antenna is to track various frequency range signals and to communicate with the communication satellites to send or receive information. ACSS is used for tracking low earth orbit satellites and can be modelled in many ways. For accurate tracking, the antenna should be synchronous with the satellite, and feedback control is required for precision control. Simulink is used for modelling feedback control, whereas Simscape is for plant modelling which involves link dynamics. ACSS uses individual servo control for each axis and incorporates independent control of two axes of antenna mechanism. The link dynamics is modelled by taking kinematics, dynamics, and the effect of gravity into consideration. A single-axis servo control system (SASCS) is developed, followed by the dual axis servo control system and simulated for various signal trajectories. Results indicate that the rigid link closely follows the desired position, thereby confirming the validity of the proposed model.
