Application Of Boundary Conditions Research Articles

IGA Approximations of Elastic Interfaces and their Defects in an Elastic Medium with Couple Stress

AbstractThe objective of this work is to develop and implement a computational algorithm for calculating stress and couple-stress fields induced by bulk and interfacial line defects such as dislocations and generalized disclinations within phase/grain boundaries. The thermodynamic driving forces on line and planar defects, responsible for coupled plasticity and interface motion, fully coupled to stress, couple-stress and applied boundary conditions are also computed. A continuum approach for small deformations is considered following the formulation outlined in Acharya and Fressengeas (Continuum mechanics of the interaction of phase boundaries and dislocations in solids. In: Differential Geometry and Continuum Mechanics, pages 123–165, 2015), extended herein in the thermodynamics to accommodate physically necessary ingredients that arose in the modeling in Zhang and Acharya (J Mech Phys Solids 119:188–223, 2018), Zhang et al. (J Mech Phys Solids 114:258–302, 2018). Constitutive relations are derived from kinematics, balance laws and from the use of the second law of thermodynamics in global form. One of the challenges presented by this approach is the inclusion of couple stresses, Toupin (Arch Rational Mech Anal 17(2):85–112, 1964), and the consequent treatment of 4th order systems arising from the equations of balances of linear and angular momentum. In order to deal with these equations, the classical FEM approach is replaced by iso-geometric analysis (IGA), as proposed by Hughes et al. (Comput Methods Appl Mech Eng 194(39):4135–4195, 2005). Results on stress and couple stress fields of the various defects involved are computed. Further, the coupling of the dislocation density with the eigenwall allows for the capturing of the shear parallel to the grain boundary, which has been observed experimentally and through molecular dynamics.

Finite Element Analysis and Design Optimisation of Welding robot base using ANSYS

The study on Finite Element Analysis and Design Optimization of a welding robot base using ANSYS explores the crucial role of welding robots in enhancing industrial productivity and quality. It addresses the challenges of structural integrity, operational efficiency, and durability under harsh conditions. The research focuses on optimizing the robot base design to withstand high production demands, using ANSYS for detailed modelling and simulation. It reviews previous studies highlighting the importance of vibrational characteristics and structural dynamics in robot design. The methodology involves creating a geometric model, defining material properties, meshing, and applying boundary conditions and loading scenarios. The results indicate that the optimized design significantly improves stress distribution, reduces deformation, and enhances the dynamic response, making the robot base more robust and reliable. The study concludes with recommendations for broader applications in robotic systems to improve safety and productivity in industrial settings.

Applying the Adomian Method to Solve the Fokker–Planck Equation: A Case Study in Astrophysics

The objective of this study is to model astrophysical systems using the nonlinear Fokker–Planck equation, with the Adomian method chosen for its iterative and precise solutions in this context, applying boundary conditions relevant to data from the Rossi X-ray Timing Explorer (RXTE). The results include analysis of 156 X-ray intensity distributions from X-ray binaries (XRBs), exhibiting long-tail profiles consistent with Tsallis q-Gaussian distributions. The corresponding q-values align with the principles of Tsallis thermostatistics. Various diffusion hypotheses—classical, linear, nonlinear, and anomalous—are examined, with q-values further supporting Tsallis thermostatistics. Adjustments in the parameter α (related to the order of fractional temporal derivation) reveal the extent of the memory effect, strongly correlating with fractal properties in the diffusive process. Extending this research to other XRBs is both possible and recommended to generalize the characteristics of X-ray scattering and electromagnetic waves at different frequencies originating from similar astronomical objects.

Parallel isogeometric boundary element analysis with T-splines on CUDA

We present a framework for parallel isogeometric boundary element analysis (BEA) of elastic solids on CUDA. To deal with traction discontinuities, we propose a BEA model that supports multiple nodes and semi-discontinuous elements. The multiplicity of a node is defined by the number of regions containing any element influenced by the node. A region is a group of connected elements delimited by a closed crease curve. The default shape function of an element is determined by a linear operator applied to a set of basis functions. A BEA model is supposed to be generated from a watertight boundary representation of a solid. In this paper, we employ bicubic analysis-suitable T-splines. In this case, the shape of an element is defined by its Bézier extraction operator applied to the tensor product of Bernstein polynomials of degree 3. We describe the data structures of the BEA model and the main algorithms of the analysis pipeline on CUDA. In particular, we describe two strategies for parallel assembling of the linear system of equations. We also introduce a novel approach for inside integration based on the subdivision of the singular region in triangles with constant aspect ratio. In the T-splines context, we extend the Bézier extraction to handle unstructured T-meshes with crease edges. Moreover, we propose a scheme for embedding the influence of linked tangency handles on the shape of an element directly into the Bézier extraction operator. Such an embedding enables the removal of the corresponding nodes from the BEA model and the application of an alternative collocation method we discuss in the paper. We present several experiments to evaluate the accuracy and efficiency of the proposed framework. The results demonstrate that the GPU can be advantageously employed for parallelizing T-spline-based isogeometric analysis using boundary elements, achieving a speedup of up to 29x compared to the sequential code on a current laptop. We make the BEA code available in a prototype in MATLAB with a graphical interface that allows users to apply boundary conditions and visualize analysis results on the boundary.

An approximate solution of the Blasius problem using spectral method

This paper aims at finding the numerical approximation of a classical Blasius flat plate problem using spectral collocation method. This technique is based on Chebyshev pseudospectral approach that involves the solution is approximated using Chebyshev polynomials, which are orthogonal polynomials defined on the interval [−1, 1]. The Chebyshev pseudospectral method employs Chebyshev- Gauss- Lobatto points, the extrema of the Chebyshev polynomials. The differential equation is approximated as a sum of Chebyshev polynomials. A differentiation matrix, based on these polynomials and their derivatives at the collocation points, transforms the differential equation into a system of algebraic equations. By evaluating the differential equation at these points and applying boundary conditions, the original boundary value problem reduced the solution to the solution of a system of algebraic equations. Solving for the coefficients of the polynomials yields the numerical approximation of the solution. The implementation of this method is carried out in Mathematica and its validity is ensured by comparing it with a built in MATLAB numerical routine called bvp4c.

In-Plane and Out-of-Plane Bending Vibration Analysis of the Laminated Composite Beams Using Higher-Order Theories

In this paper, higher-order shear deformation theories for a thorough analysis of the in-plane and out-of-plane vibrational characteristics of laminated composite beams have been presented. Through the introduction of new displacement fields and the consideration of rotary inertia and Poisson's effect, the kinetic and potential energies of the beams have been derived. This formulation, displaying significant generality, accommodates arbitrary stacking sequences. Utilizing the finite element method, a new element has been presented for calculating the beam's vibrational characteristics. Featuring three nodes, each with seven degrees of freedom, this higher-order element provides a detailed representation of complex behaviors. Mass and stiffness matrices have been derived using the energy method and apply boundary conditions through the penalty approach. The results exhibit a high degree of consistency and alignment with those obtained from the 3D commercial software ANSYS, validating the accuracy and reliability of the proposed methodology for structural analysis. This comprehensive approach contributes to advancing the understanding and modeling of laminated composite beams in diverse engineering applications. The effects of different parameters on the in-plane and out-of-plane vibration analysis of laminated composite beams have been investigated in detail.

Variational approaches to the elasticity of deformable strings with and without mass redistribution

AbstractThe catenary is a curve that has played a significant role in the history of mathematics, finding applications in various disciplines such as mechanics, technology, architecture, the arts, and biology. In this paper, we introduce some generalizations by applying the variational method to deformable strings. We explore two specific cases: (i) in the first case, we investigate the nonlinear behavior of an elastic string with variable length, dependent on the applied boundary conditions; specifically, this analysis serves to introduce the variational method and demonstrate the process of finding analytical solutions; (ii) in the second case, we examine a deformable string with a constant length; however, we introduce mass redistribution within the string through nonlinear elastic interactions. In the first scenario, the deformation state of the string always describes elongation, as compression states prove to be unstable for fully flexible strings. In contrast, in the second scenario, the finite length constraint induces compressive states in specific configurations and regions of the string. However, it is worth noting that the solution to this problem exists only for values of the elastic constant that are not too low, a phenomenon that is studied in detail. We conduct here both analytical and graphical analyses of various geometries, comparing the elastic behavior of the two aforementioned types of strings. Understanding the elastic behavior of deformable strings, especially the second type involving mass redistribution, is crucial for enhancing comprehension in the study of biological filaments or fibers and soft matter. For instance, these investigations can contribute to understanding the mechanisms employed by cells to sense gravity or other mechanical conditions.

A development of a surface frost prediction model for hydrogen fueling nozzle

This study presents a simulation model to predict the nozzle surface freezing phenomenon that causes delays in refueling hydrogen vehicles. Nozzle surface freezing is known to occur when vehicles are refueled consecutively. The developed model allows consecutive refueling of vehicles and incorporates the actual nozzle material to accurately calculate the nozzle surface temperature. The simulation results indicate that, under the applied boundary conditions, the nozzle surface temperature reaches freezing conditions during the third refueling cycle, suggesting the potential suitability of using hot air or nitrogen after the second refueling. Future applications include exploring different boundary conditions in the developed hydrogen refueling model to simulate internal refueling pressure, temperature and nozzle icing conditions. This optimisation could facilitate decision making for the implementation of hot air or nitrogen, which could potentially reduce refueling time and contribute to cost savings at hydrogen refueling stations, depending on specific environmental conditions.

Extremization to fine tune physics informed neural networks for solving boundary value problems

We propose a novel method for fast and accurate training of physics-informed neural networks (PINNs) to find solutions to boundary value problems (BVPs) and initial boundary value problems (IBVPs). By combining the methods of training deep neural networks (DNNs) and Extreme Learning Machines (ELMs), we develop a model which has the expressivity of DNNs with the fine-tuning ability of ELMs. We showcase the superiority of our proposed method by solving several BVPs and IBVPs which include linear and non-linear ordinary differential equations (ODEs), partial differential equations (PDEs) and coupled PDEs. The examples we consider include a stiff coupled ODE system where traditional numerical methods fail, a 3+1D non-linear PDE, Kovasznay flow and Taylor–Green vortex solutions to incompressible Navier–Stokes equations and pure advection solution of 1+1 D compressible Euler equation.The Theory of Functional Connections (TFC) is used to exactly impose initial and boundary conditions (IBCs) of (I)BVPs on PINNs. We propose a modification to the TFC framework named Reduced TFC and show a significant improvement in the training and inference time of PINNs compared to IBCs imposed using TFC. Furthermore, Reduced TFC is shown to be able to generalize to more complex boundary geometries which is not possible with TFC. We also introduce a method of applying boundary conditions at infinity for BVPs and numerically solve the pure advection in 1+1 D Euler equations using these boundary conditions.

Comparative thermal assessment and emission analysis of various green biodiesel from novel feedstocks for CI engines: a sustainable approach towards emission reduction.

In order to replace conventional diesel, biodiesel from various feedstocks is being researched for diesel engines. This study explores novel biodiesel blends produced from unconventional resources such as mentha piperita (peppermint), pontederia crassipes (water hyacinth), tamarindus indica (tamarind), and trichosanthes cucumerina (snake gourd) to assess the outcomes of a diesel engine. The fuel samples are designated as MP20, PC20, TC20, and TI20, which consist of 80% biodiesel and 20% diesel. The assessment is carried out on a four-stroke, one-cylinder diesel engine that is water-cooled and set to operate at 1500rpm with a 17.5 compression ratio under various engine loading scenarios with quarter-incremental loading from one-fourth to full loading conditions. The fuel samples are injected with 220bar injection pressure into the combustion chamber 23° before TDC. An extensive analysis of engine parameters is performed using engine configuration, fuel characteristics, and applied boundary conditions. This comprises brake-specific energy consumption (BSEC), fuel consumption (BSFC), thermal efficiency (BTE), cylinder pressure (CP), heat release rate (HRR), particulate matter (PM), nitrogen oxide (NOx), and carbon dioxide (CO2) emissions. At 100% load, the biodiesel blends show an increase in BSFC (2.8-12.6%) and BSEC (1.1-7.1%) but a minor decrease in CP (0.9-6.9%), HRR (0.8-16.2%), and BTE (1.2-2.9%). For biodiesel blends at full engine load, the emissions of PM (8.9-21.4%), NOx (1.4-16.2%) and CO2 (2.4-7.9%) are all significantly reduced. The results emphasize the distinct benefits of biodiesel blends, demonstrating enhanced engine performance and substantial decreases in emissions, which supports the aim of providing sustainable energy solutions.

Performances of the sandwich panel structures under fire accident due to hydrogen leaks: Consideration of structural design and environment factor using FE analysis

Abstract This study presents a comprehensive analysis using the finite element method (FEM) to examine and evaluate the behavior of fuel carrier ship structure. Sandwich panels are effective structures for use in ship structures due to their lightweight yet robust nature. Sandwich panels used in ship structures have various core shapes, such as hexagonal, circular, and square, as needed. The sandwich panel structure can be widely implemented in ship construction, for example, on the deck, hull, and bulkhead of the ship’s cabin. Hydrogen is an alternative fuel that can replace fossil fuels. In this modern era, hydrogen is high valuable energy commodity, so accidents involving carrier ships could have significant consequences. Hydrogen is produced from liquefied natural gas (LNG), so if a leak occurs, for instance, in a storage tank or fuel tank, it has the potential to lead to accidents such as fires. Corrosion is a significant concern for the maritime industry, as it can jeopardize the structural integrity of these vessels and pose substantial safety and environmental risks. In this research, FEM was utilized to model and simulate the effects of corrosion on hydrogen carrier ships when exposed to fire, considering various environmental and operational factors. Through a systematic investigation, it is aimed to gain insights into the impact of corrosion on ship structural components during fires, such as hulls and storage tanks. The result of this study will contribute to improving corrosion and fire mitigation strategies, ensuring the safety and longevity of hydrogen and LNG carrier ships, and supporting the sustainable transportation of hydrogen to meet global energy demands. No research has been conducted on the structural behavior resulting from hydrogen fires and corrosion simultaneously. To achieve this, it is assumed to use the corrosion properties of steel in heavily traveled ship routes such as the Panama Canal Zone, Barent Sea, North Sea, and Suez Canal Zone. This study utilized an approach by modeling corrosion using shell thickness in Abaqus Quasi-Static and applying boundary conditions in the form of temperature increase up to 800°C and subsequent cooling back to the initial temperature. At the maximum temperature, the most significant mid-span displacement occurred in the circular core sandwich panel, with a value of 4 mm. The axial force in the structure was inversely proportional to the mid-span displacement. In the case of the circular core sandwich panel, the axial force was 96 kN. The most resilient core type was hexagonal because it experiences the least deformation when compared to circular and square cores.

Physics‐informed neural network assisted automated design of power amplifier by user defined specifications

AbstractThis article presents a model that can automatically produce a power amplifier's (PA) design parameters, that is, transmission lines (TLs) dimension, from a dataset of user‐specified design goals like gain, efficiency, linearity, and scattering (S‐) parameters. Based on the applied boundary conditions, a synthetic dataset is generated with the best range of design parameters (W and L). This dataset is utilized for training the physics‐informed neural network (PINN) model with user‐specified design goals as input and design parameters as target to produce the optimum value of W and L as the resultant output. Furthermore, utilizing the obtained dimensions, design, simulation, fabrication, and measurement of a PA are performed to validate our proposed model. The results of large signal measurements of PA are drain efficiency (DE) of 26.9%, power added efficiency (PAE) of 24.7%, output power (Pout) of 30.98 dBm at an input power of 19 dBm, and gain of 12.41 dB at an operating frequency of 1.625 GHz. It has been observed that the design parameters produced by the model have a significant agreement with the validated output. Also, the statistical error analysis is done by calculating the error metrics between the validated output and the actual output of the PA design.

Numerical modeling and analysis of fluid-filled truncated conical shells with ring stiffeners

This study uses a hybrid finite element method to predict dynamic behavior of truncated conical shells with ring stiffeners under fluid loading. The proposed approach combines classical shell theory and the finite element method, making use of displacement functions derived from exact solutions of Sanders’ shell equilibrium equations for conical shells. The analysis of the shell-fluid interface involves leveraging the velocity potential, Bernoulli’s equation, and impermeability conditions to determine an explicit expression for fluid pressure. To the best of our knowledge, this paper is the first to compare the methods applied to ring-stiffened shells against other numerical and experimental findings. Our results on conical shells in various conditions, with and without ring stiffeners, are largely consistent with previous findings. This study also explores the influence of geometric parameters, stiffener quantity, cone angle, and applied boundary conditions on the natural frequency of fluid-loaded ring-stiffened conical shells. The paper concludes with a discussion of several useful implications for further research.

Boosting energy levels in graphene magnetic quantum dots through magnetic flux and inhomogeneous gap

We study the effects of a magnetic flux and an inhomogeneous gap on the energy spectrum of graphene magnetic quantum dots (GMQDs). By considering the Dirac equation in the infinite mass framework, we can analytically obtain eigenspinor expressions. By applying boundary conditions, we obtain an energy spectrum equation in terms of system parameters such as radius, magnetic field, energy, flux, and gap. In the infinite limit, we recover Landau levels for graphene in a magnetic field. We show that the energy spectrum increases significantly in the presence of flux and a gap inside the GMQDs, which prolongs the lifetime of the trapped electron states. We show that higher flux also produces new Landau levels of negative angular momentum. Meanwhile, we find that the gap increases the separation between the electron and hole energy bands. As shown in the radial probability analysis, flux and gap emerge as influential factors in controlling electron mobility, affecting confinement, and prolonging the presence of quasi-bound states.

Experimental investigation of the oscillation threshold to limit state operation of a single branch pulsating heat pipe

The study investigates the characteristics of oscillations and associated thermo-hydrodynamic phenomena for startup, limit state, and intermediate transitional behavior of a pulsating heat pipe (PHP) with the help of its single branch. Experiments are performed on a transparent single branch PHP (SBPHP) at different orientations, evaporator and condenser section temperatures using n-pentane as the working fluid. The entire two-phase flow behavior is recorded with the help of shadowgraph based high speed imaging synchronized in real-time domain with pressure data acquisition at evaporator end. Instability threshold is determined in terms of evaporator temperature at different tube orientations and condenser temperatures. The oscillation startup mechanism along with the associated intermittency is studied in detail. The SBPHP is found to have characteristic variations in oscillation amplitude and frequency as it undergoes a gradual transition from its oscillation threshold to limit state. The mechanism by which the limit state creeps-in and intumesces further is an intrinsic function of liquid-vapor distribution in SBPHP, which in turn depends on the applied boundary conditions. The operational limit is governed by evaporator dryout exceeding permissible limits marked by the steep rise in the dry length of evaporator. As SBPHP approaches or operates at its limit state, evaporator is found to have different regimes across its length, viz., mild convective evaporation combined with subcooled nucleate boiling, saturated nucleate boiling, forced convective boiling, film breakdown and permanent dryout. The liquid film distribution, pressure fluctuations, and heat transfer components in evaporator at the limit state have also been studied.

Enhancing Sensitivity of Double-Walled Carbon Nanotubes with Longitudinal Magnetic Field

In this study, the behavior of double-walled carbon nanotubes (DWCNTs) used as mass sensors is explored under various boundary conditions; particular attention is paid to the crucial topic of resonant nanomechanical mass sensors. In the presented approach, nanotubes are subjected to a distributed transverse magnetic force and supported by an elastic foundation. The impacts of the longitudinal magnetic field, elastic medium, and diverse physical parameters on the responsiveness of the sensors are assessed. Using the energy method, governing equations are formulated to determine the frequency shifts of the mass nanosensors. Our findings reveal significant variations in the frequency shifts due to a longitudinal magnetic field, which depends on the applied boundary conditions. This research holds significance in the design of resonant nanomechanical mass sensors and provides valuable insights into the interplay of factors affecting their performance. Through exploring the intricate dynamics of DWCNTs used as mass sensors and thus contributing to the broader understanding of nanoscale systems, the implications for advancements in sensor design are offered and applications are introduced.

Natural frequencies and modal shapes of folded sandwich plates made of porous core and FG-CNTRC coating layers resting on two parameters elastic foundation

Folded structures hold significant importance in aerospace technology due to their distinct design, effectively reconciling strength with a lightweight framework. Within aerospace applications, these structures fulfill diverse roles, serving as pivotal elements in aircraft wings, fuselage sections, and essential components of spacecraft and satellites. This study delves into the free vibration behavior of folded sandwich plates composed of a porous core and functionally graded carbon nanotube-reinforced composite (FG-CNTRC) coatings, resting on a two-parameter elastic foundation. Leveraging first-order shear deformation plate theory (FSDT), elasto-dynamic equations are established for each individual plate segment. Utilizing the two-dimensional generalized differential quadrature method (2D-GDQM), these equations are discretized. Subsequently, by applying boundary conditions to all six edges, including traditional clamped, simply supported, and free configurations, and incorporating continuity conditions for displacements, forces, and moments at the joint borders, natural frequencies and modal shapes are extracted for the folded plate structure. The validity of the proposed formulation and results is demonstrated by comparing them with numerical examples for both composite flat and folded plates. This comparison provides strong support for the accuracy and reliability of the present study. The study comprehensively examines the influence of various parameters on natural frequencies, including modal shape visualizations under different boundary configurations, plate thickness, crank angle, porosity parameter, core thickness, foundation stiffness, and CNTs distribution type.

Optimization and Analysis of Drive Shaft Using CAE Tools

Drive shaft or propeller shaft is the essential part of Automobiles. It is used to deliver torque from transmission to the differential and further to the wheel to cause the motion of the vehicle. The drive shaft is used to connect with the transmission shaft with the help of universal joint whose axis intersects and the rotation of one shaft about its own axis results in the rotation of the other shaft about its axis. In present work the model of the drive shaft has been generated in Solid works and further imported in ANSYS workbench. A finite element analysis of the drive shaft has been carried out as a case study. In the present work the static analysis of a drive shaft has been carried out with the new design changes. The results for equivalent von-Mises stress, strain and deformation have been calculated by applying boundary conditions and compared with the existing results.

Numerical Solution of Eighth Order Two Point Boundary Value Problems by Taylor Series Method

A Taylor series method which is taught at undergraduate levels and which has been hitherto used for the solution of initial value problem is successfully used in this work for the solutions of eighth-order two point boundary-value problems. The method is based on successive differentiation of the governing equation to obtain high order derivatives and then evaluated at the boundary point x=a. The solution is expressed inform a Taylor series with the unknown coefficients at a point x=a. By applying boundary conditions at x=b in the Taylor series solution, the system of unknown coefficient is obtained. After solving the system, then unknown coefficient are determined. The procedure is applied on both linear and nonlinear boundary-value problems. A comparison of the results obtained by the present method with results obtained by other methods reveals that the present method is simple, effective and also is in good agreement with the previous result and exact solution as showing in the tables and figures.

Computation of TM Scattered Fields Induced by a Truncated Semi-Elliptic Cavity in a PEC

This study investigated the scattered transverse-magnetic (TM) electromagnetic field from a truncated semi-elliptic embedded in a perfectly electric conducting plane. Boundary value analysis and the region-point-matching technique are employed to address the issues considered. The analyzed region is divided into three sub-regions, after which the tangential fields are expanded in terms of Mathieu functions into two different coordinate systems. By applying boundary conditions at two auxiliary boundaries and using the region-pointmatching technique, several independent equations are constructed and subsequently simplified to generate a system of linear equations. For the validation of the obtained results, the suggested procedure is compared to the method of moment. Finally, the effects of cavity depth and incident angle on the scattering signature are inspected.