Continuous Boundary Conditions Research Articles

A two-dimensional semi-analytic solution on two-layered liquid sloshing in a rectangular tank with a horizontal elastic baffle

A semi-analytic study on two-layered liquid sloshing in a horizontal excited two-dimensional rectangular tank with a horizontal elastic baffle was performed. The present work is a further development of the semi-analytical technique for solving the single-layer liquid sloshing problem. The horizontal elastic baffle was located in the lower liquid or upper liquid. First, the complex liquid domain in a baffled tank was divided into several simple sub-domains to solve the analytic solution. The wet mode of a horizontal baffle was presented according to the Eulerian Bernoulli beam. The continuity boundary condition on the interfaces between two liquids and the virtual interfaces was given. Then, the formal solution was derived for each sub-domain and a horizontal baffle using the superposition principle and the method of separation of variables. Then, the total velocity potential subject to lateral excitation was summed over the container potential function and the liquid disturbance potential. The dynamic response equation for two-layered liquid sloshing was established. Multiple methods verified the semi-analytic solution's correctness and agreed well with other methods. Finally, the numerical analysis mainly shows that the density ratio becomes more significant for the coupled frequency when the baffle is in the upper liquid. A large baffle's width suppresses the liquid flow in the baffled tank effectively. Furthermore, adjusting the baffle and the layered liquid parameters can significantly suppress layered liquid sloshing. For the seismic response, the elevation energy is mainly located after 2.5 s.

Application of improved physics-informed neural networks for nonlinear consolidation problems with continuous drainage boundary conditions

Application of improved physics-informed neural networks for nonlinear consolidation problems with continuous drainage boundary conditions

Development of numerical scheme using boundary element method for heat conduction problems

This paper deals with the boundary element method solution of set of parabolic differential equations of heat conducting problems with continuous and discontinuous boundary conditions. Time-dependent terms have been used as a non-homogeneous forcing function by changing a parabolic differential equation into a Poisson's equation. The suggested approach for solving the Poisson equation has been modified which decreases the number of algebraic equations and reduces the computational time. The constant coefficient matrix and LU decomposition provide an economical means for the solution of the concern problem. The discretization of the boundary of parabolic differential equations with respect to (w.r.t.) time is one of the main features of this article. Direct determination of unknown at interior points is also trademark of the proposed method. The method has been supported by examples, which include discontinuous boundary conditions and non-homogeneous forcing terms to highlight its effectiveness and accuracy.

A semi-analytical method for vibro-acoustic characteristics of orthogonal stiffened laminated cylindrical shells

This paper presents a semi-analytical model for vibro-acoustic characteristics of submerged orthogonal stiffened laminated cylindrical shells strengthened with orthogonal stiffeners. The first-order shear deformation theory (FSDT) combined with the Lekhnitsky smeared stiffener technique is adopted to describe the displacement field, and the spectral boundary element method is utilized to model the sound field. For modeling of a complex stiffened shell, the shell is divided into several main structures with the additional stiffness and mass of the smeared stiffeners. Then, the main structure is separated into sub-segments that match the boundary elements to ensure high accuracy of acoustic calculations. The continuous boundary conditions between sub-segments are simulated by using the artificial spring technique. The Fourier series and Legendre orthogonal polynomials are selected as admissible functions to describe the displacement field and the sound field. The vibration governing equations and Helmholtz integral equation are coupled with each other and solved simultaneously. High accuracy is demonstrated by comparing the results of the developed model with the literature. In numerical investigations, the influences of different external fluids, layup schemes, quantities and shapes of stiffeners (width and height) on vibro-acoustic characteristics of orthogonal stiffened laminated cylindrical shells (OSLCS) are investigated.

Analytical modeling of contaminant transport along sloping coastal beaches in presence of tidal waves and exponential rainfall infiltration

Coastal beaches are the most important part of the marine environment and are highly influenced by the interactions taking place between groundwater and surface water of any form. Generally, the purity index of the groundwater is based on the concentration of Total Dissolved Solids (TDS) in it. Analytical solutions are the best tools for groundwater flow and transport modeling. However, contaminant transport along the sloping coastal beaches with complex boundaries cannot be addressed with available analytical solutions. In the present study, new analytical models are developed for groundwater flow and contaminant transport for sloping coastal beaches with continuity and tidal boundary conditions. To assess the performance of the new analytical solution and to validate the range of aquifer parameters, numerical simulation is performed using Du-Fort Frankel (DFF) Scheme. Numerical experimentation is carried out using the Tchebycheff and L2 norms. It is observed that the new analytical solution for the contaminant transport gives acceptable results over the wide range of the aquifer parameters. To show the effectiveness of the developed models, two case studies from Indian coastal aquifers namely, Kalpakkam, Tamil Nadu, and Bhavnagar, Gujarat are considered. The profiles of the contaminant concentration are obtained to study the TDS behavior along these complex coastal beaches in the spatiotemporal directions. The results are compared with numerical model results and found to be satisfactory. The combined effect of the initial rainfall and rainfall decay constants showed a significant impact on the concentration of TDS. TDS concentrations are observed to be varying highly with the variation in the tidal constituents and bed slope.

Meshless generalized finite difference method with a domain-selection method for solving degenerate boundary problems

This paper is dedicated to presenting a combined Generalized Finite Difference Method (GFDM) and Domain-Selection Method (DSM) approach for solving degenerate boundary problems which are usually encountered in engineering simulations. Compared with traditional Domain-Decomposition Method (DDM), the most critical advantage of the present GFDM-DSM is that it is entirely free from matching continuous boundary conditions for different parts of the fluid domain of interest, which is sometimes hard to perform for specific situations. Instead, the only prerequisite of the present GFDM-DSM is to identify which sub-domain each computational node belongs to, and then a linear algebraic system can be assembled according to the pattern of domain-selection. Four benchmarks are performed to validate the convergence and accuracy of the present GFDM-DSM. It is shown that the present GFDM-DSM holds satisfactory accuracy for solving degenerate boundary problems. In particular, the present DSM is a flexible strategy since it can be also combined with other localized domain-type meshless methods in practical applications.

Airway Resistance and Respiratory Distress in Laryngeal Cancer: A Computational Fluid Dynamics Study.

Obstructive upper airway pathologies are a great clinical challenge for the airway surgeon. Protection against acute obstruction is critical, but avoidance of unnecessary tracheostomy must also be considered. Decision-making regarding airway, although supported by some objective findings, is largely guided by subjective experience and training. This investigation aims to study the relationship between clinical respiratory distress and objective measures of airway resistance in laryngeal cancer as determined by computational fluid dynamic (CFD) and morphometric analysis. Retrospective CT and clinical data were obtained for series of 20 cases, defined as newly diagnosed laryngeal cancer patients who required admission or urgent airway surgery, and 20 controls. Cases and controls were matched based on T-staging. Image segmentation and morphometric analysis were first performed. Computational models based on the lattice Boltzmann method were then created and used to quantify the continuous mass flow, rigid wall, and constant static pressure inlet boundary conditions. The analysis demonstrated a significant relationship between airway resistance and acute obstruction (OR 1.018, 95% CI 1.001-1.045). Morphometric analysis similarly demonstrated a significant relationship when relating measurements based on the minimum cross-section, but not on length of stenosis. Morphometric measurements also showed significance in predicting CFD results, and their relationship demonstrated that airway pressures increase exponentially below 2.5 mm. Tumor subsite did not show a significant difference, although the glottic subgroup tended to have higher resistances. Airway resistance analysis from CFD computation correlated with presence of acute distress requiring emergent management. Morphometric analysis showed a similar correlation, demonstrating a radiologic airway assessment technique on which future risk estimation could be performed. 4 (case-control study) Laryngoscope, 133:2734-2741, 2023.

Scattering of aggregated multi-layered biological cells by Bessel beams

Interactions between collective multi-layered cells and an off-axis high-order Bessel beam (HOBB) are investigated. The generalized Lorenz-Mie theory is applied to derive the expansion of HOBB. Based on the additional theorem, multiple scattering of collective multi-layered nanoparticles is obtained by considering the tangential continuous boundary conditions. The present theory and codes are proven to be effective by comparing with the simulations obtained from the computer simulation technology (CST) software. Numerical results concerning the effects of beam order, beam conical angle, spherical layer number, core radius and outer layer radius, outer layer refractive index and the spherical number on the scattering of various types of aggregated multi-layered particles are displayed in detail, which may provide critical support for analytically understanding the optical scattering characteristics of aggregated multi-layered biological cells of complex shapes and may find important applications in manipulating multi-layered biological structures.

Analysis of One-Dimensional Consolidation for Double-Layered Soil with Non-Darcian Flow Based on Continuous Drainage Boundary

The boundary drainage performance controls the rate of pore water discharge in the soil and plays an important role in the prediction of soil consolidation and settlement. Based on a continuous drainage boundary that can reflect the change of boundary drainage performance with time, a one-dimensional consolidation model of double-layered soil considering non-Darcian flow is established. The finite-difference method and semianalytical method are used to solve the consolidation equation, and the reliability of the two methods is verified by comparing with existing solutions. Based on the proposed solution, the consolidation behaviors of the double-layered soil are explored in depth through a systematic parametric study. The results show that, if the time effect of drainage boundary and the influence of non-Darcian flow are ignored, the estimated consolidation rate is relatively fast in the whole consolidation stage. The non-Darcian flow has a greater influence on soil consolidation under the continuous drainage boundary condition compared with that under the traditional drainage boundary condition. The consolidation rate of the foundation can be improved by appropriately increasing the permeability of the underlying soil layer or decreasing the compressibility of the underlying soil layer.

Analytical solution of horizontal SV wave response considering pile shear deformation and soil free-field shear stress

An analytical solution is developed to investigate the horizontal SV wave responses of end-bearing pile considering shear deformation of Timoshenko beam and soil free-field shear stress. Firstly, the beam used is a Timoshenko beam that is more in line with the actual engineering project, in which taken into account the additional deflection caused by the bending and shear deformation of the pile. Meanwhile, the conditional transformation method is used to transform the coupled equation controlled by the two independent variables of displacement and rotation angle in the beam model into the decoupled governing equation. Then, the impedance of the soil to the pile under horizontal SV wave is obtained based on the fixed bottom and free top boundaries of the soil, and the continuous boundary conditions of the pile-soil interface. Furthermore, the closed solution of the problem is obtained according to the relationship of the governing equation of Timoshenko beam, the interaction between pile and soil, and the fixed bottom and free top boundaries of the end-bearing pile. In addition, the free vibration and forced vibration of the present solution are compared with the commercial finite element software ABAQUS and the existing analytical solutions of Euler beam to verify the rationality of the present analytical solution. Finally, the influence of soil free-field shear stress and pile shear deformation are emphatically analyzed. The results have certain guiding significance for engineering structure design.

One-dimensional nonlinear rheological consolidation analysis of soft ground under continuous drainage boundary conditions

This work presents an upgraded one-dimensional (1D) nonlinear rheological system of soft ground consolidation. In the system, the boundaries are characterized by the time-dependent drainage boundary conditions at the surface and bottom of the layer. Meanwhile, the modified UH relationship and non-Newtonian index flow model are used to simulate the viscous effect of clay and the flow of excess pore-water during consolidation, respectively. Then, two numerical discretization formats of the system, namely the finite volume method (FDM) and finite difference method (FVM), are given, and corresponding calculation programs are compiled. The model solutions have been validated by degraded analytical solutions, FDM and FVM comparison solutions, and available laboratory data. Further, the consolidation behaviour under different model parameters is illustrated. The calculated results indicate that the change of interface parameters and flow mode does not influence the final foundation settlement, but both significantly affect the overall dissipation process of EPWP of soils. At last, an efficient method for determining CDB parameters is proposed and verified by available test data.

Theoretical research and simulation of GaAs nanowire arrays in reflection-type photon-enhanced thermionic emission solar converters

In this paper, GaAs was used as the cathode of the photon-enhanced thermionic emission (PETE) solar converter. Based on the one-dimensional continuity equation and boundary conditions, a reflection-type PETE theoretical model was established to simulate the effects of solar concentration, electron affinity, cathode temperature and electron recombination velocity on the current density and the conversion efficiency. For optimizing the performance of the solar converter, we used GaAs nanowire (NW) arrays as the cathode and calculated the influences of NW arrays’ period, duty ratio, and height on the absorbance and the conversion efficiency by combining the theoretical model with the three-dimensional finite-difference time-domain (3D FDTD) method. The results were used to design the structure size of NW arrays, which improved the conversion efficiency of the solar converter to 23.07%. It shows that the GaAs NW arrays are promising PETE cathode materials.

Space-Time Finite Element Method for Fully Intrinsic Equations of Geometrically Exact Beam

In this paper, a space-time finite element method based on a Galerkin-weighted residual method is proposed to solve the nonlinear fully intrinsic equations of geometrically exact beam which are first-order partial differential equations about time and space. Therefore, it is natural to discretize it in time and space simultaneously. Considering the continuity and intrinsic boundary conditions in the spatial direction and the continuity and periodic boundary conditions in the time direction, the boundary value scheme of space-time finite element for solving the full intrinsic equations is derived. This method has been successfully applied to the static analysis and dynamic response solution of the fully intrinsic equations of nonlinear geometrically exact beam. The numerical results of several examples are compared with the analytical solution, existing algorithms, and literature to illustrate the applicability, accuracy and efficiency of this method.

Analysis of one-dimensional consolidation of fractional viscoelastic saturated soils under continuous drainage boundary conditions

Analysis of one-dimensional consolidation of fractional viscoelastic saturated soils under continuous drainage boundary conditions

Wellbore Integrity After a Blowout: Stress Evolution Within the Casing-Cement Sheath-Rock Formation System

A robust evaluation of the casing-cement sheath-rock formation system is foundational in ensuring wellbore integrity throughout a well's lifecycle. Analytical theory for a multi-layer, thick-walled cylinder is used to evaluate the aggregate stress distributions within the casing-cement sheath-rock formation system, honoring boundary conditions of radial stress and displacement continuity. These stress distributions are adjusted for scenarios that a well may experience in its lifetime. Each layer of the casing-cement sheath-rock formation system is evaluated separately against various possible mechanical failure mechanisms, all of which can compromise wellbore integrity.A blowout scenario after a mismanaged loss-of-well-control situation induces high stress loads in the casing-cement sheath-rock formation system, with the wellbore pressure rapidly decreasing during post-blowout discharge, followed by a rapid increase following successful well capping. Casing and cement sheath failures can expose the surrounding rock formation to the pressurized fluid inside the wellbore, risking hydrocarbons broaching the surface, or the seafloor. The aggregate stress distribution model is applied on a case study performed using parameters from the MC 252–1 “Macondo Well” blowout from April 20, 2010 in the deepwater Gulf of Mexico. The stress evolution suggests stability against mechanical failure mechanisms within the casing (collapse/burst and tensile/compressive), cement-sheath (inner or outer debonding, and shear cracking), and rock-formation layers (longitudinal or transverse tensile fracture initiation, along with shear-slippage along pre-existing faults in the near-well vicinity), throughout the blowout aftermath. Nevertheless, tendencies towards radial cracking and disking (tensile) failures were indicated for the cement-sheath layer as the system reaches radial stress and displacement continuity, after cement setting.

An exact solution for vibration analysis of pipe coupled with conical-ring stiffened cylindrical shells with arbitrary boundary condition

In this paper, an analytical impedance synthesis method (ISM) is proposed to analyze the vibration characteristics of a pipe-hull coupled system, in which the hull of a submarine can be simplified to a combined conical-stiffened cylindrical-hemisphere shell. Wave solution and power series solution are used to describe the displacement of cylindrical and conical shell respectively. Rib stiffened and bulkhead are modeled as annular plate and circular plate. Based on exact general solutions, the impedance matrix of each segment is established separately and assembled in the global coordinate by displacement continuity and force balance boundary conditions. Natural frequency and forced responses are compared with open literature and FEM results to verify the correctness of the method. In the numerical examples, the effects of direction of external force and stiffness of support on the forced vibration characteristics are discussed, which can provide some guides for acoustic design of pipe in submarine.

Application of the method of continued boundary conditions to the solution of the problems of wave diffraction on various types of scatterers with complex structure

The article considers the application of the method of continued boundary conditions to the two-dimensional problem of diffraction of electromagnetic waves by a dielectric body with a cross section of complex geometry and to the problem of diffraction by a Janus sphere in the form of a permeable sphere partially covered by an absolutely soft or an absolutely rigid spherical screen. The results of calculating the scattering pattern for a large set of bodies of different geometry, including fractal-like scatterers, are obtained. It is illustrated that in the case of a smooth body boundary, the algorithm based on the Fredholm equations of the 1st kind makes it possible to obtain results with greater accuracy than for equations of the 2nd kind. The correctness of the method was confirmed by verifying the implementation of the optical theorem for various bodies and by comparing with the results of calculations obtained by other methods.

Theoretical analysis and experimental research of photon-enhanced thermionic emission solar energy converters with InN photocathode

In this study, an InN photocathode consisting of ZnO nanowire arrays was proposed as a cathode for a photon-enhanced thermionic emission (PETE) solar energy converter. To optimize the performance of the device, we applied InN with a phonon bottleneck effect to the PETE converter. The theoretical model for PETE conversion with this complex photocathode was developed based on one-dimensional continuous equations and boundary conditions. We simulated and analyzed the conversion efficiency as a function of operating temperature, solar concentration, surface electron affinity, and operating voltage. Furthermore, we verified the feasibility of the proposed cathode through experiments on the current-voltage characteristics of the InN photocathode at different temperatures. The results of simulations and experiments indicated that InN is a promising photocathode material and may enable high-performance PETE devices. • An InN photocathode consisting of ZnO nanowire arrays is proposed and applied to a PETE solar converter. • By using one-dimensional continuity equations, the theoretical model with this complex photocathode is deduced. • The relationships between PETE conversion efficiency of InN photocathode and various parameters are simulated and analyzed. • The feasibility of the proposed cathode is verified by experiments on the I-V characteristics at different temperatures.

Smoothness of Generalized Solutions of the Second and Third Boundary-Value Problems for Strongly Elliptic Differential-Difference Equations

In this paper, we investigate qualitative properties of solutions of boundary-value problems for strongly elliptic differential-difference equations.Earlier results establish the existence of generalized solutions of these problems. It was proved that smoothness of such solutions is preserved in some subdomains but can be violated on their boundaries even for infinitely smooth function on the right-hand side. For differential-difference equations on a segment with continuous right-hand sides and boundary conditions of the first, second, or the third kind, earlier we had obtained conditions on the coefficients of difference operators under which there is a classical solution of the problem that coincides with its generalized solution. Also, for the Dirichlet problem for strongly elliptic differential-difference equations, the necessary and sufficient conditions for smoothness of the generalized solution in Hölder spaces on the boundaries between subdomains were obtained. The smoothness of solutions inside some subdomains except for ε-neighborhoods of angular points was established earlier as well. However, the problem of smoothness of generalized solutions of the second and the third boundary-value problems for strongly elliptic differential-difference equations remained uninvestigated.In this paper, we use approximation of the differential operator by finite-difference operators in order to increase the smoothness of generalized solutions of the second and the third boundary-value problems for strongly elliptic differential-difference equations in the scale of Sobolev spaces inside subdomains.We prove the corresponding theorem.

Free vibration analysis of a spinning functionally graded spherical–cylindrical–conical shell with general boundary conditions in a thermal environment

Based on the first-order shear deformation theory (FSDT) for shells, the free vibration of a spinning functionally graded (FG) spherical–cylindrical–conical (SCC) shell with arbitrary boundary conditions subjected to a thermal environment is investigated. The centrifugal forces, the Coriolis forces, and the initial hoop tension caused by spin are all considered in the theoretical modeling. The model is analyzed using the domain decomposition method. The penalty method is used to model the continuity and arbitrary boundary conditions. Validity study is performed by comparing with the results from finite element analyses for special cases. Finally, the effects of the power-law index, the temperature loads, the spinning speed, and the geometrical parameters on the free vibration characteristics, as well as the influences of structural configuration on the critical spinning speed, are investigated. It is found that the configuration of a spinning SCC shell has significant effect on its natural frequency and critical speed under a fixed shell weight. The natural frequencies approximately converge into three values with increases in the circumferential wave number. The FG–SCC shell’s cone angles at which the minimum and maximum natural frequencies occur are not affected by the spinning speed and the power-law index.