Rotational Boundary Conditions Research Articles

Effects of boundary conditions on RC beams subjected to accidental thermal load in nuclear power plants

Reinforced concrete (RC) beams in nuclear safety related structures should be designed for accidental thermal gradient combined with mechanical loads. Design capacity and structural behavior of those beams are affected by constraint boundary conditions at beam ends. In design approaches widely used in nuclear power plants (NPPs), it is commonly assumed that the thermal curvature of a RC member is fully constrained while axial constraint condition is often not specified. In this paper, RC beams with various constraint boundary conditions that are subjected to accidental thermal gradient combined with mechanical loads are studied using both experimental tests and nonlinear finite element (NLFE) models. Both rotational and axial stiffness ratios at boundary and their effects on thermal moments and ultimate flexural capacity of RC beam are evaluated. Results shows that the assumption of a fully constrained rotational boundary condition is practically accurate for most RC beams in NPPs subjected to thermal gradient. On the other hand, results also show that axial constraint boundary condition has considerable influence on both thermal moment and usable design flexural strength thus neglecting its effect may lead to insufficient design of RC beam. In addition, this study established relationship between axial constrain stiffness ratio and thermal moment, as well as relationship between axial constrain stiffness ratio and usable design flexural strength for different accidental temperature gradients and reinforcement ratios. That information can be used for correction of thermal moment and usable design flexural strength in design practice.

Solute dynamics of a hydrophobic molecule in a menthol-thymol based type-V deep eutectic solvent: effect of composition of the components.

Type-V deep eutectic solvents (DESs) are a newly emerging unique class of solvents obtained by physical mixing and heating of non-ionic components. These solvents show deviation from the thermodynamic ideality. Compared to type-I to IV DESs, type-V DESs are less explored and their physical chemistry is in its nascent stage. In this work, we have chosen a type-V DES based on menthol-thymol (MT) for our working media. Solvent and rotational dynamics were studied with varying temperature using a well-known solvatochromic probe, Coumarin 153 (C153). We prepared the MT-based DES using a reported procedure at three molar ratios: 1 : 1 (M1T1), 1 : 1.5 (M1T1.5), and 2 : 1 (M2T1) of menthol (M) and thymol (T). Time-resolved emission spectra (TRES) were constructed with varying temperature. Utilizing TRES, the decay of the solvent correlation function (C(t)) was plotted. We have correlated the solvent relaxation time in these DESs as a function of viscosity. The time-resolved anisotropy decays were also collected to perceive the rotational relaxation dynamics of C153 as a function of temperature. The decay of solvent relaxation was found to be bi-exponential, and the average solvation time (〈τs〉) in M2T1 was found to be longer than those of M1T1.5 and M1T1. The rotational reorientation times (〈τrot〉) also follow the same trend. We have analysed the rotational dynamics of C153 in type-V DESs employing the Stokes-Einstein-Debye (SED) hydrodynamic model. The rotational dynamics in DESs demonstrate a good correlation with the SED model with a little deviation. In MT-based DESs, the solute's rotational relaxation times approach hydrodynamic stick boundary condition at low viscosity (or at high temperatures) for all molar compositions. Using the Arrhenius-type equations, we have correlated the activation energies for the rotational motion of C153, along with the viscous flow and non-radiative pathways for all the DESs.

Radiation hydrodynamical self-similar accretion disc winds

ABSTRACT Self-similar supersonic winds from an accretion disc around a central object are examined with/without radiation fields under the fully self-similar treatment of two-dimensional outflows. The thermal pressure and viscosity are ignored for simplicity. In the case without radiation fields, many solutions are not outflowing winds, but bound flows, except for limited cases which satisfy the escape condition with sufficiently large initial launch speed and rotational one. In the case with radiation fields, the radiation force acts as a driving force, and therefore, the winds blow easier. However, several solutions are unphysical, since the radiative energy density becomes negative. As a result, depending on the rotational motion and boundary conditions, the radiatively driven self-similar cold disc winds are divided into three types; bound solutions lacking launch speed or radiative acceleration, unphysical ones with a negative energy density, and escaping winds confined in the conical region or extending in the whole space as a special type.

Rotational Bloch Boundary Conditions and the Finite-Element Implementation in Photonic Devices

This article described the implementation of rotational Bloch boundary conditions in photonic devices using the finite element method (FEM). For the electromagnetic analysis of periodic structures, FEM and Bloch boundary conditions are now widely used. The vast majority of recent research, however, focused on applying Bloch boundary conditions to periodic optical systems with translational symmetry. Our research focused on a flexible numerical method that may be applied to the mode analysis of any photonic device with discrete rotational symmetry. By including the Bloch rotational boundary conditions into FEM, we were able to limit the computational domain to the original one periodic unit, thus enhancing computational speed and decreasing memory consumption. When combined with the finite-element method, rotational Bloch boundary conditions will give a potent tool for the mode analysis of photonic devices with complicated structures and rotational symmetry. In the meantime, the degenerated modes we calculated were consistent with group theory. Overall, this study expands the numerical tools of studying rotational photonic devices, and has useful applications in the study and design of optical fibers, sensors, and other photonic devices.

A Comparative Computational Investigation on the In-Plane Behavior and Capacity of Dry-Joint URM Walls

ABSTRACT Predicting the lateral load-carrying capacity of dry-joint unreinforced masonry (URM) walls is often challenging due to the complex interactions between the governing parameters (i.e. geometrical and mechanical properties). The capacity and behavior of dry-joint URM walls depend on boundary conditions, size and location of the openings, bond pattern, vertical load, and aspect ratio, among other factors. In this context, the present research investigates the effect of bond pattern, aspect ratio, vertical load, and boundary condition on the in-plane (IP) behavior and capacity. Two computational methods, the discrete element method (DEM) and micro limit analysis (micro LA), are employed. Through a comprehensive parametric assessment, the result indicates a good agreement between the two approaches. The computational investigations underline the direct relationship of the IP capacity of walls with respect to aspect ratio and applied vertical pressure. Furthermore, fixed-no rotation boundary condition is associated with the increased IP capacity. Finally, a simple analytical equation is proposed to predict the lateral capacity of dry-joint URM walls.

Particle Collision Study Based on a Rotational Boundary Condition

The main engineering machinery for the hydrodynamic lifting of seafloor mineral particles is rotor machinery with rotating impeller motion. It is important to study the rebound mechanism of collisions between particles and rotating walls to improve the accuracy of numerical simulation of rotor machinery. In this study, the law of motion change after collisions between particles and rotating walls is investigated using an experimental research method. The results show that the deflection angle of the particles after collision decreases with increases in the rotational speed of the wall, and the spin angular velocity increases with increases in the rotational speed of the wall. The normal velocity coefficient of restitution under the rotating wall is not affected by the rotational speed of the wall. The tangential coefficient of restitution under rotational boundary condition is smaller than the tangential coefficient of restitution under the stationary wall, and the higher the rotational speed, the closer it is to the coefficient of restitution under the stationary wall. During collision in the experiment, the main mode of contact between the particle and the rotating wall is sliding contact. Sliding friction between the particle and the rotating wall results in energy loss in the tangential velocity of the particle, and also provides energy for deflection of the particle’s trajectory and increased kinetic energy from the spin angular velocity; sliding friction loss is affected by the speed of the wall.

A dynamic stiffness formulation for the vibration analysis of rotating cross-ply laminated coupled conical–cylindrical–conical shells

In this paper, a dynamic stiffness formulation is reported to analyze the free vibration characteristics of a rotating cross-ply laminated coupled conical–cylindrical–conical shell. In order to ensure the stability of the numerical results, the whole system is firstly divided into substructures, and each substructure is divided into several segments. The theoretical formulation of the rotating shell segment is derived by the first-order shear deformation theory and Hamilton’s principle. The effects of centrifugal force and Coriolis acceleration on the initial hoop tension are considered in the formulation. The dynamic stiffness matrix of the shell segment is derived from the relationship between the state vector and its derivative, where the state vector consists of the resultant force and displacement components of the shell segment. The dynamic stiffness matrix of the whole system is assembled by the displacement coordination relationship. After the number of segments is determined by the convergence analysis, it is compared with the results of the existing literature and finite element software to ensure the accuracy of the dynamic stiffness formulation. Based on this, the effects of rotational speed, geometry and boundary conditions on the structure are studied.

Teğet Sınır Şartlarının Ortasından Tekil Yüklü Katmanlı Kompozit Silindirik Panellerin Nonlineer Davranışlarına Etkisi

In this study, the influence of straight edge tangential restraints on the nonlinear response of symmetrically laminated and balanced composite cylindrical panels subject to a pinching force is investigated. An 8-node degenerated nonlinear shell element, formulation of which is based on the Total Lagrangian Formulation, is employed for geometrically nonlinear analysis and the Arc-Length Method is used to trace the nonlinear path. First, the element is validated for geometrically non-linear analysis by solving two verification problems. Then, numerical results for different rotational boundary conditions are presented for two different stacking sequences, and thickness values. The numerical results presented show that there is no significant difference between the tangentially unrestrained and restrained clamped panels when only one edge is tangentially unrestrained. However, it is observed that the simply supported panels demonstrate a much less stiff behavior when one of the straight edges is tangentially unrestrained.

A cell-based smoothed radial point interpolation method applied to kinematic limit analysis of thin plates

The cell-based smoothed radial point interpolation method in conjunction with a second order cone programming is proposed for kinematic limit analysis of rigid-perfectly plastic thin plates in this paper. The transverse displacement field is interpolated by the radial point interpolation method (RPIM) and no rotational degrees of freedom are involved. The gradient smoothing technique is utilized to construct smoothed curvature field in every smoothing domain and there is no need to compute the second derivatives of shape functions. The rotational boundary conditions are satisfied in the process of curvature smoothing and the translational boundary conditions can be directly enforced without any special treatment. The limit analysis problem of thin plates is formulated by minimizing the dissipation power subject to a set of equality constraints and this minimization problem can be expressed easily as a standard second order cone programming. It is testified from the computational results that the proposed procedure can provide reasonable and satisfactory upper bound limit load multipliers for thin plates.

Numerical Simulations of Liquid-Solid Flows in A Vertical Pipe by MPS-DEM Coupling Method

In the process of deep-sea mining, the liquid-solid flows in the vertical transportation pipeline are very complex. In the present work, an in-house solver MPSDEM-SJTU based on the improved MPS and DEM is developed for the simulation of hydraulic conveying. Firstly, three examples including the multilayer cylinder collapse, the Poiseuille flow and two-phase dam-break are used to validate the precision of the DEM model, the pipe flow model and MPS-DEM coupling model, respectively. Then, the hydraulic conveying with coarse particles in a vertical pipe is simulated. The solid particle distribution is presented and investigated in detail. Finally, the coupling method is successfully applied for the simulation of the liquid-solid flows in a vertical pipe with rotating blades, which shows the stability of the solver under rotating boundary conditions. This fully Lagrangian model is expected to be a new approach for analyzing hydraulic conveying.

Modeling method for analyzing veering and nonlinear vibration of rotating hard-coated drum-disk structures considering the strain-amplitude dependency

This paper proposes a modeling method of rotating hard-coated drum-disk structures considering the strain-amplitude dependency of coatings and studies the veering of frequency curves and nonlinear coupled vibration. Firstly, Sanders’ shell theory and Kirchhoff's plate theory are used to derive the energy expressions of the hard-coated drum and hard-coated disk, respectively. The arbitrary multi-arc joints between disk and drum and arbitrary boundaries are presented based on the artificial spring. Furthermore, the displacements of the drum and disk are expanded by using the orthogonal polynomials, and Lagrange's equations are employed to derive the linear semi-analytical model. Secondly, the multi-domain dividing approach is used to develop a general method considering the strain-amplitude dependency in the rotation state, and the nonlinear semi-analytical model of rotating hard-coated drum-disk structures is created and further solved by an efficient algorithm proposed in the present work. The convergence and validation of the semi-analytical model are verified. Finally, the veering of frequency curves caused by the variations in rotation speeds, connection and boundary conditions, and thickness of coatings and substrates is revealed. The variation law and mechanism of nonlinear coupled vibration during veering are also investigated. The proposed modeling method can provide helpful references for the modeling and vibration analysis of multi-stage hard-coated drum-disk structures in aero-engine and other rotating hard-coated structures.

A consistent finite-strain plate model for wrinkling of stretched anisotropic hyperelastic films

Stretch-induced wrinkles usually occur in a thin, clamped–clamped, hyperelastic film and eventually disappear upon excess stretching, with wrinkling direction being perpendicular to the stretching direction within isotropic elasticity framework. Here, we consider in-plane anisotropy induced by infilling fibers in thin films, which significantly affects the orientation and amplitude of wrinkles. To precisely predict the isola-center bifurcation (“birth” and “death” of wrinkles) and to capture wrinkling morphology evolution under large in-plane anisotropic deformations, we develop a consistent finite-strain plate model by accounting for anisotropic hyperelastic constitutive laws. Advantages of this plate model lie in its asymptotic consistency with the 3D field equations and its applicability to large deformations. A new type of rotational symmetric boundary conditions is proposed to reduce the computational cost and to achieve robust convergence. We reveal that the fiber orientation plays a critical role in the wrinkling and restabilization behavior of stretched films. The fibers parallel or perpendicular to the stretching direction can resist the appearance of wrinkles, while the oblique fiber orientation (15°∼75°) can advance wrinkle formation. Besides, oblique wrinkling patterns can be regulated by fiber/matrix shear modulus ratio, and we draw phase diagrams on stability boundary to demonstrate the interactive parametric effects. Our results could provide quantitative guidance to design wrinkle-tunable surfaces for fiber-composite or biomimetic films.

Energy analysis of a detonation combustor with a bladeless turbine, a propulsion unit for subsonic to hypersonic flight

This paper details an energy conversion unit for the combined power extraction and thrust increase from high subsonic to hypersonic flows. The energy transfer is achieved through a wavy hub surface that promotes shocks and expansion fans. First, a design procedure and the non-dimensional steady-state performance characteristics (the reduced torque, non-dimensional mass flow, and non-dimensional speed) are presented (including an exergetic analysis) at on– and off-design conditions through time-averaged Reynolds Averaged Navier Stokes simulations. A cycle analysis was performed on a Mach 3 vehicle to demonstrate the feasibility of this technology. Second, energy extraction is achieved from the highly unsteady exhaust of rotating detonation combustors without needing an additional intermediate diffuser or nozzle. The rotating boundary conditions were computed from a reactive unsteady simulation. The influence of three shock parameters (pressure ratio across the shock, shock wave Mach number, and the number of waves) is investigated through a sensitivity study to assess the robustness of the new device. Furthermore, depending on the sense of rotation of the bladeless turbine relative to the rotation of the incoming shock and the helix angle, we can define two different modes of operation in which power extraction was achieved, namely, the shock mode and reversed mode.

Free vibrations of rectangular plates simply supported at two opposite edges and elastically restrained at the two other edges. An analytical and a semi-analytical method

The present study provides a novelty in treating rectangular plates simply supported at two opposite edges and elastically restrained at the two other edges using two approaches. On one hand, the analytical solution of the plate vibration equation satisfying the rotational and translational spring boundary conditions is obtained for different plate aspect ratios leading to the corresponding modes and frequencies. On the other hand, the Rayleigh-Ritz method (RRM) is applied using plate functions defined as products of beam functions satisfying the beam appropriate end conditions in each direction. i.e. simply supported in the direction of the two opposite edges, and elastic end conditions in the other direction. The results obtained by the two methods coincide for all frequencies and modes examined, showing the effectiveness of the RRM applied to this problem in a general and systematic way. This makes the RRM ready for use in further studies concerning similar plates with added point masses or springs, or plate vibrating in the nonlinear regime. Also, useful numerical results corresponding to both the frequencies and mode shapes are presented for various plate modes, stiffness values and plate aspect ratios.

Virtual Gas Turbines Part II: An Automated Whole-Engine Secondary Air System Model Generation

Abstract The design and analysis of the secondary air system (SAS) of gas turbine engine is a complex and time-consuming process because of the complicated topology and iterative nature of SAS design. The conventional SAS design-analysis model generation process is quite tedious and inefficient. It is still largely dependent on human expertise and thus incurs high time-cost. This paper presents an automated, whole-engine SAS flow network model generation methodology. This method accesses a prebuilt feature-based whole-engine geometry model and transforms the geometry features into the features suitable for SAS flow network analysis. The proposed method extracts both the geometric and non-geometric information from the engine geometry model such as rotational frames, materials, and boundary conditions. Apart from ensuring geometric consistency, this methodology also establishes a bidirectional information exchange protocol between the engine geometry model and the SAS flow network model, which enables to make engine geometry modifications based on SAS analysis results. The application of this feature mapping methodology is demonstrated by generating the SAS flow network model of a modern three-shaft gas turbine engine. This flow network model is generated within a few minutes, without any human intervention, which significantly reduces the SAS design-analysis time cost. The proposed methodology seamlessly links the geometry and the air system modelers of Virtual Gas Turbines simulation framework and thus allows performing a large number of whole-engine SAS simulations, design optimizations and fast redesign activities.

Closed-form solution for free vibration of variable-thickness cylindrical shells rotating with a constant angular velocity

Based on the classical Donnell’s and Love’s shell theories, free vibration behavior of variable-thickness thin cylindrical shells rotating with a constant angular velocity is analyzed. The equations of motion and corresponding boundary conditions of rotating homogenous cylindrical shells with axisymmetric variation of thickness are derived using Hamilton’s principle. This formulation includes effects of initial hoop tension due to the centrifugal force as well as Coriolis and centrifugal accelerations. Considering the variation of stiffness coefficients in axial direction, the classical Love’s theory results in a coupled system of two second-order and one fourth-order partial differential equations with variable coefficients in terms of kinematic variables. The Galerkin’s method is used to obtain a closed-form expression of sixth-order frequency equation with coefficients in terms of rotation speed (Ω) for with boundary conditions. The natural frequencies of stationary and rotating cylindrical shells with constant thickness, as special cases, are validated with existing ones in the literature. Case studies are presented for three different patterns of thickness variation in forms of arbitrary power, axisymmetric modal and stepwise functions. It is seen that the influence of thickness variation on the natural frequencies and mode shapes is a function of different parameters including rotation speed, boundary conditions, and geometric ratios, especially this effect is much more pronounced for cantilever long shells with a high rotation speed. Also, differences in results predicted by the Donnell’s and Love’s theories become larger for long and cantilever shells in vibration mode shape corresponding to (m=1,n=2), i.e., the ovalization of cross section.

Vibration characteristics of rotating functionally graded circular cylindrical shell with variable thickness under thermal environment

This paper deals with the vibration characteristics of rotating functionally graded circular cylindrical shells (FG-CS). The thickness of the shell varies linearly along the longitudinal direction. The material properties are graded continuously with a power law (P-FGM) in the radial direction and depend on the temperature. The system of motion equation is established by using the first-order shear deformation theory (FSDT) and Hamilton's principle. The model considers the effects of centrifugal forces, Coriolis forces, and initial hoop tension due to rotation. The natural frequencies of the shells with various boundary conditions are obtained by Galerkin's method. Several competition examples validated the accuracy of the present model. Some numerical studies are then conducted to identify the effects of rotational speed, material properties, geometrical parameters, and boundary conditions (BCs) on the vibration response of rotating FG-CS in detail.

Geometrically nonlinear multi-patch isogeometric analysis of spatial Euler–Bernoulli beam structures

This study presents a novel isogeometric Euler–Bernoulli beam formulation for geometrically nonlinear analysis of multi-patch beam structures. The proposed formulation is derived from the three-dimensional continuum theory where the beam axis and the director vectors of cross-sections are used to characterize beam configurations. The translational displacements of the beam axis and the axial cross-sectional rotation along the beam axis are considered as unknown kinematics. The orthogonality between the cross-sections and the beam axis is satisfied by using the smallest rotation mapping for the description of finite cross-sectional rotations. The use of the smallest rotation mapping reduces the nonlinearity of the employed strain measurements with respect to the unknown kinematics and offers highly efficient linearization. Furthermore, a penalty-free approach is introduced to deal with rigid connections in multi-patch beam structures in the context of geometrically nonlinear analysis. A novel nonlinear transformation between the total cross-sectional rotation and the unknown kinematics is derived, which facilitates the use of the total cross-sectional rotations at the ends of patches as discrete unknowns. This approach also allows straightforward enforcement of rotational boundary conditions. The proposed formulation is investigated by several well-established examples and great accuracy and efficiency are observed.

Nitsche’s method for linear Kirchhoff–Love shells: Formulation, error analysis, and verification

Stable and accurate modeling of thin shells requires proper enforcement of all types of boundary conditions. Unfortunately, for Kirchhoff–Love shells, strong enforcement of Dirichlet boundary conditions is difficult because both displacement and normal rotation boundary conditions must be applied. A popular alternative is to employ Nitsche’s method to weakly enforce all boundary conditions. However, while many Nitsche-based formulations have been proposed in the literature, they lack comprehensive error analyses and verification. In fact, existing formulations are variationally inconsistent and yield sub-optimal convergence rates when used with common boundary condition specifications. In this paper, we present a novel Nitsche-based formulation for the linear Kirchhoff–Love shell that is provably stable and optimally convergent for general sets of admissible boundary conditions. To arrive at our formulation, we first present a framework for constructing Nitsche’s method for any abstract variationally constrained minimization problem. We then apply this framework to the linear Kirchhoff–Love shell and, for the particular case of NURBS-based isogeometric analysis, we prove that the resulting formulation yields optimal convergence rates in both the shell energy norm and the standard L2-norm. To arrive at this formulation, we derive the Euler–Lagrange equations for general sets of admissible boundary conditions and show that the Euler–Lagrange boundary conditions typically presented in the literature are incorrect. We verify our formulation by manufacturing solutions for a new shell obstacle course that encompasses flat, parabolic, hyperbolic, and elliptic geometric configurations with a variety of common boundary condition specifications. These manufactured solutions allow us to robustly measure the error across the entire shell in contrast with current best practices where displacement and stress errors are only measured at specific locations. We use NURBS discretizations to represent the shell geometry and show optimal convergence rates in both the shell energy norm and the standard L2-norm with varying polynomial degrees for all of the problems in the obstacle course.

Structural acoustic problem and dynamic nonlinear plate equations

ABSTRACT The purpose of this paper is to investigate a structural interaction model coupled with dynamic von Karman equations, without neither rotational inertia nor clamped boundary conditions. Our fundamental goal is to establish the existence and the uniqueness of the weak solution for the so-called global functional energy. The stability is also discussed. At the end, a numerical study based on the finite difference method is presented as well.