Internal Hinge Research Articles

Latent-to-sensible heat conversion kinetics during nanoparticle coalescence.

Coagulational growth in an aerosol is a multistep process; first particles collide, and then they coalesce with one another. Coalescence kinetics have been investigated in numerous prior studies, largely through atomistic simulations of nanoclusters (102-104 atoms). However, with a few exceptions, they have either assumed the process is completely isothermal or is a constant energy process. During coalescence, there is the formation of new bonds, decreasing potential energy, and correspondingly increasing internal kinetic (thermal) energy. Internal kinetic energy evolution is dependent not only on coalescence kinetics but also on heat transfer to the surrounding gas. Here, we develop and test a model of internal kinetic energy evolution in collisionally formed nanoclusters in the presence of a background gas. We find that internal kinetic energy dynamics hinge upon a power law relationship describing latent-to-sensible heat release as well as a modified thermal accommodation coefficient. The model is tested against atomistic models of 1.5-3.0nm embedded-atom gold nanocluster sintering in argon and helium environments. The model results are in excellent agreement with the simulation results for all tested conditions. Results show that nanocluster effective temperatures can increase by hundreds of Kelvin due to coalescence, but that the rise and re-equilibration of the internal kinetic energy is strongly dependent on the background gas environment. Interestingly, internal kinetic energy change kinetics are also found to be distinct from surface area change kinetics, suggesting that modeling coalescence heat release solely due to surface area change is inaccurate.

Stability of arches with internal hinge

The in-plane stability of internally hinged, end-fixed shallow arches is in the spotlight. The non-linear model accounts for the coupled effect of the bending moment and axial force on the membrane strain. The model itself can handle homogeneous or non-homogeneous material distributions along the thickness of the uniform arch. Analytical findings reveal how the typical geometrical data, like arch length, radius of gyration, and arch angle, affect the lowest buckling loads. The typical non-linear behaviour of arches is also assessed including the equilibrium path and the internal force system.

Nonlinear forced vibration and stability of an axially moving beam with a free internal hinge

Nonlinear forced vibration and stability of an axially moving beam with a free internal hinge

Kirschner wire reconstruction of medial and lateral column periosteal hinge in the treatment of multidirectionally unstable supracondylar fracture of the humerus in children

Aim and objectiveTo compare the clinical effect of reconstruction of internal and lateral column periosteal hinge-assisted treatment with Kirschner wire and internal fixation with Kirschner wire in the treatment of multidirectional unstable supracondylar fractures of humerus in children.MethodsA retrospective cohort study was conducted to analyze the clinical data of 48 patients (31 male, 17 female; mean age: 6.7 ± 2.4 years old) with multidirectionally unstable supracondylar fractures of the humerus treated in our Hospital from August 2020 to August 2022. Twenty-five cases were treated with Kirschner wire reconstruction of the internal and lateral column periosteal hinge assisted by closed reduction and Kirschner wire internal fixation (study group). Twenty-three cases were treated with closed reduction and Kirschner wire internal fixation (control group). The operation time, intraoperative fluoroscopy times, percentage of patients who underwent open reduction after failure of closed reduction, fracture healing time, Baumann angle (BA), shaft-condylar angle (SCA), range of motion (ROM), and Flynn score of elbow at the last follow-up were compared between two groups. Complications such as infection and irritation of Kirschner wire tail were observed in two groups 2 months after the operation.ResultsAll patients were followed up for 10–22 months ([13.85 ± 2.89] months). The average operation time of the control group was 82.1 min, which was significantly longer than that of the study group 32.3 min (P < 0.05). The number of intraoperative fluoroscopy (29.4 ± 9.2) in the control group was significantly higher than that in the study group (15.2 ± 6.3) (P < 0.05). The incision rate of the control group was 17% while that of the study group was 0 (P < 0.05). According to Flynn score, the excellent and good rate of the elbow joint in the control group was 86.9% (20/23). The excellent and good rate of the elbow joint in the study group was 92.0% (23/25) (P > 0.05). There was no significant difference in fracture healing time, BA, SCA, and ROM between the two groups (P > 0.05). No infection or Kirschner wire tail irritation occurred in the two groups during the 2-month follow-up.ConclusionReconstruction of internal and lateral periosteal hinges with Kirscher wire has similar effects to closed reduction and Kirschner wire fixation in the treatment of multidirectionally unstable supracondylar fractures of the humerus in children, but it can shorten the operation time and reduce intraoperative fluoroscopy times and incision rate.

Enhanced transverse displacements analysis of transversely cracked beams with a linear variation of width due to axial tensile forces

Enhanced transverse displacements analysis of transversely cracked beams with a linear variation of width due to axial tensile forces

Frequency Variation of Beam with an Internal Hinge of Rotational Restraint

The frequency variation problem of a classical beam with a rotationally restrained internal hinge arbitrarily located is studied intensively. The characteristic equations of the natural vibration are derived rigorously upon the corresponding boundary conditions and the compatibility conditions at the interconnecting point such that the effects of both the rotational restraint stiffness and the hinge position on the natural frequencies and mode shapes are described comprehensively. In the context, the critical locations of an internal hinge are investigated extensively to obtain the extreme values of a natural frequency of the beam system, and the associated requirements are explored in depth. It appears that the essential conditions for obtaining the critical points with regard to the maximum or minimum frequency come, respectively, from the same compatibility relation of the rotational flexibility in view of the opposite criteria. Numerical results are provided with two representative uniform beams to show the variations of their dynamic characteristics and to gain new insights into the transition conditions in the two distinct cases.

Study on Redistribution of Internal Force and Plastic Hinge Development of Mountainous Building Structures with Foundations at Two Different Elevations

This study was conducted to study the redistribution of internal force and the development of the plastic hinge of an MBS with foundations at two different elevations considering the torsional effect. The results indicate that the redistribution of the base shear of MBS is evident at different embedding ends, and the redistribution of story shear on different floors also took place. The redistribution of the shear force of columns is different at the upper- and lower-embedding sides, and the internal force redistribution is more prominent along the slope direction. Consequently, the redistribution of the internal force of MBS should be considered in practical seismic design. Furthermore, the damage of MBS is transferred from the floors above the upper-embedding end to the floors under the upper-embedding end with the increase in the seismic intensity, where the elements at the floors above the upper-embedding end suffer the most serious damage, and the damage is unevenly distributed in the upper-embedding story and the adjacent upper story. The lower-embedding column is more prone to hinge across the slope direction because of the torsional effect. With γintra changes, the redistributions of the shear force of the base, story, and column are different. A larger γintra would result in a weaker redistribution of base shear. The redistribution of the story shear of the 1st floor and its columns along the slope direction shows an increasing-decreasing tendency with the increase in γintra, and the redistribution is the most serious when γintra is 0.4. While across the slope direction, the redistribution of the story shear tends to be weakened as γintra increases. The forming of the plastic hinge of single-frames along the slope direction is related to γintra and γnon, especially the damage of the upper-embedding columns. The torsional effect has a significant influence on the damage of the single-frames across the slope direction. Some measures should be taken to improve the bearing capacity of the upper embedding columns and columns on floors under the upper-embedding end, as well as the drift ductility of the upper-embedding columns.

Empirical Modeling of Transverse Displacements of Single-Sided Transversely Cracked Prismatic Tension Beams

While the effects of axial compression on beams have long been known, the effect of tensile axial loads on one-sided transversely cracked beams is less known. The crack namely shifts the position of the resultant of the axial normal stresses deeper into the uncracked part of the cross-section, and the crack tends to open, causing a transverse displacement. Therefore, this paper focuses on empirical modeling of the considered phenomenon for slender prismatic beams in order to establish a suitable 1D computational model based on detailed 3D FE mesh results. This goal can be achieved through the already established simplified model, where the crack is represented by an internal hinge endowed with a rotational spring. Several analyses of various beams differing in geometry, crack locations, and boundary conditions were executed by implementing 3D FE meshes to establish the appropriate model’s bending governing differential equation. After that, the corresponding parameter definitions were calibrated from the database of 3D FE models. By redefining the model’s input parameters, a suitable solution is achieved, offering a good balance between the results’ accuracy and the required computational effort. The functionality of the newly obtained solutions was verified through some comparative case studies that supplement the derivations.

A mixed-field Timoshenko beam-column element for direct analysis of tapered I-sections members

ABSTRACT Tapered members produced by robotic fabrication techniques offer architectural and structural advantages and have the potential to become more prevalent than prismatic members. However, the conventional analysis and design methods based on simplified assumptions such as equivalent stiffness cannot be used to accurately evaluate a member's performance. To provide a reliable and practicable stability design method, a direct analysis method of tapered I sections is proposed. A mixed-field tapered beam-column element is derived for use within the modeling of structural frames. The effects of initial geometric imperfection and additional shear stress are directly considered in the element formulation. A polynomial describing the member's critical initial out-of-plumbness is adopted, and an arbitrarily located internal hinge is incorporated in the element to enhance the element's deformation capacity and capture the behaviors of the most critical section. Displacement and force interpolation matrices incorporating the shear deformation are utilized, and the Gauss quadrature method is employed to evaluate the element stiffness matrix. Finally, verification examples demonstrate that the proposed method can be used to accurately and efficiently evaluate the performance of tapered members, indicating that the element can be conveniently employed in member and frame analysis and design.

Julian Huxley and the quantification of relative growth

In 1932, Julian Huxley introduced biologists around the world to a simple method for fitting two-parameter power equations, $$ Y\, = \,b \times \, X^{k} $$, to bivariate observations that follow a curvilinear path on the arithmetic (= linear) scale. The method entails fitting a straight line to logarithmic transformations of the data and then (at least implicitly) back-transforming the resulting equation to the arithmetic domain. This general approach continues to be in wide use by students of biological allometry despite its several limitations and shortcomings. For example, Huxley’s allometric method requires that the bivariate data of interest follow the path of a straight line in log domain (i.e., that the data be loglinear). However, many datasets that are otherwise suitable for allometric analysis do not meet the requirement for loglinearity and consequently are beyond the scope of Huxley’s method. Such data can usually be examined in the untransformed state by nonlinear regression, and the regression approach enables investigators to fit models with different functional form and random error. Moreover, by combining nonlinear regression with a categorical variable, investigators can compare sets of observations that follow curvilinear paths on the arithmetic scale. The regression protocol is illustrated by re-examining data for relative growth by the internal hinge ligament in a bivalve mollusk and by the elongated snout in garfish (Actinopterygii). The methodology promoted by Huxley has played a major role in development of the field of biological allometry, but the procedure has been superseded by nonlinear regression.

Wave Number-Based Technique for Detecting Slope Discontinuity in Simple Beams Using Moving Test Vehicle

The wavelength characteristic is a useful clue for locating and assessing the severity of slope discontinuity in beams. In this study, the slope discontinuity of a beam is represented by an internal hinge restrained by elastic springs, and the wavelength of the beam is calculated indirectly from the vertical response of a test vehicle during its travel over the beam. The key parameters of the problem at hand are first unveiled using an approximate, closed-form solution for the response of the vehicle moving at low speeds over the bridge. Then a two-beam element model with slope discontinuity is formulated for the vehicle–bridge interaction (VBI) system for use in numerical simulation. In the examples, the wavenumber-based response of the test vehicle is used to identify the location and severity of the discontinuity in the beam. It is demonstrated that the wavelength-based technique presented herein by using the moving test vehicle as a moving sensor system offers a promising, alternative approach for damage detection in girder type bridges.

Multi-level residue harmonic balance solution for the nonlinear natural frequency of axially loaded beams with an internal hinge

ABSTRACTIn this article, an analytical approach, namely, multi-level residue harmonic balance is introduced and developed for the nonlinear free vibration analysis of axially loaded beams with an internal hinge. The main advantage of this method is that only one set of nonlinear algebraic equations is required to be solved for obtaining the zero level solution while the high accuracy of the higher level solutions can be obtained by solving a set of linear equations. The new approximate analytical solution method is developed for solving the governing differential equations. The accuracy and efficiency of the proposed method are verified by a numerical method. In the comparison, the results obtained from the proposed method well agree with those from other methods. The effects of vibration amplitude, axial force, and hinge location on the fundamental frequencies of various beam cases are investigated. The optimum and worst hinge locations are also studied.

Foam-Filled Grooved Tubes with Circular Cross-Section Under Axial Compression: A Theoretical Analysis

In this article, some theoretical relations are derived to predict the instantaneous folding force and the absorbed energy by the empty and polyurethane foam-filled grooved tubes with circular cross-section during the first fold formation under the axial loading. Five different modes of deformation are considered in the theoretical model of deformation: bending around two internal circular hinge lines, bending around an external circular hinge line, extensional deformation in the folding arms, axial compression of the polyurethane foam, and interaction effects between polyurethane foam and inner wall of the grooved tube. Also, based on the experiments, a semi-empirical relation is suggested to predict the effective axial displacement at the end of a complete fold creation in the polyurethane foam-filled grooved tubes. To verify the theoretical analyses, some axial compression tests were carried out on the empty and filled grooved tubes. Comparison of the theoretical predictions with the corresponding experimental results showed a good correlation.

Estimating seismic demands for performance-based engineering of steel buildings

Author(s): Reyes, Juan Carlos | Advisor(s): Chopra, Anil K | Abstract: Earthquake engineering practice is increasingly using performance-based procedures for evaluating existing buildings and proposed designs of new buildings. Both nonlinear static and nonlinear response history analyses (RHA) are used for estimating engineering demand parameters (EDPs)--floor displacements, story drifts, internal forces, hinge rotation, etc--in performance-based engineering of buildings. Topics related to both analysis procedures are investigated in this dissertation.In the first part, the original modal pushover analysis (MPA) to estimate seismic demands due to one component of ground motion is extended to consider two horizontal components simultaneously in three-dimensional analysis of buildings, and to estimate internal forces and plastic hinge rotations directly from pushover analyses. Subsequently, the accuracy of MPA in estimating EDPs for tall buildings and unsymmetric-plan buildings is evaluated. Seismic demands for recently designed and built 48- and 62-story buildings with ductile concrete core walls--designed according to the alternative provisions of the 2001 San Francisco Building Code (SFBC)--due to an ensemble of 30 ground motions are computed by MPA and nonlinear RHA, and compared. We demonstrate that MPA procedure shows degree of accuracy that is sufficient for practical application in estimating median values of EDPs for tall buildings subjected to two horizontal components of ground motion. The accuracy of the extended MPA procedure is also evaluated for low- and medium-rise unsymmetric-plan buildings with ductile frames designed in accordance with the 1985 Uniform Building Code (UBC85) and the 2006 International Building Code (IBC06). Seismic demands are computed for six unsymmetric-plan buildings due to 39 ground motions acting simultaneously in two orthogonal horizontal directions. Comparing these results with those from nonlinear RHA, we demonstrate that MPA provides good estimates of EDPs whereas the procedures specified in the ASCE/SEI 41-06 standard and the Eurocode 8 are not satisfactory for estimating seismic demands for unsymmetric-plan buildings.The second part of the dissertation concerns nonlinear response history analysis of buildings. With the goal of developing effective procedures for selection and scaling of multi-component ground motions to be used in nonlinear RHA, a modal-pushover-based-scaling (MPS) procedure is developed in this investigation. The developed MPS procedure is an extension of the original MPS procedure for one component of ground motion to two horizontal components. In this investigation, each horizontal component of ground motion is scaled by a factor selected to match the deformation of its inelastic SDF system to a target inelastic deformation that may be estimated using a design (or response) spectrum. The properties of the inelastic SDF system are determined by pushover analysis of the building using the first-mode distribution. Based on the results for medium-rise symmetric-plan and unsymmetric-plan buildings with ductile frames, we demonstrate that the MPS procedure provides much superior results than the scaling procedure specified in the ASCE/SEI 7-05 standard.

An Efficient Computational Method for Semi-rigid Steel Frame with Elements of Internal Plastic Hinge

This paper proposes an efficient computational method for semi-rigid steel frame with elements of internal plastic hinge. The yield function of I or H section is derived by using section assemblage concept, and residual stress is considered in the initial yield function. Element with springs-in-series at each end is presented to consider the effect of semi-rigid connections and material nonlinearity. Based on the proposed method, it is demonstrated that internal plastic hinge can be well predicted by only using one element for the members subjected to distributed loads. The proposed element has the same nodal degrees of freedom as conventional element by condensing the non-nodal degrees of freedom introduced in the derivation. Other factors influencing the capacity of steel frames, such as shear deformation, geometric nonlinearity and initial imperfection, are explicated. Using FORTRAN, an improved nonlinear analysis program of semi-rigid steel frame is compiled. Numerical analysis shows that the proposed method has high efficiency and accuracy.

Free vibrations of a trapezoidal plate with an internal line hinge.

This paper deals with a general variational formulation for the determination of natural frequencies and mode shapes of free vibrations of laminated thin plates of trapezoidal shape with an internal line hinge restrained against rotation. The analysis was carried out by using the kinematics corresponding to the classical laminated plate theory (CLPT). The eigenvalue problem is obtained by employing a combination of the Ritz method and the Lagrange multipliers method. The domain of the plate is transformed into a rectangular domain in the computational space by using nonorthogonal triangular coordinates and the transverse displacements are approximated with a set of simple polynomials automatically generated and expressed in the triangular coordinates. The developed algorithm allows obtaining approximate analytical solutions for mentioned plate with different geometries, aspect ratio, position of the line hinge, and boundary conditions including translational and rotational elastically restrained edges. It allows studying the influence of the mentioned line on the vibration frequencies and respective mode shapes. The algorithm can easily be programmed and it is numerically stable. Additionally, as a particular case, the results of triangular plates can be easily generated.

Free Vibrations of Beam System Structures with Elastic Boundary Conditions and an Internal Elastic Hinge

The study of the dynamic properties of beam structures is extremely important for proper structural design. This present paper deals with the free in-plane vibrations of a system of two orthogonal beam members with an internal elastic hinge. The system is clamped at one end and is elastically connected at the other. Vibrations are analyzed for different boundary conditions at the elastically connected end, including classical conditions such as clamped, simply supported, and free. The beam system is assumed to behave according to the Bernoulli-Euler theory. The governing equations of motion of the structural system in free bending vibration are derived using Hamilton's principle. The exact expression for natural frequencies is obtained using the calculus of variations technique and the method of separation of variables. In the frequency analysis, special attention is paid to the influence of the flexibility and location of the elastic hinge. Results are very similar with those obtained using the finite element method, with values of particular cases of the model available in the literature, and with measurements in an experimental device.

Nonlinear Analysis of the Motion Structures

In this paper, the nonlinear analysis of the motion structures is studied by using the vector form intrinsic finite element (VFIFE, V-5) method. The main object of this research is to develop an internal hinge of two ends of the plane frame element. In this study, the hinge function of frame element is used to compute the nonlinear dynamic responses of the motion structures. A fictitious reversed rigid body motion can be used to separate the rigid body motions and the pure deformations of the frame element. It is not requires any iteration or any parameters for the VFIFE method during computation process. Four examples illustrate the accuracy of the proposed procedures in computing large motions of a flying flexible structure.

Free vibrations of a generally restrained rectangular plate with an internal line hinge

This paper deals with the study of free transverse vibrations of rectangular plates with an internal line hinge and elastically restrained boundaries. The equations of motion and its associated boundary and transition conditions are rigorously derived using Hamilton’s principle. The governing eigenvalue equation is solved employing a combination of the Ritz method and the Lagrange multipliers method. The deflections of the plate and the Lagrange multipliers are approximated by polynomials as coordinate functions. The developed algorithm allows obtaining approximate solutions for plates with different aspect ratios, boundary conditions, including edges elastically restrained by both translational and rotational springs, and arbitrary locations of the line hinge. Therefore, a unified algorithm has been implemented. Sets of parametric studies are performed and the results are given in graphical and tabular form.

Boundary value problems for anisotropic plates with internal line hinges

This paper deals with the formulation of an analytical model for the dynamic behavior of anisotropic plates, with an arbitrarily located internal line hinge with elastic supports and piecewise smooth boundaries elastically restrained against rotation and translation among other complicating effects. The equations of motion and its associated boundary and transition conditions are derived using Hamilton’s principle. By introducing an adequate change of variables, the energies that correspond to the different elastic restraints are handled in a general framework. The concept of transition conditions and the determination of the analytical expressions are presented. Analytical examples are worked out to illustrate the range of applications of the developed analytical model. One of the essential features of this work is to demonstrate how the commonly formal derivations used in the applications of the calculus of variations can be made rigorous.