Initial Curvature Research Articles

Coupled bending-torsion behaviour of single-box multi-cell curved composite box-girders with corrugated-steel-webs

Due to initial curvature, curved composite box-girder with corrugated steel webs (CCBG-CSWs) exhibits complex behaviour. This study develops an analytical solution for describing coupled bending-torsion behaviour of CCBG-CSWs with arbitrary single-box multi-cell cross-section in elastic stage under arbitrary loads. First, governing differential equations are deduced with energy-variational principle and solved by Galerkin-method. Next, experimental studies and finite element analysis are performed, which validates the analytical solution. It also identifies governing parameters. Discussion of analytical solution's calculated items shows steel webs' shear deformation has significant effects on flexural deflection, but no effects on torsional angle and normal stress at section corner. The additional restrained torsion has little impact on flexural deflection and torsional angle while non-negligible influence on normal stress. Shear lag effect of flanges has larger effects on the normal stress than that of on the flexural deflection and torsional angle. Furthermore, parametric study presents span-radius ratio and bending-torsion stiffness ratio have substantial impacts on bending-torsion behaviour. The corrugated steel web thickness and the eccentricity between torsional centre and centroid have relatively less effects. Diaphragm spacing effects are the least. The study may provide new insights to understand the coupled bending-torsion behaviour of CCBG-CSWs and finally guide better design.

Wavelet solution for hygrothermomechanical bending of initially defected plate undergoing large deformation on nonlinear elastic foundation

An efficient wavelet approach has been developed for geometrically nonlinear bending analysis of largely deformed plate with arbitrary initial curvature on nonlinear Winkler–Pasternak foundation loaded with sinusoidally hygrothermal stresses. Translational and rotational constraints have been analyzed and equivalently transformed into the Cauchy-type boundary conditions of Airy stress function, which are efficiently approached by interpolating Coiflet-type wavelet. A newly hygrothermomechanical bending model of plate subjected to the adiabatically impermeable edges or with boundaries of sinusoidal temperature and humidity has been firstly formulated. The highly coupled and nonlinear governing equations have been decomposed into linear differential terms by homotopy transformation and successfully solved by the Coiflet-type wavelet Galerkin method. The wavelet strategy has been validated superior in dealing with extremely nonlinear bending and high-precision reconstitution of initial deflection in hygrothermal environment, while the obtained solutions are in excellent agreement with published results. Effect of initial deflection, hygrothermal load and elastic foundation has been investigated, which implies the hygrothermal effect on plate in linear bending is prominent but gradually negligible in large deformation, while the nonlinear effects of elastic foundation become significant by the increase of deflection but not obvious at smally deformed state.

Free vibration of non-shallow, laminated cylinders submerged in a fluid with general boundary conditions

This paper presents a theoretical approach to analyze the free vibration of laminated cylinders with general boundary conditions submerged in a fluid. Based on the assumption that the fluid is inviscid, irrotational and incompressible, the equation of motion of the fluid is established. Fluid-structure interaction between the cylinder and the fluid is conducted by satisfying the continuity conditions of the force and of the vibration velocity at the interfaces of the cylinder and the fluid. The curvature–deflection relations are modified to include the effect of the initial curvatures in the circumferential direction of the non-shallow shell. According to the mechanics of composite materials, governing equations for the cylinder undergoing out-of-plane vibration are derived and are solved using Rayleigh-Ritz method. Likely functions of the displacements for cylinders with general boundary conditions are proposed. Furthermore, finite element simulations are fulfilled using ABAQUS. A good agreement between the analytical solutions and finite element results illustrates the efficiency and accuracy of the proposed approach. With the established models, the influence of the slenderness ratio, radius-thickness ratio, the material properties and the fluid-structure interaction on the vibration performance of the laminated cylinder submerged in the fluid is evaluated.

Evolution equations dynamical system of the Lemaître–Tolman–Bondi metric containing coupled dark energy

In this paper, we consider inhomogeneous spherically symmetric models based on the Lemaître–Tolman–Bondi (LTB) metric, assuming as its source an interactive mixture of ordinary baryonic matter, cold dark matter and dark energy with a coupling term proportional to the addition of energy densities of both dark fluids. We reduce Einstein’s field equations to a first-order seven-dimensional autonomous dynamical system of evolution equations and algebraic constraints. We study in detail the evolution of the energy density and spatial curvature profiles along the phase–space by means of two subspace projections: a three-dimensional projection associated with the solutions of the Friedman–Lemaître–Robertson–Walker metric (invariant subspace) and a four-dimensional projection describing the evolution of the inhomogeneous fluctuations. We also classify and study the critical points of the system in comparison with previous work on similar sources, as well as solving numerically the equations for initial energy density and curvature profiles that lead to a spherical bounce whose collapsing time we estimate appropriately.

Deformation mechanism analysis of three-roller continuous and synchronous calibration process of straightness and roundness for LSAW pipes

The continuous and synchronous calibration process for straightness and roundness of LSAW (longitudinally submerged arc welding, LSAW) pipes with three rollers is a bidirectional reciprocating bending process. It includes both axial and circumferential directions. It is particularly important to reveal the deformation mechanism, which provides theoretical support for the calibration process to be applied to actual production. Based on this, through the combination of references, theoretical analysis and numerical simulation, the deformation mechanism is analyzed in this paper. The whole deformation process of pipe is modeled and then numerically simulated with FEM software of ABAQUS. The results show that reciprocating bending can eliminate the difference of initial curvature, so that the axial curvature and circumferential curvature are unified to the same direction and value, respectively. The calibration process of LSAW pipes is realized by the synergy between the axial reciprocating bending straightening process and the circumferential reciprocating bending rounding process. The simulation and experimental results support the theoretical results, and the deformation is mainly caused by axial stress and circumferential stress.

Snap-through load improvement of bistable composite shell with initial curvature by an adjustive angle

Bistable composite shells with an initial curvature have been extensively studied owing to their light weight and morphing. The bistable behaviour is influenced by the thermal residual stress generated during the manufacturing of bistable composite shells with initial curvature. Hence, this study proposes a method based on an adjustive angle to improve the snap-through load and enhance the load-bearing capacity of bistable composite shells with an initial curvature. The critical snap-through and snap-back loads at different adjustive angles are obtained by experiments and the finite element method, while the adjustive angle for the maximum critical load is captured. Moreover, the effect of the initial radius on the adjustive angle is provided, and the load displacement after adjustment at different radii and cross-section angles are presented.

Tool-part interaction effect on configurations of bistable composite shell with initial curvature

Tool-part interaction during the manufacture of the bistable composite shells with initial curvature is inevitable, which has a noticeable influence on stable configurations. The effect of tool-part interaction is considered by introducing a shear layer whose parameters are determined by a series of experiments. This paper develops an analytical model with shear layer effect based on the Rayleigh-Ritz model to capture the configuration variation with bistable composite shell with initial curvature. The model reveals the rule of curvature change in different radii and plies, which provides a criterion for the existence of bistability. The results show tool-part interaction has a significant influence on thin bistable composite shells with initial curvature whose prediction accuracy is improved. The analytical predictions are verified by results based on the experiments and finite element models. Moreover, the influences of initial radius, cross-section angle, stacking sequence, and twisting response are analyzed. The twist behavior of two stable configurations is investigated, which can provide a guide for designing the bistable composite structures.

Nonlinear forced vibrations of a slightly curved pipe conveying supercritical fluid

Vibrations of pipes caused by axially flowing fluids are very common in engineering applications. Due to material imperfections, guide misalignment, and improper supports, the installed pipes are prone to the initial curvature. Though small, the initial curvature can significantly change the dynamic characteristics of the slightly curved pipe system. This study investigates the non-linear forced vibration of a slightly curved pipe conveying supercritical fluid around the curved equilibrium, with the emphasis on amplitude–frequency responses around two asymmetric non-trivial equilibrium configurations. The governing equations for the forced vibration of a slightly curved pipe conveying supercritical fluids are derived using the generalized Hamilton principle. Then, the equations of motion are discretized into a set of coupled ordinary differential equations via the Galerkin truncation method and solved by the harmonic balance method combined with the pseudo-arc length technique. The approximate analytical results are verified by the numerical integration results. The obtained results demonstrate that the initial curvature has a significant effect on the dynamic characteristics of pipes conveying supercritical fluids, and can lead to significant differences in the dynamic response of the pipe system near different equilibrium configurations.

A cell-centered finite volume formulation of geometrically exact Simo-Reissner beams with arbitrary initial curvatures.

This article presents a novel total Lagrangian cell‐centered finite volume formulation of geometrically exact beams with arbitrary initial curvatures undergoing large displacements and finite rotations. The choice of rotation parameterization, the mathematical formulation of the beam kinematics, conjugate strain measures, and the linearization of the strong form of governing equations are described. The finite volume based discretization of the computational domain and the governing equations for each computational volume are presented. The discretized integral form of the equilibrium equations is solved using a block‐coupled Newton–Raphson solution procedure. The efficacy of the proposed methodology is presented by comparing the simulated numerical results with classic benchmark test cases available in the literature. The objectivity of strain measures for the current formulation and mesh convergence studies for both initially straight and curved beam configurations are also discussed.

Curved beams with circular cross‐sections under pure in‐plane bending

AbstractThis paper deals with the phenomenon of flattening or inflation of cross‐sections caused by pure bending on beams of hollow circular cross‐section with or without initial curvature. Both initially straight and initially bent tubes are analyzed under in plane bending. Results over a wide range of initial curvature values are presented. Finally, the area of validity of the expressions used is studied, as well as the deformations and stresses that occur in practice.

Microlensing constraints on clustered primordial black holes

The discovery of black-hole-binary mergers through their gravitational wave (GW) emission has reopened the exciting possibility that dark matter is made, at least partly, of primordial black holes (PBHs). However, this scenario is challenged by many observational probes that set bounds on the relative PBH abundance across a broad range of viable PBH masses. Among these bounds, the ones coming from microlensing surveys lead to the strongest constraints in the mass range from $\ensuremath{\sim}{10}^{\ensuremath{-}10}$ to a few ${M}_{\ensuremath{\bigodot}}$. The upper part of this range precisely corresponds to the mass window inside which the formation of PBHs should be boosted due to the QCD phase transition in the early Universe, which makes the microlensing probes particularly important. However, it has been argued that taking into account the inevitable clustering of PBH on small scales can significantly relax or entirely remove these bounds. While the impact of PBH clustering on the GW event rate has been studied in detail, its impact on the microlensing event rate has not yet been fully assessed. In this paper, we address this issue, and show that clusters arising from isocurvature perturbations, that originating from PBHs formed from Gaussian initial curvature perturbations, do not alter the current microlensing constraints, as they are not sufficiently compact.

Influence of geometric imperfections on the nonlinear forced vibration characteristics and stability of laminated angle-ply composite conical shells

The forced vibration characteristic of laminated composite truncated conical shell has been analyzed by including von Karman kinematic non-linearity. The geometric imperfection is included in the analysis by providing an initial doubly sinusoidal transverse displacement. The finite element analysis has been carried out using the displacement field of FSDT and the constrained strain terms are interpolated using field consistent modified shape functions in order to avoid membrane/transverse shear locking. The steady state periodic response has been obtained by solving the governing equations in time domain using modified shooting method and arc length/pseudo-arc length continuation techniques. The main aim of the paper is to explore the effects of initial imperfections, fiber-angle and curvature on the nonlinear periodic response characteristics. Further, the stability of the periodic response has also been investigated and the ensuing bifurcations resulting in loss/gain of stability has been discussed. The parameters affecting the softening/hardening nonlinear behavior of the conical shells have also been assessed. The nonlinear frequency response reveal greater amplitude during inward half cycle due to destabilizing nature of the nonlinear membrane stress resultants during inward motion at large amplitudes. Multiple stress reversals is observed during a periodic cycle which has large ramifications on the fatigue design.

СХОДИМОСТЬ ЧИСЛЕННОГО ДИАГРАММНОГО МЕТОДА НЕЛИНЕЙНОГО РАСЧЁТА СТЕРЖНЕВЫХ ЖЕЛЕЗОБЕТОННЫХ ЭЛЕМЕНТОВ

Earlier, authors considered the under-examined question of accuracy (error) in the theory of the diagram method for calculating reinforced concrete core elements. The notion of convergence of the numerical implementation of the method under consideration is closely related to it, which has so far remained undisclosed. The article presents a theoretical justification of the convergence criterion of a numerical diagram method for calculating the strength of reinforced concrete bendable elements. The resulting criterion coincides in form with the Chebyshev norm. It implies a criterion for stopping the iterative calculation process and an estimate of the error of the numerical diagram method. Using the example of a reinforced concrete element with a rectangular cross section and double reinforcement, the issue of convergence of iterative strength calculation with varying concrete class and percentage of reinforcement is investigated. It is established that for all the considered design variants, the iterative calculation process converges after the 6th iteration at the initial curvature approximation and after the 4th iteration at , with a relative calculation error of δ<1 %. In addition, it is found that with an increase in the percentage of reinforcement, the convergence of the calculation improves: with the number of iterations equal to 4, the error in the design variant B60, µ = 0.5 % is 10.3 %, and with B35, µ = 3.0 %–0.98 %.

Development of a Machine Learning Algorithm for at Home Curvature Assessment

ABSTRACT Introduction Peyronie's disease prevalence estimates suggest that 11-15% of men suffer from this disease, although only 1% seek evaluation. When patients do seek help, tools for penile curvature assessment are lacking. This represents a barrier for both patient engagement with a health care provider, and for proper assessment by their treating clinician. Objective We set out to develop a tool for patient and clinician led assessment of Peyronie's disease using a neural network system capable of plaque assessment of photographic images. Methods Men underdoing penile curvature assessment in a sexual medicine clinic were recruited to enroll in this study. Images were taken of the erect penis from the left, right and top sides using an Apple iPad™. Model training was conducted with a residual neural network (ResNet), a neural network-based framework used for image recognition, to identify male genitals. To assess basic curvature a mathematical formulation was created to calculate the penile curvature after fitting linear lines from genital tip to curvature point and from curvature point to the base of the penis. To validate the algorithms performance two urologic surgeons with extensive experience performing curvature assessments were asked to use the labelling software Rectlabel™ to place linear lines identifying the penile curvature on the same photographs used to train the model. Results Initial training of the image analysis model has allowed for identification of the presence of a curvature of a penis, with ongoing training for curvature quantification (Figure 1). We have trained the model to remove background images, isolating the genitals (Figure 1) to aid in patient privacy. When assessing the models ability to measure penile curvature the algorithm calculated the curvature with a median difference of 7.7 degrees between model and physician assessment across the photographic library. Conclusions This study presents an algorithm capable of performing accurate curvature assessment based on photographic images. With demonstration of curvature assessment via photographic images this will allow patients to perform an initial curvature assessment at home, improving motivation for patients to seek help. Furthermore, this technology can augment clinician led curvature assessment, providing an objective and easy means for documenting disease severity. Disclosure No

Buckling enhancement of tubular metamaterial with axial zero thermal expansion by integrating two adjustment mechanisms

Artificially designed mechanical metamaterials with desired property of zero thermal expansion (ZTE) have already made great progress motived by the urgent needs of high-end equipment and instruments served in large fluctuating temperature environment. Various thermal expansion adjustment mechanisms are developed to achieve controllable thermal deformation. However, only designing ZTE is not normally sufficient, but must be combined with enough mechanical performances for carrying mechanical loads. Hence in this study, a method of bucking enhancement for designing tubular metamaterials with axial ZTE is firstly proposed by integrating two existing adjustment mechanisms. Compared with the previous design under the single Poisson contraction mechanism, the present axial ZTE property is mainly achieved through thermally bending-adjustment mechanism, and therefore avoid the unfeasibility of requiring too large thermal expansion coefficient difference for constituent materials. Meanwhile, the significant buckling capacity loss caused by the introduced initial curvature used for triggering thermally bending-adjustment mechanism is prominently improved by taking the advantage of Poisson contraction mechanism. The results obtained from detailed numerical simulations verify the design targets of simultaneous axial ZTE and buckling enhancement. The proposed design strategy of mechanism combination is also proved effective to enhance the buckling capacity of present dual-mechanism metamaterial without obvious increase of structural mass.

Parametric resonance of bi-directional axial loads shallow arch microresonators

In this work, we investigate analytically and experimentally parametric resonances of an in-plane clamped-guided shallow arch microresonator. The arch is connected to a T-shaped moveable mass, which is sandwiched between two electrodes to electrostatically activate the device and to offer bi-directional axial loads option. The device is tested under primary and secondary parametric resonances. In addition, an analytical model is presented taking into account the initial rise of the microbeam and the sliding motion at the guided side. The static and free vibration problems are solved using the Differential Quadrature Method, and the dynamic response is simulated using an assumed mode Galerkin approximation. The theoretical results of the static and dynamic behavior of the device are compared to experimental data showing good agreement. Moreover, we demonstrate the use of parametric excitation to significantly amplify the axial motion. It is found that the second parametric resonance, corresponding to the fundamental mode of the arched microbeam, has a higher amplitude than the principal parametric case, due to the initial curvature of the beam. Thus, the proposed device can be a promising candidate for variety of sensing applications.

Steered fiber paths for improved in-plane compressive response of aerostructural panels: Experimental studies and numerical modeling

Results for the manufacturing and structural testing of steered fiber composite panels are presented in this paper. A detailed algorithm and implementation of a surrogate model based optimization procedure in conjunction with a global optimizer such as multi-objective Genetic Algorithm (GA) was introduced for steered fiber composite panels in previous studies by the authors . Three designs were chosen based on the criteria that the total gain in mass be less than 10%, the decrease in global stiffness capped at 10% and more than 25% increase in buckling load compared to a unidirectional laminate. By necessity, the optimal designs incorporated manufacturing induced unintended deviations also known as manufacturing signature(MS). Details of a pixelated Finite Element model to capture as-manufactured behavior of these panels including initial curvature and thickness variations are discussed in detail, and the numerical results are compared against results from the experimental study.

Exact Solution of Nonlinear Behaviors of Imperfect Bioinspired Helicoidal Composite Beams Resting on Elastic Foundations

This paper presents exact solutions for the nonlinear bending problem, the buckling loads, and postbuckling configurations of a perfect and an imperfect bioinspired helicoidal composite beam with a linear rotation angle. The beam is embedded on an elastic medium, which is modeled by two elastic foundation parameters. The nonlinear integro-differential governing equation of the system is derived based on the Euler–Bernoulli beam hypothesis, von Kármán nonlinear strain, and initial curvature. The Laplace transform and its inversion are directly applied to solve the nonlinear integro-differential governing equations. The nonlinear bending deflections under point and uniform loads are derived. Closed-form formulas of critical buckling loads, as well as nonlinear postbuckling responses of perfect and imperfect beams are deduced in detail. The proposed model is validated with previous works. In the numerical results section, the effects of the rotation angle, amplitude of initial imperfection, elastic foundation constants, and boundary conditions on the nonlinear bending, critical buckling loads, and postbuckling configurations are discussed. The proposed model can be utilized in the analysis of bio-inspired beam structures that are used in many energy-absorption applications.

Natural Frequencies and Modes of Electrostatically Actuated Curved Bell-Shaped Microplates

Configuration-dependent spectral behavior of initially curved circular microplates loaded by a distributed nonlinear electrostatic force is investigated. The structures under consideration are distinguished by two interesting features. The first is that the plates are initially bell-shaped, rather than flat or spherical, and therefore have regions of both positive and negative curvature. Second, the plates are sufficiently curved to exhibit snap-through buckling and bistability. The structure is described in the framework of the nonlinear Föppl von Kármán shallow plate theory. The influence of the initial curvature and loading on the free vibrations around unloaded and deformed equilibria is investigated. The results of the Galerkin model backed by the finite elements analysis show that the modes of even slightly curved bell-shaped unloaded plates differ significantly from those of the initially flat plates. As a result, when the natural modes of a curved plate are used as the base functions, a significantly better convergence of the RO model is achieved. In the vicinity of the critical snap-through and snap-back configurations, the sensitivity of the natural frequencies to the plate deflection is much higher than in the unloaded state. This high tunability opens new opportunities for the design of better resonant sensors with enhanced performance.

Modeling of the oscillation amplitude of a statically indeterminate flat frame subjected to the impact load with account taken of the contact deformation

Introduction. The article addresses transverse vibrations of a post in a rigidly fixed statically indeterminate flat frame subjected to the falling load, having pre-set mass and pre-impact velocity. The post of a vertical frame has initial curvature affecting the maximum amplitude of transverse vibrations triggered by the impact.
 Materials and methods. In the course of modeling, the frame beam impact takes account of deformations in the contact area to ensure the accuracy of calculations, because otherwise the impact force value will be overestimated. It is assumed that the falling load has the shape of a cylinder featuring a certain length, when the transverse load impact on a frame beam is simulated. The linearization of the relationship between the force and the deformation of cylindrical surfaces is used. The frame post, connected to the beam and the base, is a homogeneous rod rigidly fixed at both ends. Following the load impact on the frame beam, the top end of the post absorbs the initial bending moment and the shear force, whose values depend on the mass the and pre-impact velocity of the load, the beam attachment method, and the ratio between axial moments of inertia in beam and post sections in the plane of the frame. Using the method of initial parameters, the maximum deflection of a perfectly straight and curved post is calculated for different pre-impact velocity values of the load. The maximum deflection was modeled for curved and perfectly straight posts at different pre-impact velocities of a load having the same mass.
 Results. The dependence between the value of maximum deflection of a vertical frame post and the pre-impact velocity of the falling load was obtained.