Deflection Curvature Research Articles

A detection method integrating modal deflection curvature difference and natural frequency for structural stiffness degradation

A detection method integrating modal deflection and natural frequency is proposed to locate and quantify the damage of the beam. A damage identification index using modal deflection curvature difference is developed to locate damage. Note that the modal deflection is derived from the flexibility matrix and virtual force. A damage quantification equation is established by the transfer matrix method, which includes the parameters of natural frequencies, damage coefficients and damage location. Since the damage location parameters are determined by the proposed damage identification index, the damage coefficients of the damaged segments can be determined from the natural frequencies according to the damage quantification equation. The proposed damage detection method is verified numerically and experimentally. The results indicate that the proposed method can well locate and quantify the local damage of beams, especially for the beams with non-uniform damage degradation. The proposed damage localization index is more appropriate to locate damage than the index using modal flexibility curvature (MFC) or modal flexibility curvature matrix (MFCM).

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.

FEM Free Damage Detection of Beam Structures Using the Deflections Estimated by Modal Flexibility Matrix

The deflection of the beam estimated from modal flexibility matrix (MFM) indirectly is used in structural damage detection due to the fact that deflection is less sensitive to experimental noise than the element in MFM. However, the requirement for mass-normalized mode shapes (MMSs) with a high spatial resolution and the difficulty in damage quantification restricts the practicability of MFM-based deflection damage detection. A damage detection method using the deflections estimated from MFM is proposed for beam structures. The MMSs of beams are identified by using a parked vehicle. The MFM is then formulated to estimate the positive-bending-inspection-load (PBIL) caused deflection. The change of deflection curvature (CDC) is defined as a damage index to localize damage. The relationship between the damage severity and the deflection curvatures is further investigated and a damage quantification approach is proposed accordingly. Numerical and experimental examples indicated that the presented approach can detect damages with adequate accuracy at the cost of limited number of sensors. No finite element model (FEM) is required during the whole detection process.

In Situ Substrate Curvature Measurement of BaTiO3 Films Deposited by Aerosol Deposition

Residual stress plays an important role in the properties and performance of coatings, such as coating–substrate adhesion. With in situ residual stress measurements, further insight into the coating formation process can also be obtained. Substrate curvature deflection measurements during the aerosol deposition of BaTiO3 were employed to calculate the coating’s residual stress via the Stoney formula and compared to x-ray diffraction measurements. Analysis of the substrate deflection behavior during coating application is discussed and compared to related spray processes.

Design optimization of a contact-aided continuum robot for endobronchial interventions based on anatomical constraints

PurposeA laser-profiled continuum robot (CR) with a series of interlocking joints has been developed in our center to reach deeper areas of the airways. However, it deflects with constant curvature, which thus increases the difficulty of entering specific bronchi without relying on the tissue reaction forces. This paper aims to propose an optimization framework to find the best design parameters for nonconstant curvature CRs to reach distal targets while attempting to avoid the collision with the surrounding tissue.MethodsFirst, the contact-aided compliant mechanisms (CCMs) are integrated with the continuum robot to achieve the nonconstant curvature. Second, forward kinematics considering CCMs is built. Third, inverse kinematics is implemented to steer the robot tip toward the desired targets within the confined anatomy. Finally, an optimization framework is proposed to find the best robot design to reach the target with the least collision to the bronchi walls.ResultsExperiments are carried out to verify the feasibility of CCMs to enable the nonconstant curvature deflection, and simulations demonstrate a lower cost function value to reach a target for the nonconstant curvature optimized design with respect to the standard constant curvature robot (0.11 vs. 2.66). In addition, the higher capacity of the optimized design to complete the task is validated by interventional experiments using fluoroscopy.ConclusionResults demonstrate the effectiveness of the proposed framework to find an optimized CR with nonconstant curvature to perform safer interventions to reach distal targets.

МАТЕМАТИЧЕСКОЕ ОПИСАНИЕ НАПРЯЖЕННО-ДЕФОРМИРОВАННОГО СОСТОЯНИЯ ЦАПФЫ ШАРОВОЙ МЕЛЬНИЦЫ ПОД ДЕЙСТВИЕМ СИЛЫ ТЯЖЕСТИ И ВРАЩЕНИЯ

The article discusses the pin of a ball mill under the action of constant loads of the body with grinding material, the simultaneous action of gravity and rotation due to the moment of external forces. During the operation of a ball mill, a dangerous section of the bottoms is the place where the cylindrical part of the trunnion becomes conical. The stress-strain condition of the ball mill’ pin is estimated on the basis of a mathematical model that includes a complete system of equilibrium equations, defining ratios of elastoplastic deformation. It takes into account the effects of cyclic loading of the material, with the corresponding initial and boundary conditions. The dynamic load that occurs during rotation is taken into account, according to the D'Alembert's principle, which means inertia forces are added to all acting external forces. The bend equation of pin's axle is obtained; it considers the action of inertia forces. The dependences of the deflection, deflection curvature and stress on the longitudinal coordinate under the action of gravity and rotation on the pin’s axle are obtained. The value of the shear stress from the action of torque is determined. The general expression of equivalent stress is examined. It includes the complex stress-strain condition of the ball mill’s pin, which experiences tensile stress from bending loads and shear stress of torque.

Semi-analytical solutions of ultimate load for a rectangular concrete-filled tubular column subjected to eccentric compression

This paper presents a semi-analytical method (SAM) to predict accurately the ultimate capacity of a rectangular concrete-filled tubular (RCFT) column subjected to eccentric compression. In this method, the analytical equations are established based on all the possible stress states of the section. Specifically, each equation set contains the equilibrium equations, extremum equations, curvature–deflection equation and stress–curvature equation. The predicted ultimate load is solved by numerical solution of equation sets. The proposed approach chose an accurate piecewise-nonlinear constitutive model for confined concrete considering beneficial confinement effect of rectangular steel tube. The pre-existing relevant tests and finite element method (FEM) were compared with the proposed SAM to verify the accuracy and applicability of predicted ultimate loads by SAM, and parameters analyses for aspect ratio, steel strength, depth-to-thickness ratio and length-to-depth ratios were studied by proposed SAM to determine these effects on N–M interaction curve of RCFT columns. The comparison indicates that the proposed SAM is accurate in predicting the ultimate loads of RCFT columns under eccentric compression.

Robotic-Assisted Needle Steering Around Anatomical Obstacles Using Notched Steerable Needles.

Robotic-assisted needle steering can enhance the accuracy of needle-based interventions. Application of current needle steering techniques are restricted by the limited deflection curvature of needles. Here, a novel steerable needle with improved curvature is developed and used with an online motion planner to steer the needle along curved paths inside tissue. The needle is developed by carving series of small notches on the shaft of a standard needle. The notches decrease the needle flexural stiffness, allowing the needle to follow tightly curved paths with small radius of curvature. In this paper, first, a finite element model of the notched needle deflection in tissue is presented. Next, the model is used to estimate the optimal location for the notches on needle's shaft for achieving a desired curvature. Finally, an ultrasound-guided motion planner for needle steering inside tissue is developed and used to demonstrate the capability of the notched needle in achieving high curvature and maneuvering around obstacles in tissue. We simulated a clinical scenario in brachytherapy, where the target is obstructed by the pubic bone and cannot be reached using regular needles. Experimental results show that the target can be reached using the notched needle with a mean accuracy of 1.2 mm. Thus, the proposed needle enables future research on needle steering toward deeper or more difficult-to-reach targets.

An illustrated introduction to general geomorphometry

Geomorphometry is widely used to solve various multiscale geoscientific problems. For the successful application of geomorphometric methods, a researcher should know the basic mathematical concepts of geomorphometry and be aware of the system of morphometric variables, as well as understand their physical, mathematical and geographical meanings. This paper reviews the basic mathematical concepts of general geomorphometry. First, we discuss the notion of the topographic surface and its limitations. Second, we present definitions, formulae and meanings for four main groups of morphometric variables, such as local, non-local, two-field specific and combined topographic attributes, and we review the following 29 fundamental morphometric variables: slope, aspect, northwardness, eastwardness, plan curvature, horizontal curvature, vertical curvature, difference curvature, horizontal excess curvature, vertical excess curvature, accumulation curvature, ring curvature, minimal curvature, maximal curvature, mean curvature, Gaussian curvature, unsphericity curvature, rotor, Laplacian, shape index, curvedness, horizontal curvature deflection, vertical curvature deflection, catchment area, dispersive area, reflectance, insolation, topographic index and stream power index. For illustrations, we use a digital elevation model (DEM) of Mount Ararat, extracted from the Shuttle Radar Topography Mission (SRTM) 1-arc-second DEM. The DEM was treated by a spectral analytical method. Finally, we briefly discuss the main paradox of general geomorphometry associated with the smoothness of the topographic surface and the non-smoothness of the real topography; application of morphometric variables; statistical aspects of geomorphometric modelling, including relationships between morphometric variables and roughness indices; and some pending problems of general geomorphometry (i.e. analysis of inner surfaces of caves, analytical description of non-local attributes and structural lines, as well as modelling on a triaxial ellipsoid). The paper can be used as a reference guide on general geomorphometry.

Curvature Evolution of Porcelain Tile during Firing

Planarity is one of indispensable attribute of a ceramic tile quality. During the firing changes on curvature may be permanent causing damage on quality and productivity. The objective was to evaluate curvature evolution on porcelain tile during heating stage of firing. Effects of engobe and glaze coating were evaluated. The performance of two compositions of porcelain tile was studied on industrial (1000 mm x 500 mm x 10 mm) and laboratorial (100 mm x 50 mm x 6 mm) scale. Industrial test pieces were fired at 950 and 1200 °C. Final curvature was measured by conventional dial indicator. Curvature evolution of laboratorial test pieces was evaluated by thermal fleximetry from 25 to 1200 °C. This characterization was capable to identify very significant positive curvature deflection on temperature range from 930 to 1200 °C, directly associated to permanent planarity defects. Differences on composition affect significantly the curvature evolution.

Analysis on Nonlinear Curvature Deflection for Reinforced Concrete Two-Way Slabs under Uniformly Distributed Load

Reinforced concrete two-way slabs are widely used in industrial, civil, public buildings. However, the calculation method of curvature of deflection wasn’t clearly put forward in Code for design of concrete structures in China. Considering the nonlinear characteristics of concrete and bidirectional bending the formula of curvature deflection for reinforced concrete two-way slabs was derived based on plate theory in this paper. The iterative method is adopted in order to solve stress and strain of reinforced and concrete in reinforced concrete two-way slabs. The whole calculation process was realized by MATLAB software programming. The correctness of method in this paper was confirmed by comparing the results and the test data of the literature.

A Study of the Semi-Perpetual Pavement Performance in Queensland

Abstract This paper presents the characteristics of a long-term pavement performance site constructed with semi-perpetual materials. The design life of a perpetual pavement is normally specified as greater than 40 years. The design requires asphalt overlays at the tenth, 20th, and 30th year for extending the life of the pavement structure. A case study of a semi-perpetual pavement with an application of the stage construction technique will be presented. The study shows that the falling weight deflectometer (FWD) central deflection of the semi-perpetual pavement was reported to be between 230 to 240 microns and the deflection curvature is less than 100 microns. The horizontal tensile strain of the semi-perpetual structure varies from 102 to 187 micro-strains and the vertical compressive strain was analyzed to be between 65 to 98 micro-strains. For the structural overlay at the 30th year of service life would improve the tensile and compressive strains of the structure to the levels which would satisfy the fatigue endurance limit and limiting subgrade strains of that of a perpetual pavement. The non-linearity behaviour of the subgrade material of the semi-perpetual pavement was analyzed by computing the surface modulus using Boussinesq’s equation and material constant of subgrade material model. The results obtained from both methods showed that the subgrade material of the semi-perpetual pavement exhibits linear elastic behaviour.

ELECTRICAL ACTIVATION OF THERMO-RESPONSIVE PVC-CFRP LAMINATE ACTUATORS

A bimorph actuator of PVC-CFRP laminate (PVC: polyvinylchloride; CFRP: carbon fiber reinforced plastic) is fabricated, where its bending results from the large disparity between the coefficients of thermal expansion of PVC and CFRP. Thermal expansion is brought about by applying a voltage to the CFRP layer of the PVC-CFRP laminate to generate Joule heat. Thus, the PVC-CFRP laminate acts as an electroactive polymer actuator. The authors experimentally confirmed that laminate temperature due to Joule heat completely determines laminate deflection curvature, and also demonstrated that temperature determines the blocking force generated by PVC-CFRP laminate.

Postbuckling analysis of beams of arbitrary cross section using BEM

In this paper, the postbuckling analysis of beams of arbitrary cross section is presented taking into account moderate large displacements, large angles of twist and adopting second order approximations for the deflection–curvature relations. The beam is subjected to the combined action of the arbitrarily distributed or concentrated axial, transverse and torsional loading, while it is supported by the most general boundary conditions including elastic support or restraint. Starting from a displacement field without any simplifying assumptions about the angle of twist amplitude and based on the total potential energy principle, four highly coupled nonlinear governing differential equations are derived taking into account the shortening and warping effects and the Wagner’s coefficients due to the asymmetric character of the cross section. The arising four boundary value problems with respect to the transverse displacements, to the axial displacement and the angle of twist are solved using the Analog Equation Method, a BEM based method. The geometric, inertia, torsion and warping constants of the arbitrary beam cross section are evaluated employing only boundary integrals. The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross section’s torsional rigidity is evaluated exactly without using the so-called Saint–Venant’s torsional constant. Numerical examples are worked out to illustrate the efficiency, accuracy and range of applications of the developed method. Conclusions of great practical interest are drawn.

Curvature optical fiber sensor by using bend enhanced method

Deflection curvature measurement can offer a number of advantages compared with the well-established strain measurement alternative. It is able to measure thin structure; fiber has no resistance with force, which leads to a high precision. There are many kinds of curvature gauges with different operation principles. A low-cost curvature optical fiber sensor using bend enhanced method to improve its curvature measurement sensitivity was developed in recent years. This sensor can distinguish between convex bending and concave bending and has a good linearity in measuring large curvature deformation. Whisper gallery ray theory and Monte Carlo simulation are new achievements by computer experiment. The operation mechanism of this curvature optical fiber sensor is presented based on light scattering theory. The attenuation is ascribed to the transmission mode changing by the curvature of the fiber, which affects the attenuation of the surface scattering. The mathematical model of relationship among light loss, bending curvature, surface roughness, and parameters of the fiber’s configuration is also presented. We design different kinds of shapes of sensitive zones; each zone has different parameters. Through detecting their output optical attenuations in different curvatures and fitting the results by exponential decaying functions, the proposed model is demonstrated by experimental results. Also, we compare the experimental results with the theoretical analysis and discuss the sensitivity dependence on bending direction.

CURVATURE EFFECT OF INTERLAYER VAN DER WAALS FORCES ON AXIAL BUCKLING OF A DOUBLE-WALLED CARBON NANOTUBE

The curvature effect of interlayer van der Waals (vdW) forces on an axially compressed double-walled carbon nanotube is studied. Unlike existing models which assume that the interlayer vdW pressure at any point between the inner and outer tubes depends merely on the difference of their deflections at that point, the present model considers the dependence of the interlayer vdW pressure on the curvature of the difference of deflections at that point. A simple formula is derived for the critical axial strain, which clearly indicates the role of the interlayer vdW forces affected by the curvature of deflection. In particular, the critical axial strain predicted by the present model is higher than or equal to that given by the existing models without the curvature effect provided that the coefficient for the curvature dependence of the interlayer vdW pressure is negative. Furthermore, the curvature effect on the critical axial strain is more significant for buckling modes of smaller wavelengths. These results indicate that the curvature effect, which has been neglected in all existing models, could play a significant role in various buckling problems especially for multi-walled carbon nanotubes of smaller radii.

Structural deflection measurement

The concept of measuring deflection curvature of structures under bending loading with a device called a ‘curvature gauge’ is described. The application domain is specified in which this concept offers advantages over the alternative of measuring strain in terms of the measurement sensitivity, flexibility to choose the location for the sensor placement and immunity to the effects of microstructural interfacing between dissimilar materials that the sensor presence introduces. Details of the curvature gauge sensor are also given.

Longitudinal anisotropic stress and deformation in multilayered film heterostructures due to lattice misfit

A modified shear lag analysis based on the formulation of elastic anisotropy is proposed and developed to calculate the longitudinal stress in multilayered heterostructures of semiconductor materials with interfacial lattice misfit strain. The shear lag approach to analyze layered structures was adopted in Nakajima’s model, in which the misfit strains were considered by imposing an internal force on each imaginary layer along the edges. Since lateral deflection and internal moment are not introduced in shear lag analysis, the moment balance cannot be satisfied even if the imaginary layer is very thin. Moreover, the internal force, imposed on the boundary of the layered structure, is determined based on the condition of isotropic elasticity; this method cannot evaluate the distributions of anisotropic longitudinal stress and deflection curvature in layered structures. In this study, a modified shear lag method, which is formulated based on the theory of anisotropic elasticity and also takes account of both the effects of lateral deflection and moment balance, is proposed. A realistic traction boundary condition, instead of imaginary internal force evaluated under the condition of infinite length, is imposed on the both edges of the structure. In convenience of formulation as well as to facilitate the efficiency of computation, the matrix and eigenvalue methods are also applied to decouple and solve the linear systems of differential equations. Since the moment balance, misfit strain and curvature are all considered in analysis, compared to the Nakajima’s model, this method provides a more accurate and efficient approach to investigate the deflection and distributions of lateral stress induced by misfit strains and thermal loadings in multilayered heterostructures under the condition of anisotropic elasticity.

Thin structure deflection measurement

Deflection curvature is easily observed during bending of thin structures. There are, however, few practical means available for measuring it. As a consequence, curvature measurements are extremely rare. Strain is usually the preferred measurand of choice. This preference is disadvantageous in the case of thin structures because strain can then be so small that very high resolution sensors are required despite the apparently large deflection curvature. A method of measuring such curvature is presented in this paper. Its conceptual advantages over strain measurement include: (1) position-invariant readings throughout the structural section; (2) sameness of the true and apparent measurands irrespective of the microstructural effects introduced by the sensor; (3) higher sensitivity in the case of thin structures.

DYNAMIC STABILITY OF A VISCOELASTIC BEAM SUBJECTED TO HARMONIC AND PARAMETRIC EXCITATIONS SIMULTANEOUSLY

In this paper the dynamic stability is studied of a simply supported viscoelastic beam, which is subjected to harmonic and parametric excitations simultaneously. Considering the viscoelastic differential constitutive law, the large deflection curvature and the non-linear effects of inertia, stiffness and damping, the generalized differential governing equation of the viscoelastic beam is obtained. By choosing a simple example of the three-parameter viscoelastic model and using the Galerkin approximation, the governing equation is reduced to a third order non-linear ordinary differential equation. The Stevens method is followed to analyze the stability of the linear system and apply both the method of variation of parameters and the method of averaging to analyze the non-linear system, with the assumption of small harmonic excitation. In this paper, the Routh-Hurwitz criterion is used to investigate the stability of steady state solutions of the parametric resonance, and the non-linear effects of the spring, mass and damping terms of the subsystem are also studied.