Static Deflection Research Articles

Computer vision-based real-time deflection monitoring of complex and sizeable steel structures

Deflection, as an intuitive index, plays a pivotal role in assessing the load-bearing capability and structural integrity of complex and sizable steel structures. Notwithstanding, the conventional contact measurement is limited to static deflection and necessitates work stands and manual readings. Therefore, it hinders the attainment of dynamic deflection and fails to cater to the engineering demands of real-time and prolonged monitoring. By leveraging the advancements in computer vision technology, we propose an innovative system for real-time deflection monitoring of complex and sizable steel structures, particularly suitable for monotonic deformation induced by prolonged loading. Specifically, the off-axis-based displacement measurement method was adopted to surmount the constraint of requiring the optical axis of the camera to be perpendicular to the target. Additionally, the inverse compositional Gauss-Newton (IC-GN) algorithm and parallel computation based on seed point diffusion were exploited to boost the matching and computing efficiency for attaining real-time monitoring of multi-points. To validate the efficacy of the proposed system, we conducted static load monitoring tests on a Bailey beam, with a height of 29.5 m and length of 16.5 m per span, as part of the Alibaba Jiangsu headquarters project in Nanjing. The collected test data were compared with the results from a laser displacement sensor and the ABAQUS model. The outcomes substantiate that the system is capable of non-contact, expeditious, and straightforward installation, besides achieving high accuracy and real-time deflection monitoring. This system serves as a sophisticated solution for health monitoring in constructing complex and sizeable steel structures and further contributes to realizing construction intelligence.

High Aspect Ratio Composite Wings: Geometrically Nonlinear Aeroelasticity, Multi-Disciplinary Design Optimization, Manufacturing, and Experimental Testing

In the field of aerospace engineering, the design and manufacturing of high aspect ratio composite wings has become a focal point of innovation and efficiency. These long, slender wings, constructed with advanced materials such as carbon fiber and employing efficient manufacturing methods such as vacuum bagging, hold the promise of significantly lighter aircraft, reduced fuel consumption, and enhanced overall performance. However, to fully realize these benefits, it is imperative to address a multitude of structural and aeroelastic constraints. This research presents a novel aeroelastically tailored Multi-objective, Multi-disciplinary Design Optimization (MMDO) approach that seamlessly integrates numerical optimization techniques to minimize weight and ensure structural integrity. The optimized wing configuration is then manufactured, and a Ground Vibration Test (GVT) and static deflection analysis using the Digital Image Correlation (DIC) system are used to validate and correlate with the numerical model. Within the fully automated in-house Nonlinear Aeroelastic Simulation Software (NAS2) package (version v1.0), the integration of analytical tools offers a robust numerical approach for enhancing aeroelastic and structural performance in the design of composite wings. Nonlinear aeroelastic analyses and tailoring are included, and a population-based stochastic optimization is used to determine the optimum design within NAS2. These analytical tools contribute to a comprehensive and efficient methodology for designing composite wings with improved aeroelastic and structural characteristics. This comprehensive methodology aims to produce composite wings that not only meet rigorous safety and performance standards but also drive cost-efficiency in the aerospace industry. Through this multidisciplinary approach, the authors seek to underscore the pivotal role of tailoring aeroelastic solutions in the advanced design and manufacturing of high aspect ratio composite wings, thereby contributing to the continued evolution of aerospace technology.

Static deflection of pre-twisted beam subjected to transverse load

In the current research, the static deflection of the pre-twisted beam has been calculated experimentally and numerically using finite element approach (ANSYS workbench 2020R1) and under the effects of different twist angles, different lengths, four boundary conditions of edges support of the beam. The beam was manufactured from PETG filament material by a 3D printer at room temperature. The obtained results showed reasonable acceptance between the experimental and numerical pre-twisted beam deflection. The numerical maximum deflection of the pre-twisted beam decreased with the increase of twisted angle of the beam for clamped-simply and simply-simply edges support. While it was irregularly various for clamped-clamped edge support with a minimum value of the maximum deflection occurred at the twist angle 135o. The maximum deflection of the pre-twisted beam is disappeared gradually at the twist angles greater than 270o for claimed-free edge support. In addition, the maximum deflection of the pre-twisted beam increased due to the beam length increment.

Rice husk silica blended fillers for engine mount application

The functional properties of engine mounts largely depend on the rubber compound formulation. This study proposes the use of rice husk–derived silica (RHS) blended with carbon black (N772) as an effective and environmentally friendly substitute for fillers used in rubber engine mounts (REMs). CV-60 natural rubber was filled with the blended fillers at various ratios, and their compatibility for use as rubber engine mounts (REMs) was assessed. Grey Relational Analysis was utilised to determine the optimal blend loading levels for use in rubber engine mounts, resulting in 40 phr of N772 and 20 phr of RHS cured at 130 °C and 2.5 MPa for 20 min. The developed REMs and conventional REMs had low vibration data variation during the performance assessment. Their resonance transmissibility was 5.03 and 3.74, corresponding to natural frequencies of 24.27 Hz and 26.94 Hz, respectively. The RHS/N772 REMs had excellent damping characteristics and lower transmissibility in the isolation zone of the vibration isolation curve, which is outside of the resonant frequency region. The efficiency curves showed that the blended fillers are a better and more effective material for REMs at all frequencies, balancing static deflection and vibration isolation.

Intermolecular forces and surface stress residual effects on the size-dependent performance analysis of nanocrystalline micro/nano gyroscopes

This work investigates an electrostatically-actuated vibrating beam micro/nano-gyroscope made of nanocrystalline silicon material. The comprehensive size-dependent micro/nanogyroscope model is developed by couple stress and surface elasticity theories. Then, considering the effects of intermolecular forces (Casimir force and van der Waals force) and surface stress residual, an in-depth investigation was conducted on the performance of the micro/nanogyroscope. The calculation results display that the maximum static deflection, pull-in voltage and natural frequency change obviously with the increase of surface stress residual as the scale varies from micrometer to nanoscale. However, the effect of intermolecular forces on the performance of gyroscopes is exactly the opposite, which improves the prediction of system structural softening deformation phenomenon. Considering the influence of the Casimir and van der Waals forces in micro/nano gyroscopic system will help gyroscopes to obtain reliability and functionality sensitivity, increase the accuracy of predicting static deformation, natural frequency and differential frequency. Moreover, a frequency-domain method using the difference between the two vibration natural frequencies is studied, with changing the scale of the gyroscope under the effect of the intermolecular forces. The numerical simulations exhibit that when considering smaller structure sizes of the gyroscope, strong coupling occurs between the intermolecular forces and surface stress residual, which is helpful for the design of micro/nano gyroscopes.

Effect of wooden floorboards on the vibration of timber floor

This study is aimed at investigating those parameters related to timber flooring that can affect the acceptability of vibration behaviour of a timber floor in a residential building in view of the criteria stated in Eurocode EC5. The timber floor investigated is made of OSB/3 floorboards and timber joists. The parameters that are investigated in this study are thickness of flooring, floor joist span, joist spacing and connection of floorboards to the joists. In this context, two cases are considered. First: the flooring is nailed or screwed to the joists and no composite action or interaction is obtained between joists and floorboards. Second: the flooring is glued sufficiently to the joists and full interaction is obtained. The result suggests that glued floorboards perform much better with respect to natural frequency, static deflection and peak floor velocity than nailed or screwed floorboards. In almost all cases of glued floorboards, the result complies fully with the Eurocode 5 design vibration requirements. However, as floor lengths increase, the static deflection will increase beyond the allowable limit, especially for relatively thin floor panels and relatively widely spread joists. For both cases, increasing floorboards thickness and decreasing the joist span by adding more beams can yield even better results to satisfy the requirement of vibration comfort.

Design and Testing of a Single-Tentacle Soft Gripper with an Embedded Suction Cup

In this work, the design and the experimental characterization of a soft gripper which takes inspiration from the octopus tentacle is presented. The system is a single silicone–based pneumatic soft actuator which is able to perform bending motion thanks to its particular geometry and, due to the presence of an embedded suction cup, it can provide enhanced adhesion to the object surface of the goods to be grasped. Firstly, the design aspects as well as the fabrication process of the single-tentacle soft gripper are described. Then, its performances in terms of bending behavior, static deflection, shape variation under applied load and detachment force of the suction cup are evaluated. The experiments include grasping tests of spherical payloads with different weights. This gripper might have impact in the grasping and manipulation of delicate products like mozzarella in the agrifood field.

Improving dynamic process stability in finishing of thin-walled workpieces by optimal selection of stock shape

In 5-axis milling of thin-wall parts, flexibility of the in-process-workpiece (IPW) governs static and dynamic deflections, especially at the semi-finishing and finishing stages. Thus, the near net shape preform, i.e. the stock shape left for semi/finishing is crucial for chatter stability. In this study, a methodology is presented to design the stock shape for improved stability. Coupled process simulation, which includes material removal, finite element analysis (FEA) and process stability simulations, is used to show the effect of stock shape on chatter stability. Spindle speed is optimized along the toolpath based on the varying process dynamic behavior for selected cutter locations (CL). The proposed method is experimentally demonstrated on case studies.

Mathematical and computer modeling of transmission with non-traditional engagement for mining equipment drive

In modern gear mechanics, transmission mechanisms play a crucial role in converting the rotational motion of a driving shaft into the rotational motion of another shaft with varying angular speeds and torque. To achieve optimal designs for the next generation of transmission mechanisms, it is essential to develop mathematical models of their dynamic behavior, conduct computer simulations of the meshing geometry of key components, and visualize the operation of the mechanism. Despite the widespread use of involute gearing in mechanical transmissions, there is ongoing research into new types of gearing that offer advantages over traditional systems. The main challenges facing the industry include increasing the gear ratio in a single stage, enhancing load capacity, and improving efficiency compared to standard gear transmissions. This paper presents the results of mathematical and computer modeling, along with a comparative analysis of the eccentric-cycloid (EC) engagement with the involute gear transmission. Through analytical calculations, the energy-force parameters of the EC gearbox were determined, equivalent stresses and static deflections of transmission shafts were obtained. The paper includes the results of static analysis of elements of the new EC transmission, as well as an algorithm for computer modeling of contact stresses occurring in the engagement. Conclusively, by comparing contact stresses in traditional involute gear transmission, calculated using various analytical methods, with those in EC engagement determined through computer simulation, the advantages of the new transmission type and its potential application in mining equipment transmission mechanisms are highlighted.

Quantifying the effect of end support restraints on vibration serviceability of mass timber floor systems: Testing

Design of mass timber floor systems is commonly governed by vibration serviceability due to high stiffness-to-weight ratio and low inherent damping of timber. Research and design practice have shown that static deflection under a concentrated load and fundamental natural frequency can be effective and robust indicators for vibration performance of mass timber floors. These design parameters are normally calculated by assuming simply supported conditions in existing design methods. However, such an assumption deviates from actual floor supports, especially in platform-framed buildings, and in-situ end support restraints have been widely recognized as a significant factor affecting the vibration performance. The purpose of the study is to quantify the influence of end support restraints on vibration serviceability of mass timber floors in platform construction through a comprehensive experimental program and analytical treatment. This paper is the first part and focus specifically on the experimental work on cross-laminated timber (CLT) panels. In particular, extensive laboratory tests have been conducted on different CLT floor panels with various end support restraints induced by top loads, self-tapping screws and steel angle brackets. The fundamental natural frequency and mid-span deflection under a concentrated load were measured for each end support configuration. The rotational restraint stiffness was determined by comparing results of restrained supports to those of simple supports and represented as end fixity factors. The analysis of test results shows that the CLT floor-to-wall connection exhibited inherent non-linear behaviour and such characteristic was more significant for higher top loads. Compared with screws and brackets, the top loads dominated the partially restrained effect but such dominance gradually diminished for lower-level top loads. In addition, support wall thickness notably impacts the support restraint. It was then suggested that the clear span could be used to determine deflection and frequency in the design, but further investigation is needed.

Numerical and experimental investigation of a high-static-low-dynamic stiffness vibration isolator with tunable stiffness and damping

Nonlinear vibration isolators that take advantage of negative stiffness elements can simultaneously meet the requirements of acceptable static deflection and frequency band of isolation and are thus superior to their linear counterparts. Incorporating electromagnetic elements into the vibration isolator is a common approach to provide the required negative stiffness. Electromagnetic mechanisms are low-cost, tuneable, and operate without friction. Also, they can extract or dampen the energy of the host system through electromechanical coupling. Therefore, electromechanical elements are ideal choices for designing multi-purpose vibration control mechanisms. In this study, three coils surrounded by arrays of permanent magnets are considered. When the system vibrates, their magnetic fields interact with that of a moving magnet attached to a rod supporting an isolated mass. The electromagnetic properties of the proposed system are simulated using the finite element method (FEM) and experimental measurements are used to validate the numerical simulations. Different scenarios for a system consisting of three coaxial coils are considered and compared, including powering the coils, open circuit coils, short circuit coils and coils shunted with an external circuit. Features of each case are discussed and general guidelines for designing a multipurpose vibration controller are given.

A refined first-order shear deformation theory for large dynamic and static deflection investigations of abruptly/harmonically pressurized/blasted incompressible circular hyperelastic plates

In this paper, nonlinear large-deformation dynamic and static responses of the suddenly and harmonically pressurized or blasted compliant incompressible hyperelastic circular plates are investigated through the development of a novel enhanced circular plate theory that in contrast to the available plate theories, utilizes transverse normal strains whose order is much higher than those of the in-plane strains. For this reason, no shear correction factor is needed for the new plate theory. The deformation gradient and Green's strain tensors are first determined based on the first-order shear deformation plate theory as predictors and then, corrected by simultaneously including the transverse compliance and volume conservation concepts in the neo-Hookean framework of hyperelasticity. The equations of motion are obtained using Hamilton's principle. The resulting highly nonlinear equations that include both large deformation and constitutive nonlinearities are solved by a hybrid iterative/updating technique that utilizes a combination of the differential quadrature (DQ) spatial-discretization and Newmark's time-marching methods, after an exhaustive order analysis for the identification of the extremely small terms. The effects of the changes in geometric parameters, material properties, and loading rate and type are investigated on the dynamic lateral deflection of the plate and the approximate fundamental natural frequency. Results reveal that the contribution of the higher vibration modes in the responses is much more remarkable in the high-rate and high-frequency loadings. Furthermore, the deformed shape of the plate that indicates the superimposed effects of the higher vibration modes is plotted for successive time instants.

Size-dependent coupled bending-torsional analysis of piezoelectric micro beams

Nowadays, piezoelectric micro-beam structures are used in various industries, and knowing and analysis of these smart microstructures is important. However, in the modeling of these electromechanical microbeams, the torsion during bending is generally omitted for simplicity. Considering that in some cases, twisting and bending cannot be omitted and must be modeled simultaneously. Therefore, this article presents a coupled bending-torsion model for the first time for static deflection and free vibration analysis of piezoelectric microbeams with nonclassical continuum theories. The governing equations of the motion and boundary conditions of the Timoshenko beam at the micro-scale have been obtained using size-dependent electromechanical theory and Hamilton’s principle. In addition, the Laplace transform is used to solve the static equations, while the generalized differential quadratic (GDQ) method is used to discretize and solve the free vibration equations. In the following, the influence of various parameters, such as the effect of size and geometric conditions, on the static displacements and the natural frequency of the microbeam is discussed.

The harmonic resonance and singularity analysis of bifurcation for the magnetized elastic plate with action of time-varying magnetic potential

This paper deals with the superharmonic resonance of a ferromagnetic thin rectangular plate in the air-gap magnetic field excited by armature magnetic potential. Electromagnetic forces applied on the plate by the air-gap magnetic field cause the plate to transversal vibrate, which affects the air-gap magnetic field in turn, resulting the vibration and magnetic field coupling. According to the basic electromagnetic field theory and considering the magnetoelastic coupling effect, the air-gap magnetic field intensity is obtained by solving the Laplace's equation satisfied the air-gap magnetic boundary conditions. The electromagnetic force model of soft ferromagnetic plates is determined based on theories of electromagnetic and elasticity. According to the large deflection theory of plates, basic energy relationships and variational equations of the elastic plate are given. Eventually, the nonlinear magnetoelastic vibration equation of ferromagnetic thin plates is derived using Hamilton's principle and Galerkin method. The multi-scale method is used to solve the superharmonic resonance to obtain the amplitude-frequency response equation and the stability discriminant of solutions. The topological analysis of amplitude-frequency equation is carried out using singularity theory, and the bifurcation characteristics of systems on physical parameter planes in different regions are obtained according to the transition set. The correctness of analytical solutions is verified by comparison with numerical solutions. Through numerical calculations, curves of the static deflection and equivalent magnetic force of plate with parameters are given, and the amplitude curves, dynamic phase plane trajectories and time history diagrams of system response with changes in electromagnetic and structural parameters are plotted. Results show that both the decrease of armature magnetic potential amplitude and the increases of plate thickness and initial air-gap thickness reduce the static deflection. The increase of armature magnetic potential amplitude increases the equivalent magnetic force. As the decrease of initial air-gap thickness and the increases of armature magnetic potential amplitude and excitation force amplitude, the amplitudes of the upper branch and lower branch curves representing stable solutions decrease and increase, respectively, and the single-value solution region increases.

Sensitivity Analysis of a Damage Detection Method Through High-Resolution Photos on Various Statically Deflected Beams

In this manuscript, the authors deeply investigate and test a modern technique that allows the analysis of a structure starting from a photo to identify and locate damage present on it, rapidly and non-destructively without any physical interaction with the analyzed structure. The technique suitability is tested on four statically deformed beams, on which notches represent the defects. The core of the proposed method is the correlation between the curvature that each beam presents under load conditions and its flexural stiffness. The proposed methodology consists in taking a photo of the inflected beam; subsequently, the acquired photo is manipulated with specifically designed image processing tools, and the second derivative of the beam axis is estimated using two distinct numerical differentiator filters (Lanczos filter and Gaussian wavelets) along with suitable processing to reduce border distortions. The tests conducted demonstrate that it is possible, with an opportune static deflection amplitude, to accurately detect the position of the notch with the proposed procedure; a sensitivity analysis is also conducted by testing the procedure with different beam thicknesses, notch positions, and amplitude of the static deflection. Although the authors realize that the technique can generally require sensibly large displacements, the results seem promising.

Magneto-thermo-elastic coupling vibration and bifurcation characteristics of functionally graded rotating cylindrical shell

The magneto-thermo-elastic coupling vibration of rotating ferromagnetic functionally graded cylindrical shell is investigated in this paper. Based on the physical neutral surface theory and Donnell's theory, the expressions of kinetic energy and strain energy are obtained by introducing geometric nonlinearity. The magneto-thermo-elastic vibration equations of the rotating ferromagnetic functionally graded cylindrical shell in multi-physical field are derived via the Hamilton's principle. Considering the magnetization effect of ferromagnetic shell in magnetic field, the expression of magnetization force is obtained according to the nonlinear magnetic constitutive relation. For simply supported boundary conditions, Galerkin's method is used to obtain the discretized ordinary differential equations, and the static deflection of the shell under static load is solved. The steady-state response of the system during primary resonance and the stability of solutions are given by the multi-scale method and the Lyapunov stability theory. Through numerical examples, the characteristic curves and surfaces of amplitude are plotted, and the parameter ranges corresponding to regions of multi-valued solutions and stable solutions are determined. The system dynamics laws describing the coupling effect between multiple parameters such as force, magnetism, heat, and rotational speed are evaluated. The Global bifurcation diagrams and the maximum Lyapunov exponent spectrums under different control parameters are plotted to analyze the effect of parameter changes on the dynamic response of system. The results show that the vibration characteristics of the system are significantly influenced by the external physical fields, in addition to the shell size and material volume fraction. Slight changes in parameters can lead to violent changes in the dynamic response of the system, exhibiting intermittent, jumping, and chaotic characteristics.

A general simplified method for static and free vibration analysis of coupled shear walls of a bay

In recent years, coupled shear walls have been used more often because they provide a significant percentage of the total stiffness of a tall building total horizontal bracing system. This article presents an analytical procedure for the static and dynamic analysis of coupled shear walls of a bay using a continuous model type – CTB of three fields. The coupled shear wall is modeled as a continuous structure consisting of the parallel coupling of a Timoshenko extensible beam and a shear beam. Using a variational approach, the equilibrium equations, constitutive laws, and boundary conditions are derived by applying Hamilton’s principle to the relevant Lagrangian function. Closed-form solutions are provided for the static deflection of the coupled shear wall under general profile lateral loads and the periods of vibration of the coupled shear wall under vertical loads uniformly distributed along its height. A validation of the static analysis was carried out, and to find the range of validity of the continuous model and proposed solution methods, a parametric analysis was carried out. The results are encouraging and show that the proposed analytical solutions have excellent correspondence with respect to the finite element method; they are accurate, reliable and involve low computational cost at a preliminary stage, and can be used as a verification method at the final stage of structural analysis and design.

On the Structural Behavior of MEMS Shallow Arch under Combined Effects of In-Plane Parallel Fields and Out-of-Plane Fringing-Fields

We propose to study the nonlinear stroke and lower-order modal interactions of a clamped–clamped shallow-arch flexible micro-electrode. The flexible electrode is electrically actuated through an in-plane parallel-plates field superimposed over out-of-plane electrostatic fringing fields. The in-plane electrostatic fields result from a difference of potential between the initially curved flexible electrode and a lower stationary parallel-grounded electrode. Moreover, the out-of-plane fringing fields are mainly due to the out-of-plane asymmetry of the flexible shallow arch and two respective surrounding stationary side electrodes (left and right). A nonlinear beam model is first introduced, consisting of a nonlinear partial differential equation governing the flexible shallow-arch in-plane deflection. Then, a resultant reduced-order model (ROM) is derived assuming a Galerkin modal decomposition with mode-shapes of a clamped–clamped beam as basis functions. The ROM coupled modal equations are numerically solved to obtain the static deflection. The results indicate the possibility of mono-stable and bi-stable structural behaviors for this particular device, depending on the flexible electrode’s initial rise and the size of its stationary side electrodes. The eigenvalue problem is also derived and examined to estimate the variation of the first three lower natural frequencies of the device when the microbeam is electrostatically actuated. The proposed micro-device is tunable with the possibility of pull-in-free states in addition to modal interactions through linear coupled mode veering and crossover processes. Remarkably, the veering zone between the first and third modes can be electrostatically adjusted and reach 22.6kHz for a particular set of design parameters.

Mechanical Behavior of Honeybee Forewing with Flexible Resilin Joints and Stripes.

The flexibility of insect wings should be considered in the design of bionic micro flapping-wing aircraft. The honeybee is an ideal biomimetic object because its wings are small and possess a concise vein pattern. In this paper, we focus on resilin, an important flexible factor in honeybees' forewings. Both resilin joints and resilin stripes are considered in the finite element model, and their mechanical behaviors are studied comprehensively. Resilin was found to increase the static deflections in chordwise and spanwise directions by 1.4 times and 1.9 times, respectively. In modal analysis, natural frequencies of the first bending and first torsional modes were found to be decreased significantly-especially the latter, which was reduced from 500 Hz to 217 Hz-in terms of resilin joints and stripes, closely approaching flapping frequency. As a result, the rotational angle amplitude in dynamic responses is remarkable, with an amplification ratio of about six. It was also found that resilin joints and stripes together lead to well-cambered sections and improve the stress concentrations in dynamic deformation. As resilin is widespread in insect wings, the study could help our understanding of the flexible mechanism of wing structure and inspire the development of flexible airfoils.

Geometrically nonlinear static deflection of stiffened composite plates: A fifth-order equivalent model

Nonlinear reduced-order models (NLROM) have been developed to predict the geometrically nonlinear behaviour of structures with low computational cost. NLROMs built using non-intrusive methods are compatible with commercial FE software and have the potential for wide application in engineering. The challenge of non-intrusive NLROMs is to accurately reproduce the internal force of structures. In literature, the internal force has been assumed to be a cubic polynomial function of generalized coordinates. However, this assumption is effective only for structures with small rigid rotations but not for structures with significant rigid rotations such as cantilever structures. In this paper, we propose a fifth-order polynomial approximation of the internal force for such cases. The nonlinear stiffness tensors of the reduced-order model are built using explicit formulas, ensuring applicability to all structures. Our proposed reduced-order model accurately predicts the nonlinear static deflection of composite plates with complex geometries.