Minimum Deflection Research Articles

Optimized Design of Cold‐Formed Steel Elements for Serviceability and Ultimate Limit States

AbstractCold‐formed steel (CFS) sections are gaining ever increasing popularity in modern construction practice due to their advantages, such as efficient material use and sustainability. While the manufacturing flexibility of CFS cross‐sectional shapes brings innovative and complex shapes within practical reach, obtaining optimum design solutions can be a challenging task due to the complex mechanical behaviour of CFS elements, which is controlled by local, distortional and global buckling modes, as well as the need to account for manufacturing and end‐use constraints. This study presents a practical framework for the development of optimised CFS beam sections with maximum flexural strength and minimum deflections in ultimate and serviceability limit state conditions, respectively, in accordance with Eurocode 3 (EC3). A population‐based Genetic Algorithm optimisation method is employed to obtain optimum solutions for ten different CFS cross‐section prototypes, while the EC3 geometric restrictions and a number of manufacturing and end‐use constrains are also considered. It is shown that sections optimised based on serviceability limit state (SLS) and ultimate limit state (ULS) requirements can provide up to 44% higher effective stiffness and 55% higher bending moment capacity, respectively, compared to standard commercial lipped channel sections with the same amount of material. The results also indicate that using optimised plain channels and folded‐flange sections generally leads to the best design solution in SLS and ULS optimization, respectively.

Safety monitoring method of vehicle bridge stress structure based on wireless sensing technology

In the safety monitoring of bridge stress structure, the influence of surrounding environment and noise interference will cause the change of monitoring node coverage and affect the monitoring accuracy. Based on wireless sensor technology, a safety monitoring method of vehicle bridge stress structure is proposed. The interpolation fitting method is used to calculate the stress value of the sensor, and the optimal layout of the sensor is determined with the minimum deflection transfer error as the objective function. Probability sensing model is used to establish wireless overlay network, and wireless sensing technology is used to collect monitoring data. Based on the monitoring data, the static and dynamic response equation is established to establish the finite element model of bridge stress structure. The first level early warning threshold is determined according to the monitoring data under the normal operation state of the bridge, and the second level early warning threshold is determined according to the most unfavorable load distribution of the finite element model, so as to complete the bridge safety monitoring. The experimental results show that the average deformation deviation of the monitoring method proposed in this paper is 0.26mm, which is 0.77mm and 1.22mm smaller than the monitoring methods based on machine vision and GPS differential positioning technology, indicating that the monitoring method in this paper is more accurate and meets the safety requirements of bridge engineering.

Large deflection analysis of FG-CNT reinforced composite pipes under thermal-mechanical coupling loading

This study is concerned with the analysis of large deflection in composite pipes reinforced with carbon nanotubes (CNTs) resting on nonlinear elastic foundation. It is assumed that the nanocomposite pipe is subjected to uniformly distributed transverse pressure loading and also uniform temperature rise. Distribution of CNTs is functionally graded (FG) through the radius of composite pipe and material properties are assumed as temperature-dependent. Two kinds of immovable boundary conditions are considered for the composite pipe which are simply-supported and clamped. The principle of virtual displacement is employed to establish the nonlinear equilibrium equations of the composite pipe under thermo-mechanical loading. Governing equations are extracted based on the higher-order shear deformation theory and the von Kármán geometric measure. The system of nonlinear differential equations is analytically solved utilizing the two-step perturbation technique and Galerkin method. Results of this paper are compared with the available data in the literature for the homogeneous isotropic pipes. The effects of boundary conditions, geometric factors, CNTs distribution profile, foundation stiffness, and the volume fraction coefficient on the bending behavior of FG-CNT reinforced composite pipes are discussed in detail. The novel results of this study demonstrate that the maximum deflection of the nanocomposite pipe occurs in the FG-Λ pattern and the minimum deflection belongs to the FG-V case.

Manipulation of the granular fluid-structure interaction via sliding coating layers

The use of sliding coating layers on structures is investigated as an approach to manipulate the transfer of momentum during the impact of granular matter with rigid and deformable structures. We first report an experimental investigation of the momentum transfer into rigid stationary targets with fixed and sliding coating layer impacted by high velocity granular slugs. Friction between the impacting granular particles and the target surface enhances the momentum transfer during the interaction with the target. By introducing a sliding coating layer with a lubricated target surface-coating interface, the momentum transfer is reduced: the coating slides on the target surface dragged along by friction between the coating and the particles but, the low friction between the coating and the target reduces the transfer of frictional forces into the target. Coupled discrete element and Lagrangian finite element simulations with rod-shaped granular particles are shown to capture the measurements with high fidelity. This numerical approach is then used to investigate the use of sliding coatings on deformable edge-clamped plates. Introduction of a coating layer while keeping the total mass of the plate constant, reduces the thickness of the plates and this in turn reduces their bending strength. The consequence is that momentum transfer reductions are lost as a result of the reduced bending strength and the minimum plate deflection is attained when no coating layer is present. We thus conclude that sliding coating layers can result in momentum transfer reductions when used on relatively rigid targets but result in a degradation of impact resistance performance when used on highly deformable structures.

Optimizing research on large-aperture parabolic trough condenser using two kinds of absorber tubes with reflector at 500 °C

Increasing the aperture of the parabolic trough concentrator (PTC) can effectively reduce costs and help promote. This paper proposed a circle and semicircle absorber tubes (AT) with a flat reflector (FR) in it for the large-aperture PTC system and the size of the AT was determined for the PTC with 8 m aperture width and 80° half rim-angle. The result shown the PTC system using a semi-circular AT with a diameter of 100 mm has the highest average thermal efficiency of 71.6% with DNI 400–1000 W/m2 at about 500 °Cand has best uniformity of 38.8%. However, its deformation is highest and 1.7 and 1.6 times other two ATs. Therefore, how to reduce the deflection has become a research direction in the future. Currently, the circular AT with a diameter of 80 mm is the most practical with an average thermal efficiency of 69.1% and a minimum deflection.

Dynamic punching shear of impacting RC flat slabs with drop panels

Reinforced concrete flat slabs (FS) are sensitive to punching shear failure. Such failure may progress to the slab loss of supports and its downwards motion that is followed by its impact with the slab underneath. This slabs impact may initiate a progressive collapse of the entire building. The design guidelines provided by modern standards to avoid punching shear failure and to prevent post-punching loss of slab support in an attempt to prevent progressive collapse are based on static loads considerations and tests and do not include considerations and guidelines that are needed to guarantee resistance to impact loading. In our studies on the impact response of impacting slabs we learnt that increasing the slab thickness and the amount of reinforcement do not improve the slabs resistance to impact and cannot prevent the severe resulting damage. Drop panels are a common means to enhance the static resistance of slabs against punching shear as they increase the slab thickness around the column, where highest shear stresses are developed. The present paper aims at the investigation of the impact response of flat slabs with drop panels and examine their added contribution to reduce the post-impact damage and achieve a stable state of the impacted slab, thus preventing a following progressive collapse scenario. In addition to the local slab depth increase, the drop panel also limits the contact zone of the impacting slabs. Both aspects positively contribute to reducing the impact induced damage. The drop panel provides a means to locally increase the slab resistance without considerably increasing its mass, thus controlling the impact load intensity while increasing the slab’s resistance. The paper investigates the impacts of different possible combinations of two adjacent slabs with/without drop panels and finds that while flat slabs without drop panels fail upon impact, slabs with drop panels may survive the impact and avoid the following progressive collapse scenario. Opposed to static design where a drop panel contributes to the shear resistance, it was found that in the case of impact loading a large size drop panel increases the mass of the impacting slabs and may adversely affect the impact results, whereas a small size drop panel may not provide the required thickened zone. Examination of different drop panel geometries indicates that optimal drop panel dimensions exist which provide a stable final state which is associated with the minimum damage and a minimum permanent deflection. At larger or smaller drop panels the damage is larger and failure may occur. These are important findings that may help to improve the safe design of RC flat slabs.

INVESTIGATION OF THE INFLUENCE OF AN INTERMEDIATE HINGE SUPPORT IN THE PROBLEM OF BENDING OF AN ELASTICALLY RESTRAINED ORTHOTROPIC BEAM

In this paper, based on the refined theory of orthotropic plates of variable thickness, a system of differential equations is obtained for solving the problem of bending of an elastically restrained beam with an intermediate condition. The beam thickness is constant and is subject to a uniformly distributed load. The effects of transverse shear are also taken into account. Passing to dimensionless quantities, an analytical closed solution is obtained. The question of the influence of changing the place of application of the intermediate condition on the solution is discussed. Depending on the location of the hinge bearing, the question of optimality was posed and resolved according to the principle of minimum maximum deflection. The results are presented in both tabular and graphical form. Based on the results obtained, appropriate conclusions are drawn.

Многокритериальная оптимизация двухлонжеронного композитного крыла легкого самолета

The article considers the results of optimization of the two-spar composite wing for the K-8 training aircraft. The geometric characteristics of the main structural elements of the wing such as spars, ribs and skin; orientation angles of the reinforcing layers and their thicknesses for each wing structural element, as well as the type of composite material and cost were selected as optimization parameters. The proposed optimization procedure includes several steps; each step uses a multi-criteria approach. The minimum deflection, weight, and cost are taken as optimization criteria. All the necessary calculations for selecting the optimal optimization parameters were performed using nonlinear static finite element analysis in the FEMAP software package.

Transient Analysis of Laminated composite Plate using New Higher-Order Shear Deformation Theory

This work develops transient analysis using a new higher-order displacement function for simply supported cross-ply laminated plates. Muntari’s higher-order shear deformation method for elastic composite plates is used to investigate the composite laminated thick and thin plate’s transient response. The current theory accounts for an approximately parabolic distribution of the transverse shear strains on the plate boundary surface through the thickness and tangential stress-free boundary conditions. The governing equations and boundary conditions are derived by employing the principle of virtual work. These equations are solved using closed-form solutions of a Navier’s type, plates are subjected to a different distribution of transient loadings such as step pulse, triangular pulse, and sinusoidal pulse, and many design parameters are studied, as expected minimum deflection is obtained for thick, antisymmetric, and has high orthotropy ratio laminated plate. The results obtained theoretically are compared with those available in various literature and showed a high agreement.

Strength Analysis of an Aircraft Sandwich Structure with a Honeycomb Core: Theoretical and Experimental Approaches

In this paper, the strength of aircraft sandwich structure with honeycomb core under bending load was evaluated theoretically and experimentally based on failure mode maps. A failure mode map for the loading under three-point bending was constructed theoretically to specify the failure modes and corresponding load. Three point bending test for aluminum honeycomb sandwich beam has been achieved to measure the peak load and maximum deflection. The obtained results elucidated a good agreement between the theoretical solutions and experimental tests, where the error ratio was not exceeded 12%. The core height, the cell size and the cell wall thickness were selected to explore the effect of honeycomb parameters on the strength of sandwich structure. In order to obtain the optimum solution of peak load and maximum deflection and energy absorption, Response Surface Methodology (RSM) was used. Results showed that the maximum bending load, minimum deflection, and maximum energy absorption were found at 25 mm core height, 10 mm size cell and 1 mm cell wall thickness. The optimal value of maximum bending load, minimum deflection and maximum energy absorption were 1975.3415 N, 1.0402 mm and 1.0229 J respectively.

Flexural analysis of transverse joints of prefabricated T girder bridge superstructure

Rapid construction of prefabricated bridges requires minimizing the field work of precast members and ensuring structural stability and constructability. In this study, we conducted experimental and analytical investigations of transverse joints of prefabricated T-girder bridge superstructures to verify the flexural performance and serviceability. In addition, we conducted parametric studies to identify the joint parameters. The results showed that both the segmented and continuous specimens satisfied the ultimate flexural strength criterion, and the segmented specimen exhibited unified behavior, with the flexural strength corresponding to that of the continuous specimen. The segmented specimens exhibited elastic behavior under service load conditions, and the maximum crack width satisfied the acceptance criteria. The reliability of the finite element model of the joint was verified, and parametric analysis of the convexity of the joint section and the compressive strength of the filler concrete showed that the minimum deflection and crack width occurred at a specific angle. As the strength of the filler concrete increased, the deflection and crack width decreased. However, we confirmed that the reduction in the crack width was hardly observed above a specific strength. Therefore, a design suitable for prefabricated bridges and accelerated construction can be achieved by improving the joint specifications based on the required criteria.

Parametric Optimization of Load Bearing Elements for Composite Wing of an Unmanned Aerial Vehicle

This paper describes the optimizing results of structural elements of the composite wing of an unmanned aerial vehicle. The thickness and composite lay-up structure of load-bearing elements and wing skin are determined using the ANSYS software package. The optimal structure is presented using the Pareto set method of the “ideal center” basing on four criteria: minimum mass, deflection, normal stress, and maximum safety factor of the wing. Verification calculations were carried out to determine the safety factor of the load-bearing wing structure using a geometrically nonlinear model in FEMAP software.

Optimization of the Distance between Two Adjacent Multi-Story Buildings by Calculating the Earthquake Effect in Yogyakarta

Neo Malioboro and Malioboro Suite Hotels are two adjacent multi-story buildings in Yogyakarta with a fairly close distance of 2.5m (Lx) between their structures. Considering that Yogyakarta is an area prone to earthquakes, the relatively close distance between the two hotels has triggered research interest. The research was carried out by taking hotel planning data in the form of structural and architectural drawings modeled in SAP2000.14 to obtain structural behavior toward existing designs such as natural shear periods, base shear, mass participation, and to obtain deviation values between floors (drift ratio) and the center of mass deflection (δ). The largest deviation value of the two hotels in the joint reviewed occurred on the top floor, with the maximum deviation value of 0.440m (δM1) for Neo Malioboro and 0.412m (δM2) for Malioboro Suite. The minimum deflection distance between the two hotels was 0.602m (δMT), resulting in the minimum separation distance for the two hotels of 1.454m. The results revealed that the distance of the two hotels was in a safe condition because it was greater than the required minimum separation distance of 2.5m > 1.454m.

Optimization of extradosed concrete bridges subjected to seismic action

An optimization algorithm is proposed to assist in the design of extradosed concrete bridges under static and seismic loading. This procedure is composed of structural analysis, sensitivity analysis and optimization modules. The finite element method is used for the three-dimensional analysis considering static loading (dead load and road traffic live load), geometrical nonlinearities, time-dependent effects and seismic action by using a modal response spectrum analysis. The design is formulated as a multi-objective optimization problem with objectives of minimum cost, deflections and stresses including service and strength criteria. The solution of the minimax problem is obtained by minimizing a convex scalar function obtained through an entropy-based approach. The design variables are the extradosed cables and tendons forces, the extradosed cables and tendons cross-sectional areas, the deck, towers and piers sizes. The analytical discrete direct method is used to find the structural response to changes in the design variables. A convex optimization strategy with multiple starting points finds minimum cost solutions with an adequate stiffness and mass distribution that satisfy the design criteria under both, static loading and seismic action. Numerical examples concerning the optimization of a real-sized extradosed concrete bridge illustrate the features and capabilities of the proposed method.

The effect of surface plastic hardening technology, residual stresses and boundary conditions on the buckling of a beam

The complex influence of the surface plastic hardening technology, residual stresses, and boundary conditions on the bending of a hardened beam of EP742 alloy was performed. A phenomenological method of restoring the fields of residual stress and plastic deformations performed by its experimental verification in the particular case of ultrasonic hardening is given. The correspondence of the calculated and experimental data for the residual stresses is observed. For assess the influence of the formed residual stresses on convex cylinders, the calculation methods are used for initial strains based on using analogies between the initial (residual) plastic strains and temperature strains in an inhomogeneous temperature field. This allowed us to reduce the consideration of the problem to the problem of thermoelasticity, which was further solved by numerical methods. The effect of four types of boundary conditions for fixing the ends of the beams (rigid fastening and articulation of the ends and ribs in various combinations, cantilever) on the shape and size of the bending of the beam 10×10×100 mm after ultrasonic hardening is studied in detail. It was found that the minimum deflection is observed with a hard seal of both ends of the beam. The effect of the thickness of the beam, which varied from 2 to 10 mm, on their buckling under the same distribution of residual stresses in the hardened layer was studied, and the nonlinear nature of the increase in the deflection boom with decreasing thickness for all types of boundary conditions was established. It is shown that under all boundary conditions, the curvature along the length of the beam practically does not change, therefore it can be considered constant. The consequence of this is the preservation of the hypothesis of flat sections after the hardening procedure, which is confirmed by the calculated profile of the beam section in plane symmetry, close to a straight line. The influence of the anisotropy of surface plastic hardening on the buckling of the beam was found to be significant, which can serve as the basis for choosing the optimal hardening procedure. The performed parametric analysis of the task is presented in the form of graphical and tabular information on the results of the calculations.

A Perturbation Method Based Solution for Beam Vibration Excited by Moving Mass

The study of the dynamic effect of moving mass on structures such as vehicles moving on bridges or a crane trolley moving on girder beam has become an important research area in the recent past. The problems were originally modelled as moving force problems, but later on moving mass inertia effects have been also included and recently models are further modified considering vehicles as moving oscillators. Available literatures indicate that response characteristics are mostly obtained using numerical integration. This, however, does not give qualitative insight into the dependence of critical response behaviours on the variable parameters. The present work attempts to obtain an analytical expression for the response using a novel perturbation-based method, where moving mass-to-beam mass ratio is taken as the perturbation parameter. For a typical simply supported beam, expressions are derived in polynomial series form, up to second-order term. Analytical response, although truncated after the second-order polynomial term, is found to be in good agreement with numerically integrated response. Sensitivity studies are performed with respect to two parameters: mass ratios and velocity ratios. In addition, magnitude of deflection maxima and corresponding vehicle location are investigated for different velocity ratios and it is shown that low velocity ratio around 0.2 produces minimum deflection maxima than the velocities in the higher range. This is a significant observation as in case of a suspected degradation in a bridge, vehicular velocity can be monitored near a ratio of 0.2 to have minimum deflection and stresses on the bridge structure.

Active Damping of Nonstationary Vibrations of a Three-Layer Electro-Viscoelastic Composite Plate

A method for constructing nonstationary vibration equations for electro-viscoelastic composite plates with their active damping is described. The problem is solved in an integral Fourier transform frequency space. To construct a multilayer plate model, a discrete structural approach was used, i.e., the plate is divided through the thickness into computational layers, within which the displacements and electric potentials are approximated by means of quadratic Lagrange polynomials. At the edges of the plate, the Navier conditions are met. The semi-analytical nonstationary vibration equations are derived by means of the variational convolutional Lagrange equation. To represent them in a frequency space, a direct integral Fourier transform is used, which makes it possible to use experimentally determined frequency-dependent complex characteristics directly in calculations of nonstationary vibrations of plates without additional transformations of integral physical relations. Solutions of the problem of active damping of nonstationary vibrations for the frequency images of displacements and electric potentials have been found, their convergence is analyzed. The procedure has been evaluated by analyzing the active damping of nonstationary vibrations of a three-layer edge-hinged square plate under the action of a blast wave impulse. The middle layer is made of a composite material, and the outer electro-viscoelastic layers act as a sensor and an actuator. The active damping of vibrations is provided by connecting these layers of the plate into a negative feedback circuit with the proportional-differential control law. The viscoelastic and electro-viscoelastic characteristics of the materials are taken into account by means of complex elastic, dielectric and piezoelectric moduli. The results of analyzing the active damping of nonstationary vibrations of a plate are presented. The values of the proportional and differential components of the controller as characteristics of this damping were chosen taking into account the permissible electric field strength of the actuator. The research results for the case of passive damping of vibrations are also given for comparison. The dependences of the decrement of plate vibrations on the differential component of the controller and of the maximum plate deflection on the reinforcement angle of the middle layer material have been established. The optimum reinforcement angle according to the minimum plate deflection criterion has been determined, which provides an increase in the efficiency of active damping of nonstationary vibrations of the plate owing to an increase in the differential component of the controller.

Optical inspection path planning for large liquid crystal glass substrate detection instrument.

A large liquid crystal glass substrate detection instrument usually uses the air flotation platform to support a glass substrate. The glass substrate will be deformed by air pressure on the air flotation platform, which will affect the accuracy of detection. In this paper, combined with the characteristics of the detection method of the detection instrument, an optimal detection scanning path with the minimum deflection variation range of the glass substrate is planned so as to minimize the influence of glass substrate deformation on the detection accuracy. In theory, the calculation model of the deflection variation ranges of different paths on the glass substrate is established, the numerical method is used to solve it, and finally, the optimal scanning path for the optical inspection is obtained. The experimental results verify the correctness of the model.

A Novel Control Allocation Method for Yaw Control of Tailless Aircraft

Tailless aircraft without vertical stabilisers typically use drag effectors in the form of spoilers or split flaps to generate control moments in yaw. This paper introduces a novel control allocation method by which full three-axis control authority can be achieved by the use of conventional lift effectors only, which reduces system complexity and control deflection required to achieve a given yawing moment. The proposed method is based on synthesis of control allocation modes that generate asymmetric profile and lift induced drag whilst maintaining the lift, pitching moment and rolling moment at the trim state. The method uses low order models for aerodynamic behaviour characterisation based on thin aerofoil theory, lifting surface methodology and ESDU datasheets and is applied to trapezoidal wings of varying sweep and taper. Control allocation modes are derived using the zero-sets of surrogate models for the characterised aerodynamic behaviours. Results are presented in the form of control allocations for a range of trimmed sideslip angles up to 10 degrees optimised for either maximum aerodynamic efficiency (minimum drag for a specific yawing moment) or minimum aggregate control deflection (as a surrogate observability metric). Outcomes for the two optimisation objectives are correlated in that minimum deflection solutions are always consistent with efficient ones. A configuration with conventional drag effector is used as a reference baseline. It is shown that, through appropriate allocation of lift based control effectors, a given yawing moment can be produced with up to a factor of eight less aggregate control deflection and up to 30% less overall drag compared to use of a conventional drag effector.

Nonlinear buckling analysis of double-layered graphene nanoribbons based on molecular mechanics

Double-layer graphene nanoribbons promise potential application in nanoelectromechanical systems and optoelectronic devices, and knowledge about mechanical stability is a crucial parameter to flourish the application of these materials at the next generation of nanodevices. In this paper, molecular mechanics is utilized to investigate nonlinear buckling behavior, critical buckling stress, and lateral deflection of double-layered graphene nanoribbons under various configurations of stacking mode and chirality. The implicit arc-length iterative method (modified Riks method) with Ramm’s algorithm is utilized to analyze the nonlinear structural stability problem. The covalent bonds are modeled using three-dimensional beam elements in which elastic moduli are calculated based on molecular structural mechanics technique, and the interlayer van der Waals (vdW) interactions are modeled with nonlinear truss elements. An analytical expression for Young’s modulus of nonlinear truss elements is derived based on the Lennard–Jones potential function and implemented in numerical simulation with a UMAT subroutine based on FORTRAN code to capture the nonlinearity of the vdW interactions during the buckling analysis. The results indicate that the highest critical buckling stress and the minimum lateral deflection occur for armchair and zigzag chirality, both with AB stacking mode, respectively. Moreover, the critical buckling stress is found to be directly dependent on the mode shape number regardless of in-phase or anti-phase deflection direction of layers. Lateral deflection exhibits a similar trend with mode shape in anti-phase mode; however, it is decreasing by increasing mode shape number in in-phase mode.