Rigid Bar Research Articles

A discrete differential geometry-based approach to buckling and vibration analyses of inhomogeneous Reddy plates

In this paper, a novel discrete differential geometry-based numerical procedure for buckling and vibration analyses of rectangular plates with non-uniform thickness is developed. In the proposed approach a plate is discretized using a finite number of rigid bars, lumped masses, and elastic rotational springs to simulate both bending and shear deformation responses, allowing the analysis of thick plates through the adoption of the Reddy’s third-order shear deformable plate theory. An interesting analogy between the proposed model and the central finite difference method for solving a set of partial differential equations is also highlighted, showing how the former can be seen as the physical model behind the mathematical representation of the latter. The numerical results presented show both the versatility and the accuracy of the proposed approach.

Comparison of posterior residual ridge resorption in patients wearing conventional denture, two implant-retained mandibular overdenture and four implant-supported overdenture: a 5-year retrospective study.

Purpose: The aim of the following study was to assess and compare the effect of treatment with conventional complete dentures, two implant retained mandibular overdenture and four implant supported mandibular overdenture on mandibular posterior residual ridge resorption over a 5-year period. Material and methods 24 patients were selected from previous studies, where (group I) included 8 patients previously treated with conventional complete dentures. The second group (group II) 8 patients received mandibular overdenture using two osseointegrated implants, (group III)8 patients received implant supported mandibular overdenture using two implants in canine region and two implants in the first molar region connected with rigid bar. Posterior residual ridge resorption was evaluated for all groups using proportional area measurements. Results: After 5years of prosthetic treatment, regarding posterior residual ridge resorption, statistically significant bone resorption had occurred for all the three groups, also statistically significant difference was reported when comparing the two-implant overdenture group to the four-implant supported overdenture group. Conclusion Four implant supported overdenture with the posterior implants in the first molar region showed the least amount of posterior ridge resorption after 5 years of treatment in comparison to conventional complete dentures or two implant retained overdenture.

Model error propagation from experimental to prediction configuration

Full-scale system tests are often prohibitively expensive, therefore experiments on simpler configurations are used in engineering to gain insights that can be applied to the behavior prediction of the full-scale system. However, the transfer of information from the experimental configuration to the prediction configuration is not trivial. In this paper, we present a methodology for predicting the response of a dynamic system using data from tests conducted on a different experimental configuration. The experimental and prediction configurations are connected by a set of common model form errors, which are unrelated to geometry, boundary conditions, or loading. These errors cause discrepancies between the model prediction of system response and the corresponding measured values. The proposed methodology is based on estimating the model form errors for the experimental configuration, using the measured data, and propagating the estimated errors to the prediction configuration. The governing equations of the two systems – the experimental and prediction configurations – are discretized using the finite element method, using elements of the same type and dimensions. Bayesian state estimation is adopted to estimate the discrepancies in unmeasured responses of the tested configuration, and subsequently, these estimates are used to evaluate the model form errors. These errors are propagated to untested configurations using an artificial neural network (ANN). The proposed methodology is illustrated on predicting the deformation of a simply supported beam and a curved plate, and for predicting the temperature time histories along a rigid bar under one-dimensional heat conduction.

Accuracy Assessment of Two Electromagnetic Articulographs: Northern Digital Inc. WAVE and Northern Digital Inc. VOX.

Purpose This study compares two electromagnetic articulographs manufactured by Northern Digital, Inc.: the NDI Wave System (from 2008) and the NDI Vox-EMA System (from 2020). Method Four experiments were completed: (a) comparison of statically positioned sensors, (b) tracking dynamic movements of sensors manipulated using a motor-driven LEGO apparatus, (c) tracking small and large movements of sensors mounted in a rigid bar manipulated by hand, and (d) tracking movements of sensors rotated on a circular disc. We assessed spatial variability for statically positioned sensors, variability in the transduced Euclidean distances between sensor pairs, and missing data rates. For sensors tracking circular movements, we compared the fit between fitted ideal circles and actual trajectories. Results The average sensor pair tracking error (i.e., the standard deviation of the Euclidean distances) was 1.37 mm for the WAVE and 0.12 mm for the VOX during automated trials at the fastest speed, and 0.35 mm for the WAVE and 0.14 mm for the VOX during the tracking of large manual movements. The average standard deviation of the fitted circle radii charted by manual circular disc movements was 0.72 mm for the WAVE sensors and 0.14 mm for the VOX sensors. There was no significant difference between the WAVE and the VOX in the number of missing frames. Conclusions In general, the VOX system significantly outperformed the WAVE on measures of both static precision and dynamic accuracy (automated and manual). For both systems, positional precision and spatial variability were influenced by the sensors' position relative to the field generator unit (worse when further away). Supplemental Material https://doi.org/10.23641/asha.14787846.

On transmissible load formulations in topology optimization

Transmissible loads are external loads defined by their line of action, with actual points of load application chosen as part of the topology optimization process. Although for problems where the optimal structure is a funicular, transmissible loads can be viewed as surface loads, in other cases such loads are free to be applied to internal parts of the structure. There are two main transmissible load formulations described in the literature: a rigid bar (constrained displacement) formulation or, less commonly, a migrating load (equilibrium) formulation. Here, we employ a simple Mohr’s circle analysis to show that the rigid bar formulation will only produce correct structural forms in certain specific circumstances. Numerical examples are used to demonstrate (and explain) the incorrect topologies produced when the rigid bar formulation is applied in other situations. A new analytical solution is also presented for a uniformly loaded cantilever structure. Finally, we invoke duality principles to elucidate the source of the discrepancy between the two formulations, considering both discrete truss and continuum topology optimization formulations.

Stability of trusses by graphic statics.

This paper presents a graphical method for determining the linearized stiffness and stability of prestressed trusses consisting of rigid bars connected at pinned joints and which possess kinematic freedoms. Key to the construction are the rectangular areas which combine the reciprocal form and force diagrams in the unified Maxwell–Minkowski diagram. The area of each such rectangle is the product of the bar tension and the bar length, and this corresponds to the rotational stiffness of the bar that arises due to the axial force that it carries. The prestress stability of any kinematic freedom may then be assessed using a weighted sum of these areas. The method is generalized to describe the out-of-plane stability of two-dimensional trusses, and to describe three-dimensional trusses in general. The paper also gives a graphical representation of the ‘product forces’ that were introduced by Pellegrino and Calladine to describe the prestress stability of trusses.

Hencky Bar-Grid Model for Plane Stress Elasticity Problems

AbstractA novel Hencky bar-grid model (eHBM) was developed to address plane stress elasticity problems. This model comprises rigid bars arranged in a grid which are joined by frictionless hinges, f...

New design of gravitational wave detectors

We propose a novel approach to detect gravitational waves based on a semi-rigid detector. The approach relies upon the time delay that the light takes to travel from a fixed mirror at the end of a rigid bar to a nearby free mirror. We show that the dimensions of the experimental device can be shortened in comparison to the conventional ones based on two free mirrors.

Fibre optic strain measurements for bond modelling of prestressed near-surface-mounted iron-based shape memory alloy bars

Near-surface-mounted (NSM) iron-based shape memory alloy (memory-steel) bars represent a novel type of reinforcement for prestressed strengthening of concrete structures. To examine the bond behaviour of these embedded reinforcements in detail, fibre optic (FO) methods can be used. In this study, distributed FO strain measurements were performed in small-scale bond experiments and large-scale structural experiments using prestressed and non-prestressed NSM memory-steel bars. The experiments demonstrated the FO measurement technique's feasibility on memory-steel bars, provided insights into the complex strain profiles before and after prestressing, and revealed the active bond lengths. When the memory-steel bar was subjected to an external load, a reduction in the bar's stiffness resulted in an increase in active bond length. The results furthermore highlighted the importance of rigid bar fixations to avoid prestress loss. The obtained strain distributions were also processed to calculate the distributed slip and axial bar stress, and to investigate the parameters of three different bond shear stress–slip laws (BSSLs). A linear increasing BSSL with a nonlinear bar stiffness led to a realistic calculation of the axial stress in the bar, while resulting in acceptable slip and strain. The implementation of a constant Young’s modulus consistently overestimated the axial bar stress.

A simplified model of elastic column buckling under constant lateral force restraint

Buckling of a column under pre-load restraint has been found to differ from the conventional bifurcation problems and thus requires better understanding. To this end, a simple model consisting of two collinear rigid bars connected by a rotational spring, resting on a smooth surface, loaded by an axial force and restrained by a constant force at the common joint is investigated. The energy method is adopted to establish the equilibrium and stability conditions. The post-buckling response of the simple system indicates that the load-restrained buckling problem is a snap-through problem. The minimum possible buckling force and the buckling force based on the Maxwell construction are found to increase with the restraining force, and can be approximated by power-law functions. It is further shown that an energy barrier exists for the snap-through to occur and the buckling force depends on the perturbation energy. Sensitivity of this system to initial geometric imperfections is also investigated, and an energy barrier is also found to exist for the buckling of systems with imperfection amplitudes smaller than a certain critical value. The characteristic imperfection amplitude depends on the restraining force and, interestingly, transforms the snap-through problem into an eigenvalue problem identical to the conventional one, i.e., the one without imperfection and restraining force.

Metrological control of electrolytic sensors for measuring angular deviations: application in monitoring displacements of engineering structures

The work evaluates the metrological reliability of electrolytic sensors (electrolevels) used to determine angular deviations of elements of engineering structures. The motivation for the work resulted from its strategic application to control the stability of civil engineering structures, notably with application in geotechnics (e.g.: different types of dams of interest in engineering). The methodology used is based on the metrological consistency associated with the quality control process of a set of electrolevels submitted, simultaneously, to a careful calibration process, with traceability ensured to a standard angular deviation pattern. Mounted on a rigid bar, but pivoted at one of its ends to allow angular displacements, the output of each electrolevel is compared with the previously calibrated standard, for different controlled conditions of angular deviation imposed on the bar articulated to a center of rotation. The result of the analysis of typical calibration data for nine electrolevels allowed to show that the expression of the uncertainties associated with the calibration measurements performed constitutes an essential foundation to ensure the metrological reliability of the electrolevels, having allowed to validate a method of discard of electrolevels not meeting the allowable tolerance for a specific engineering application. Among the conclusions of the work, it was possible to qualify the statistical treatment of the levels of uncertainty as a sufficiently robust strategy to validate the electrolevels as a reliable instrument for angular displacement measurements, with a level of confidence appropriate to its application in civil engineering.

Оптимизационное проектирование замковых соединений из эластомера

This paper discusses the development of small boats made of polymeric composites in combination with metal skeleton based on detachable elastic connections. Lock material was polyethylene with hyperelastic properties of an elastomer. Static calculation is performed as per the finite-element method in plane formulation taking into account contact, geometric and physical non-linearity, as well as implementing a step-wise procedure. Design calculation is performed as per the research method approximating the sub-task (quadratic programming). The paper presents calculations for the process of inserting/extracting a rigid bar with round free flange to/from the lock, with determination of maximum responses, strains and stresses of the insert. Variation of geometric parameters yielded a design variant with minimum load on the insert and the same strength properties as the initial design. The study also yielded the analytical design methodology for elastic detachable connections that combines the solutions to non-linear contact problem and the optimization problem.

Tensile and Shear Testing of Basalt Fiber Reinforced Polymer (BFRP) and Hybrid Basalt/Carbon Fiber Reinforced Polymer (HFRP) Bars.

The use of sustainable materials is a challenging issue for the construction industry; thus, Fiber Reinforced Polymers (FRP) is of interest to civil and structural engineers for their lightweight and high-strength properties. The paper describes the results of tensile and shear strength testing of Basalt FRP (BFRP) and Hybrid FRP (HFRP) bars. The combination of carbon fibers and basalt fibers leads to a more cost-efficient alternative to Carbon FRP (CFRP) and a more sustainable alternative to BFRP. The bars were subjected to both tensile and shear strength testing in order to investigate their structural behavior and find a correlation between the results. The results of the tests done on BFRP and HFRP bars showed that the mechanical properties of BFRP bars were lower than for HFRP bars. The maximum tensile strength obtained for a BFRP bar with a diameter of 10 mm was equal to approximately 1150 MPa, whereas for HFRP bars with a diameter of 8 mm, it was higher, approximately 1280 MPa. Additionally, better results were obtained for HFRP bars during shear testing; the average maximum shear stress was equal to 214 MPa, which was approximately 22% higher than the average maximum shear stress obtained for BFRP bars. However, HFRP bars exhibited the lowest shear strain of 57% that of BFRP bars. This confirms the effectiveness of using HFRP bars as a replacement for less rigid BFRP bars. It is worth mentioning that after obtaining these results, shear testing can be performed instead of tensile testing for future studies, which is less complicated and takes less time to prepare than tensile testing.

Study on the Dynamic Response Characteristics of Cylindrical Coal-Rock Samples under Dynamic Loads

To research the dynamic response characteristics of cylindrical coal-rock samples under impact loads, the impact of rigid bars on cylindrical coal-rock samples is simulated under different speed conditions, based on LS-DYNA software, and the dynamic distribution characteristics of the stress, strain, and energy of cylindrical coal-rock samples are analyzed. The results demonstrated the following: (1) the cylindrical coal-rock sample failed at the center first, and the damage developed downward along the axial direction. (2) The critical effective stress and strain have an exponential function relationship with the velocity, and the critical time has a linear relationship with the velocity. (3) The energy change law of the cylindrical coal-rock sample is consistent with the destruction morphology. (4) The axial stress peaks in the severe damage part have a linear relationship with the speed, the axial stress attenuates rapidly after passing the stress yield point, and the axial strain does not increase continuously. (5) The peaks stress and strain on the central axis and the radial line obey the power function distribution, the axial stress produces tensile stress in the axial propagation direction, and the axial stress and strain peaks at the same position are larger than those of the radial stress and strain peaks. This research provides a reference for studying coal and rock dynamic disasters.

Comparing kernel damage of different threshing components using high-speed cameras

Grain damage research has been a focus of many experts in the agriculture machinery industry. A threshing test-bed was developed to investigate the movement and influence of different threshing and separating units on maize grains. The damage to maize grains was analyzed with a high-speed camera to observe the movement and damage received by the maize grains. The results showed that the threshing and separating effects of the perforated concave plate were obviously lower than that of the round steel concave plate, the threshing effects of the rigid rasp bar and polyurethane rasp bar were similar, and the damage ratio of the polyurethane rasp bar was relatively low. It also indicated that moisture content has a significant effect on the damage ratio and damage type of maize grains. The different threshing component types used in this study had an obvious effect on the degree of damage to high moisture content maize grains and the damage to high-moisture kernels during threshing could be further identified. The results can provide a reference for the design of threshing and separating devices in the maize combine harvesting machinery. Keywords: maize grain, damage, threshing process, high-speed camera DOI: 10.25165/j.ijabe.20201306.5395 Citation: Ma Z, Han M, Li Y M, Yu S C, Chandio F A. Comparing kernel damage of different threshing components using high-speed cameras. Int J Agric & Biol Eng, 2020; 13(6): 215–219.

Reconfigurable Acoustic Arrays With Deployable Structure Based on a Hoberman–Miura System Synthesis

Abstract Curved surfaces are often used to radiate and focus acoustic waves. Yet, when tessellated into reconfigurable surfaces for sake of deployability needs, origami-inspired acoustic arrays may be challenging to hold into curved shape and may not retain flat foldability. On the other hand, deployable mechanisms such as the Hoberman ring are as low-dimensional as many origami tessellations and may maintain curved shape with ease due to ideal rigid bar compositions. This research explores an interface between a Hoberman ring and Miura-ori tessellation that maintain kinematic and geometric compatibility for sake of maintaining curved shapes for sound focusing. The Miura-ori facets are considered to vibrate like baffled pistons and generate acoustic waves that radiate from the ring structure. An analytical model is built to reveal the near field acoustic behavior of acoustic arrays resulting from a Hoberman–Miura system synthesis. Acoustic wave focusing capability is scrutinized and validated through proof-of-principle experiments. Studies reveal wave focusing phenomena distinct to this manifestation of the acoustic array and uncover design and operational influences on wave focusing effectiveness. The results encourage exploration of new interfaces between reconfigurable mechanisms and origami devices where low-dimensional shape change is desired.

Stiffness metamodelling of 2D bolted extended end-plate steel connections using modal decomposition

The accurate simulation of steel structures requires a precise model of the joint behaviour. The methods proposed by the steel codes are based on either rotating springs or involved models of springs and rigid bars. In this article, a precise method to model the stiffness of 2D bolted steel connections is presented. First, the joint is accurately modelled using finite elements (FE). Then, the FE model is condensed to a cruciform element of 4 nodes (12° of freedom) by constraining each side cross-section to a node located at its centre of gravity. Subsequently, forces are applied to each node to compute the flexibility matrix, which is then used to construct the stiffness matrix that is finally decomposed through singular value factorization. Following this procedure, a parametric study is conducted to build the training and validation sets of the metamodel. Kriging and Radial Basis Functions are chosen to metamodel and predict the stiffness matrices of the cases not included in the parametric study. Finally, steel structures are analysed with both complete finite elements and surrogate models, and the results are used to confirm the accuracy of the proposed method.

Numerical simulation of the dynamic distribution characteristics of the stress, strain and energy of coal mass under impact loads

To research the dynamic response characteristics of coal mass under impact loads, based on LS-DYNA software, rigid body bars are simulated to impact coal mass under different speed conditions, and the dynamic distribution characteristics of the stress, strain and energy of coal mass are analyzed. The results demonstrate that (1) the peaks of the axial and radial stresses and strain on the central axis and the radial line obey the power function distribution; at the same position, the axial and the radial stress peaks are close, and the axial strain peak is from much larger than the radial strain peak to close to. (2) The axial and radial stresses generate tensile stresses in the axial and radial propagation directions, respectively, and the coal mass is prone to damage under tensile stress. (3) When the speed is large, the axial stress–strain curve is similar to that of the dynamic load experiment. The axial stress peak, axial strain peak, critical effective stress, critical time and secant modulus have a linear relationship with the velocity. (4) When the dynamic load is large, most of the energy is in the form of kinetic energy, and the total energy loss also increases.

On an improvement of low bass characteristics on the OLED flat panel speaker

Recently, researches using OLED flat panel displays as speakers have attracted attention. However, due to the local characteristics of the flat panel speaker, the bass characteristic below 500 Hz is insufficient. The flat panel loudspeaker drives several watts of power into the exciter attached to the back of the flat panel. The exciter of the flat plate has a characteristic that the sound is driven forward from the local region, so the characteristics of the bass region are deteriorated. Therefore, in this paper, the research was conducted to widen the sound by attaching the exciter to the rigid bar. It is a principle to compensate the bass region of the flat panel speaker using an array type exciter. In order to improve the bass sound, the rigidity bar is used instead of the array exciters to improve the manufacturing process and cost. Compared to the conventional flat panel speaker, when the rigid bar is attached, the bass bandwidth is improved to 200 Hz. In the future, it is necessary to minimize the effect of the rigid bar on the high-pitched area compared to using exciter array.

Aseismic study of the frame structure with hanging prefabricated infill plate

SummaryThe previous seismic disaster indicates that the traditional masonry infill wall was easy damaged during earthquake. The traditional masonry infill wall not only increases the load of the main structure but also injures people during collapsing. So a new aseismic structure system with hanging prefabricated infill plate was proposed. The dynamical characteristic of frame structure with hanging prefabricated infill plate was analyzed. By simplifying the hanging prefabricated infill plate as a rigid bar, the free vibration equation of aseismic structure system with hanging prefabricated infill plate was established. Furthermore, the influence of main parameters on the natural frequency of the whole aseismic structure system with hanging prefabricated infill plate was discussed. Through the vibration table test and finite element simulation, the aseismic effect of hanging prefabricated infill plate was studied. The influence factors and application conditions of aseismic structure system with hanging prefabricated infill plate were discussed.