Straight Configuration Research Articles

An introductory treatise on reduced balance laws of Cosserat beams

This paper serves as an introduction to the variational formulation of Cosserat beams. It provides a detailed derivation and treatment of reduced balance laws of Cosserat beams from the Lagrangian differential equation of motion and Hamilton’s principle. Emphasis is given to the details of the derivation, maintaining Bernoulli’s assumption of the rigid cross-section. Both the strong form and the weak form of the equilibrium equation for Cosserat beams are derived independently from the infinitesimal stress equilibrium equation. The weak form is then validated by obtaining it from the strong form of the reduced law in a purely mathematical sense. Finally, the strong form is obtained using Hamilton’s principle. Once the equations are obtained considering an initially straight reference beam configuration, the balance equation for the beam with initial curved (but unstrained) reference configuration is obtained. The D’Alembert forces are interpreted from the non-inertial director frame of reference and conclusions drawn. The energy conservation law and the conditions associated with it are obtained, establishing the relation between the Lagrangian and Hamiltonian functional for Cosserat beams.

Development of ANCF tetrahedral finite elements for the nonlinear dynamics of flexible structures

In this paper, methods for developing isoparametric tetrahedral finite elements (FE) based on the absolute nodal coordinate formulation (ANCF) are presented. The proposed ANCF tetrahedral elements have twelve coordinates per node that include three position and nine gradient coordinates. The fundamental differences between the coordinate parametrizations used for conventional finite elements and the coordinate parametrizations employed for the proposed ANCF tetrahedral elements are discussed. Two different parametric definitions are introduced: a volume parametrization based on coordinate lines along the sides of the tetrahedral element in the straight (un-deformed) configuration and a Cartesian parametrization based on coordinate lines directed along the global axes. The volume parametrization facilitates the development of a concise set of shape functions in a closed form, and the Cartesian parametrization serves as a unique standard for the element assembly. A linear mapping based on the Bezier geometry is used to systematically define the cubic position fields of ANCF tetrahedral elements: the complete polynomial-based eight-node mixed-coordinate and the incomplete polynomial-based four-node ANCF tetrahedral elements. An element transformation matrix that defines the relationship between the volume and Cartesian parametrizations is developed and used to convert the parametric gradients to structure gradients, thereby allowing for the use of a standard FE assembly procedure. A general computational approach is employed to formulate the generalized inertia, external, and elastic forces. The performance of the proposed ANCF tetrahedral elements is evaluated by comparison with the conventional linear and quadratic tetrahedral elements and also with the ANCF brick element. In the case of small deformations, the numerical results obtained show that all the tetrahedral elements considered can correctly produce rigid body motion. In the case of large deformations, on the other hand, the solutions of all the elements considered are in good agreement, provided that appropriate mesh sizes are used.

A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

The paper presents a review on large deflection behavior of curved beams, as manifested through the responses under static loading. The term large deflection behavior refers to the inherent nonlinearity present in the analysis of such beam system response. The analysis leads to the field of geometric nonlinearity, in which equation of equilibrium is generally written in deformed configuration. Hence the domain of large deflection analysis treats beam of any initial configuration as curved beam. The term curved designates the geometry of center line of beam, distinguishing it from the usual straight or circular arc configuration. Different methods adopted by researchers, to analyze large deflection behavior of beam bending, have been taken into consideration. The methods have been categorized based on their application in various formats of problems. The nonlinear response of a beam under static loading is also a function of different parameters of the particular problem. These include boundary condition, loading pattern, initial geometry of the beam, etc. In addition, another class of nonlinearity is commonly encountered in structural analysis, which is associated with nonlinear stress-strain relations and known as material nonlinearity. However the present paper mainly focuses on geometric nonlinear analysis of beam, and analysis associated with nonlinear material behavior is covered briefly as it belongs to another class of study. Research works on bifurcation instability and vibration responses of curved beams under large deflection is also excluded from the scope of the present review paper.

On global and local minimizers of prestrained thin elastic rods

We study the stable configurations of a thin three-dimensional weakly prestrained rod subject to a terminal load as the thickness of the section vanishes. By $$\Gamma $$ -convergence we derive a one-dimensional limit theory and show that isolated local minimizers of the limit model can be approached by local minimizers of the three-dimensional model. In the case of isotropic materials and for two-layers prestrained three-dimensional models the limit energy further simplifies to that of a Kirchhoff rod-model of an intrinsically curved beam. In this case we study the limit theory and investigate global and/or local stability of straight and helical configurations.

Effect of round curvature of anterior implant-supported zirconia frameworks: finite element analysis and in vitro study using digital image correlation

Two groups of 4-unit zirconia frameworks were produced by CAD/CAM to simulate the restoration of an anterior edentulous gap supported by 2 implant-abutment assemblies. Group 1 comprised straight configuration frameworks and group 2 consisted of arched frameworks. Specimens were made with the same connector cross-section area and were cemented and submitted to static loads. Displacements were captured with two high-speed photographic cameras and analysed with video correlation system. Frameworks and the implant-abutment assembly were scanned and converted to 3DCAD objects by reverse engineering process. A specimen of each group was veneered and the corresponding 3D geometry was similarly obtained after scanning. Numerical models were created from the CAD objects and the FE analysis was performed on the zirconia frameworks and on the FPDs bi-layered with porcelain (veneered frameworks). Displacements were higher for the curved frameworks group, under any load. The predicted displacements correlated well with the experimental values of the two framework groups, but on the straight framework the experimental vertical displacements were superior to those predicted by the FEA. The results showed that the round curvature of zirconia anterior implant-supported FPDs plays a significant role on the deformation/stress of FPDs that cannot be neglected neither in testing nor in simulation and should be considered in the clinical setting.

Addendum to “Local Controllability of the Two-Link Magneto-Elastic Microswimmer”

In the above mentioned note (<hal-01145537>, <arXiv:1506.05918>, published in IEEE Trans. Autom. Cont., 2017), the first and fourth authors proved a local controllability result around the straight configuration for a class of magneto-elastic micro-swimmers.That result is weaker than the usual small-time local controllability (STLC), and the authors left the STLC question open. The present addendum closes it by showing that these systems cannot be STLC.

A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

The paper presents a review on large deflection behavior of curved beams, as manifested through the responses under static loading. The term large deflection behavior refers to the inherent nonlinearity present in the analysis of such beam system response. The analysis leads to the field of geometric nonlinearity, in which equation of equilibrium is generally written in deformed configuration. Hence the domain of large deflection analysis treats beam of any initial configuration as curved beam. The term curved designates the geometry of center line of beam, distinguishing it from the usual straight or circular arc configuration. Different methods adopted by researchers, to analyze large deflection behavior of beam bending, have been taken into consideration. The methods have been categorized based on their application in various formats of problems. The nonlinear response of a beam under static loading is also a function of different parameters of the particular problem. These include boundary condition, loading pattern, initial geometry of the beam, etc. In addition, another class of nonlinearity is commonly encountered in structural analysis, which is associated with nonlinear stress-strain relations and known as material nonlinearity. However the present paper mainly focuses on geometric nonlinear analysis of beam, and analysis associated with nonlinear material behavior is covered briefly as it belongs to another class of study. Research works on bifurcation instability and vibration responses of curved beams under large deflection is also excluded from the scope of the present review paper.

A Novel Machine Vision Based Image Analysis Method for the Analysis of Mixing Elements in Rotary Drums

Mixing performance in continuous rotary drums has been studied. The video analysis method was developed to evaluate different configurations of straight lifters in the rotary drum. The method converts a captured video into a single image, called stack image. The color marker tracking was estimated based on the color saturation of the stack image. Coefficients of variation and mixing indices were calculated from the color saturation profiles for different straight blade lifter configurations. The video analysis method was confronted to the impulse response of acid concentrations in water solutions. The developed analysis method has been superior with viscous fluids compared to traditional tracer impulse method in mixing evaluations. Water and 1% CMC-water solution were used in this mixing study for covering broadly different viscous materials. The drum lengthwise results for one lifter configuration were obtained from a single experiment due to the block representation of the image analysis method. It enables mixing analysis of axial segments and interaction analysis of mixer configurations. Thus, the axial mixing can be studied in more detail with rotary drums. The increase of lifters, residence time, and tip speed improved axial mixing in the studied experimental setup.

Natural frequencies of a super-critical transporting Timoshenko beam

Abstract Super-critical transporting continua are often discussed in the context of an Euler beam model. Here Timoshenko beam theory is applied to study free vibration of high-speed transporting continua. Therefore, effects of rotary inertia and shear deformation on transverse vibration of super-critical transporting beams are discovered for the first time. The Galerkin method is applied to solve natural frequencies with the simply supported boundary conditions. Meanwhile, the weighted residual method (WRM) is employed to deal with the fixed ends. The natural frequencies of super-critical continua are verified by using the discrete Fourier transform (DFT). In the super-critical regime, the straight configuration of the beam loses its stability. The buckling configurations, due to the nonlinear stiffness, are deduced from the nonlinear static equilibrium equation. Furthermore, the governing equation for the transverse vibration of the super-critical transporting Timoshenko beam is derived based on the buckling shape. Time histories are calculated by using the finite difference method (FDM). Furthermore, natural frequencies of nonlinear free vibration are determined by using the DFT. In addition, the effect of nonlinear stiffness on the natural frequencies is discovered. On the other hand, a partially linearized equation is deduced by regarding buckling configurations and its spatial derivatives as constant coefficients. Then, natural frequencies are extracted by using the Galerkin method. The two different approaches are compared. Numerical results show that the rotary inertia and the shear deformation significantly affect vibration characteristics of the super-critical transporting beam for some configurations. Moreover, comparisons with an Euler-Bernoulli beam model reveal that the fundamental frequency of the Timoshenko beam is higher when the speed is slightly greater than the critical value.

Modelling and boundary control of slender curved beams

ABSTRACTModelling and boundary control of extensible and shearable slender curved beams in flow with large in-plane deflection are addressed in this paper. Equations of motion of the beams are derived based on the difference between purely geometric deformation and actual deformation from the reference and actual configurations to a virtual straight configuration. Two control designs based on the Lyapunov direct method are proposed for curved beams with both small and large curvature. The proposed boundary controllers guarantee globally (practically) -exponential stabilisation of the beam's motions at the origin. Two Lyapunov-type theorems are developed for nonlinear evolution systems in Hilbert space for analysis of well posedness and stability of the closed-loop system.

Age-dependent arthrosonographic reference values of the hip joint in healthy children and adolescents - a cross-sectional multicenter ultrasound study.

Musculoskeletal US is a noninvasive imaging method for diagnosing and monitoring inflammatory rheumatic diseases. To develop age- and gender-related arthrosonographic reference intervals for the hip joint of healthy children and adolescents. In a cross-sectional US study, we examined both hip joints of 445 children and adolescents with an age range of 1year to 18years. We measured the distance between the bone surface and the outer margin of the joint capsule to define the bone-capsule distance, the joint capsule and cartilage thickness, and the capsule layer thickness. Reference values were calculated. The shape of the joint capsule and bone-capsule junction zone were analyzed qualitatively. An intraobserver analysis was performed. Bone-capsule distance, capsule thickness and the anterior capsule layer increase with age. In contrast, joint cartilage decreases. The posterior capsule layer exhibited constant thickness across all age groups. The difference between both body sides and gender was collectively less than 0.5mm. The intraobserver variations were within the calculated reference intervals. The insertion of the capsule to the bone was mostly a peaked one. The capsule shape had a convex or straight configuration in a neutral position and a concave position during outward rotation. The intraobserver analysis revealed good to very good concordance. We propose age- and gender-related reference intervals for the bone-capsule distance, joint capsule and cartilage thickness of the hip.

Design and manufacture a coconut milk squeezer

The process of cooking oil production generally is started by grating the ripe coconut meat, then pressing the grated meat to obtain coconut milk, and finally heating the coconut milk to obtain the cooking oil. Pressing mechanism to obtain coconut milk is a very important step and decisive in the process of producing cooking oil. The amount of milk produced depends on the pressure applied at the time of pressing grated coconut. The higher the pressure, the more milk is obtained. Some commercial mechanical pressing tools that available in the market are not efficient due to the working steps too much and take long time per cycle of work. The aims of this study was to design and manufacture a power screw squeezer for the collection of coconut milk. Power screw produces a compressive force in the cylinder to push and press the grated coconut until the end of the cylinder while the coconut milk and coconut dregs flow out simultaneously. Screw press was designed using straight shaft configuration with square profile. Performance test was done to investigate the actual capacity and yield of milk produced. The results showed that squeezer of grated coconut worked well with capacity an average of 13,63 kg/h and coconut milk yield of 58%.

Equilibria of a clamped Euler beam (Elastica) with distributed load: Large deformations

We present some novel equilibrium shapes of a clamped Euler beam (Elastica from now on) under uniformly distributed dead load orthogonal to the straight reference configuration. We characterize the properties of the minimizers of total energy, determine the corresponding Euler–Lagrange conditions and prove, by means of direct methods of calculus of variations, the existence of curled local minimizers. Moreover, we prove some sufficient conditions for stability and instability of solutions of the Euler–Lagrange, that can be applied to numerically found curled shapes.

PEMBERIAN ANOMALI KEDALAMAN REFLEKTIF PADA SIMULASI PERSAMAAN AIR DANGKAL DENGAN KONFIGURASI SEJAJAR

The simulation of shallow water equation with straight configuration reflective depth anomaly has been performed. This program simulated wave absorber in the beach in order to prevent furthur abrasion of by sea. This program using modified Navier-Stokes equation and running on Matlab program. The result show that depth-anomaly reduced the amount on wave amplitudo by significant value.

Influence of angulation and vertical misfit in the evaluation of micro-deformations around implants

Objective: This in vitro study was to evaluate micro-strains around of implant, under the influence of angulations and vertical misfit in three-element implant-supported fixed partial dentures during axial loading by using strain gauge analysis. Materials and Methods: Three external hexagon implants with straight configuration and three external hexagon implants with angled (17°) configuration were inserted into two polyurethane blocks. To measure micro-strain, four strain gauges were bonded onto the surface of each block. Plastic copings were adapted to a standard wax pattern and cast. An axial load of 30 kgf was applied on the center of each implant for 10 seconds, using a load application device. The vertical misfit was measured at six different points by using a stereo microscope with 100-X magnification. Results: The results showed that the values for different implant angulations were significant (P= 0.0086). The Pearson’s correlation test between micro-strain and vertical misfit revealed no correlation between angled configuration (P= 0.891) and straight configuration (P= 0.568). Conclusion: The micro strain was higher for angled implants; no correlation was found between the vertical misfit and the micro strain values.

3d current density in tumors and surrounding healthy tissues generated by a system of straight electrode arrays

The knowledge of the adequate current density distribution to apply when using different electrode arrays in tumor tissue and the healthy surrounding tissue is one of the most significant challenges to improve the effectiveness of electrochemical treatment. This paper proposes a mathematical approach to obtain a three-dimensional analytical expression for the current density generated by multi-needle electrodes. Such array of electrodes can be allocated in an arbitrary shape and inserted anywhere in the tumor. Calculations of the electrical potential and electric current density distributions based on a three-dimensional model for different straight multi-needle electrode configurations are carried out by solving the Laplace equation. The results show that appropriate positioning, insertion depth and electrodes polarity are essential for tumor treatment with direct current and multiple needle electrodes, arranged in concentric circumferences, concentrate a higher electric current density in the tumor. This configuration of multiple straight needle electrodes inserted along the tumor improves the effectiveness of electrochemical treatment because the current density covers the entire volume of the tumor, unlike those configurations that are inserted in the tumor base and only partially cover its volume.

Methodology for Characterizing Representativeness Uncertainty in Orifice Plate Mass Flow Rate Measurements Using CFD Simulations

The measurement of the steam generator feedwater mass flow rate is a dominant source of uncertainty in the nominal thermal power calculation of a plant. In this paper, mass flow rate measurement by means of an orifice plate is considered. Reynolds-averaged Navier-Stokes (RANS) simulation was performed using the computational fluid dynamics code STAR-CCM+ to quantify the representativeness uncertainty of mass flow rate measured in a dedicated experimental configuration. The representativeness uncertainty arises from applying the tolerance values prescribed by the International Organization for Standardization (ISO) standard in non-straight piping geometries. The simulation results were compared with the test results and the uncertainty bounds prescribed by the ISO standard, demonstrating the feasibility of applying RANS in an industrial setting for sub-1% uncertainty applications. The RANS results were also used to identify the variability in the measurement result with respect to the angular location of the pressure tap used in the flow rate measurement. Second, a large eddy simulation (LES) was performed on a straight piping configuration to simulate unsteady coherent flow shedding at the orifice plate. The spectral results of LES were compared with data from a test. The time-averaged LES results are within 0.1% of the value prescribed by the ISO standard. Direct comparison of the temporal spectrum of the LES result to the test data is not possible due to the measurement technique. This work is a part of a wider effort to develop a methodology to characterize, assess, and quantify representativeness uncertainty in performance indicator measurements of plants. Spatial, temporal, and modeling representativeness uncertainties are presented in this current work.

Pemberian Syarat Reflektif Kecepatan Fluida di Batas Anomali Kedalaman dalam Simulasi Persamaan Air Dangkal

The simulation of shallow water equation with straight configuration reflective depth anomaly has been performed. This program simulated wave absorber in the beach in order to prevent furthur abrasion of by sea. This program using modified Navier-Stokes equation and running on Matlab program. The result show that depth-anomaly reduced the amount on wave amplitudo by significant value. DOI: http://dx.doi.org/10.17977/um024v1i12016p007

Mechanism of Axonal Contractility in Embryonic Drosophila Motor Neurons In Vivo

Several in vitro and limited in vivo experiments have shown that neurons maintain a rest tension along their axons intrinsically. They grow in response to stretch but contract in response to loss of tension. This contraction eventually leads to the restoration of the rest tension in axons. However, the mechanism by which axons maintain tension in vivo remains elusive. The objective of this work is to elucidate the key cytoskeletal components responsible for generating tension in axons. Toward this goal, in vivo experiments were conducted on single axons of embryonic Drosophila motor neurons in the presence of various drugs. Each axon was slackened mechanically by bringing the neuromuscular junction toward the central nervous system multiple times. In the absence of any drug, axons shortened and restored the straight configuration within 2–4 min of slackening. The total shortening was ∼40% of the original length. The recovery rate in each cycle, but not the recovery magnitude, was dependent on the axon’s prior contraction history. For example, the contraction time of a previously slackened axon may be twice its first-time contraction. This recovery was significantly hampered with the depletion of ATP, inhibition of myosin motors, and disruption of actin filaments. The disruption of microtubules did not affect the recovery magnitude, but, on the contrary, led to an enhanced recovery rate compared to control cases. These results suggest that the actomyosin machinery is the major active element in axonal contraction, whereas microtubules contribute as resistive/dissipative elements.

Comparative analysis of a concentric straight and a U-bend gas cooler configurations in CO2 refrigeration system

This paper compares the heat transfer performance of two gas cooler configurations using CO2 as refrigerant. Straight gas cooler vs U-bend gas cooler was analyzed using 3D numerical simulation employing ANSYS FLUENT commercial program. The importance of the structure of the mesh was discussed and the unstructured sweep method was selected. Numerical results were satisfactorily compared with those of eight different empirical correlations for the Nusselt number applicable to similar heat exchangers. Behaviors of the local CO2 thermophysical properties, turbulence parameters, and heat transfer parameters in both straight and U-bend gas cooler configurations were analyzed. The results of this analysis were used to predict the transient behavior of the heat transfer rate and the thermal effectiveness of the two configurations. An increase of 16% was observed in the thermal effectiveness of the gas cooler based on U-bend configuration compared to the straight gas cooler configuration. Finally, the transient behavior of the overall efficiency of the transcritical refrigeration facility in which the two gas cooler configurations are supposed to be installed was assessed. The installation based on U-bend gas cooler geometry has presented higher performance of about 20% of efficiency when compared with the straight geometry.