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Elastic stress solutions are required in the field of fracture mechanics and the analysis of creep failure. The published precise elastic solutions are not addressing the influence of the manufacturing process induced, inevitable cross sectional deviations called ovality and thinning. The influence of ovality on plastic limit and collapse loads are reported in literature. Hence, it is important to study the combined effect of ovality and thinning on elastic stresses of bends.

This paper relies on elastic finite element evolutions of stress components– longitudinal membrane stress, longitudinal bending stress, circumferential membrane stress and circumferential bending stresses. Based on the results, the coefficients for the equations are also obtained through the regression analysis.

New analytical solutions are prescribed to estimate the elastic stresses at the mid-section of the 90° very thin-walled bend with ovality and thinning, when subjected to in-plane bending moment. The ovality has significant influence on elastic stress whereas the thinning is not so. The proposed equations give an accurate estimation of elastic stresses at the mid-section of the bend with the incorporation of the parameters, namely R/r_m, r_m/t and ovality.

The influence of shape imperfections, namely ovality and thinning on elastic stress of 90° very thin-walled bends having r_m/t > 20, subject to in-plane bending moment is proposed.

The influence of shape imperfections, namely ovality and thinning, on elastic stress of 90° very thin-walled bends with r_m/t > 20, subject to in-plane bending moment is proposed.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

Precise assessment of elastic stress is required in the field of fracture mechanics. While bending a straight pipe, the deformation of the circular cross section out of roundness called ovality and thinning are foreseeable. The ovality has a significant effect on the structural integrity of the pipe. The sole objective of this paper is to provide new analytical solutions to predict accurate elastic stress distribution at the median section of the U-bend, with deformities such as ovality and thinning when subjected to in-plane closing moment by using elastic finite element analysis.

The quarter model of the U bend has been analysed by using ABAQUS. The elastic stress components included in this analysis are longitudinal bending stress, longitudinal membrane stress, circumferential bending stress and circumferential membrane stress. Based on finite element results, analytical elastic stress solutions are also provided for both longitudinal and circumferential stresses by using these stress components.

As the ovality has a significant effect, it is further included in the analytical solution. The thinning is not included since it has very little effect. Analytical stress solutions are provided for a wide range of bend characteristics to include ovality, mean radius and thickness.

Significance of ovality and thinning on elastic stress of U-bend has not been reported in the existing literature.

The purpose of this paper is to quantify the combined effect of shape distortion and bend angle on the collapse loads of pipe bends exposed to internal pressure and in-plane closing bending moment. Non-linear finite element analysis with large displacement theory was performed considering the pipe bend material to be elastic perfectly plastic.

One half of the pipe bend model was built in ABAQUS. Shape distortion, namely, ovality (Co) and thinning (Ct), were each varied from 0% to 20% in steps of 5% and bend angle was varied from 30° to 180° in steps of 30°.

The findings show that ovality has a significant impact on collapse load. The effect of ovality decreases with an increase in bend angle for small thickness. The opposite effect was observed for large thickness pipe bends. The influence of ovality was more for higher bend angles. Ovality impact was almost negligible at certain internal pressure denoted as nullifying point (NP). The latter increased with an increase in pipe bend thickness and decreased with increase in pipe bend radius. For small bend angles one NP was observed where ovality impact is negligible and beyond this point the ovality effect increased. Two NPs were observed for large bend angles and ovality effect was maximum between the two NPs. Thinning yielded a minimal effect on collapse load except for small bend angles and bend radii. The influence of internal pressure on thinning was also negligible.

Influence of shape distortions and bend angle on collapse load of pipe bend exposed to internal pressure and in-plane closing bending has been not revealed in existing literature.

The purpose of this study is to investigate the effect of structural deformations and bend angle on plastic collapse load of pipe bends under an in-plane closing bending moment (IPCM). A large strain formulation of three-dimensional non-linear finite element analysis was performed using an elastic perfectly plastic material. A unified mathematical solution was proposed to estimate the collapse load of pipe bends subjected to IPCM for the considered range of bend characteristics.

ABAQUS was used to create one half of the pipe bend model due to its symmetry on the longitudinal axis. Structural deformations, i.e. ovality (C_o) and thinning (C_t) varied from 0% to 20% in 5% steps while the bend angle (ø) varied from 30° to 180° in steps of 30°.

The plastic collapse load decreases as the bend angle increase for all pipe bend models. A remarkable effect on the collapse load was observed for bend angles between 30° and 120° beyond which a decline was noticed. Ovality had a significant effect on the collapse load with this effect decreasing as the bend angle increased. The combined effect of thinning and bend angle was minimal for the considered models and the maximum per cent variation in collapse load was 5.76% for small bend angles and bend radius pipe bends and less than 2% for other cases.

The effect of structural deformations and bend angle on collapse load of pipe bends exposed to IPCM has been not studied in the existing literature.

The aim of this study is to ensure the structural integrity of 90° back-to-back (B2B) pipe bends by developing a closed-form numerical solution for estimating the collapse load of shape distorted 90° B2B pipe bends using non-linear finite element (FE) analysis.

The collapse behaviour of 90° B2B pipe bends with ovality (C_o) and thinning (C_t) has been evaluated by non-linear FE approach. Moment load is applied in the form of in-plane closing moment (IPCM). The current FE approach was evaluated by the numerical solution for the plastic collapse moment of pipe bends, which has been published in the literature. The collapse moments were obtained from the twice elastic slope (TES) method using the moment-rotation curve of every individual model.

The implication of C_t/C_th on collapse load is found to be highly insignificant in terms of increasing bend radius and C_o. C_o weakens the geometry, and its effect on the collapse load is substantial. A closed-form numerical solution has been proposed to calculate the collapse load of 90° B2B pipe bend with shape imperfections.

The implications of shape distortion (C_o and C_t) in the failure analysis (collapse load) of 90° B2B pipe bends has not been investigated and reported.

In this paper a prototype actuator designed for a high bandwidth servo system is modeled and analyzed using finite elements. Natural frequencies and mode shapes of frequencies below 10kHz are extracted using frequency analysis and compared with the results from an experimental model analysis. The effects of key parameters used in the analysis on the natural frequencies are investigated. The frequency response is calculated using the natural frequencies and mode shapes. The calculated frequency response is compared with experimental results. The comparison of results shows that the numerical results are accurate. From the analysis the mechanical dynamics of the actuator can be understood and characterized. The analysis of the actuator shows that dynamic analysis using finite element modeling is accurate and effective and can be applied to other mechatronic systems.

THE purpose of the present report is to present tables and to summarize formulas which are required for the analysis of circular rings, under forces in the plane of the ring or out of the plane. Usually, rings which are redundant structures are calculated by considering strain due to bending only. It is shown that for the stress distribution in a circular ring under given loads, the solution introducing strains due to shearing and axial loads is the same as the solution conventionally used.

The purpose of this paper is to develop an analytical approach to evaluate the influence of material uncertainties on cross‐sectional stiffness properties of thin walled composite beams.

Fuzzy arithmetic operators are used to modify the thin‐walled beam formulation, which was based on a mixed force and displacement method, and to obtain the uncertainty properties of the beam. The resulting model includes material uncertainties along with the effects of elastic couplings, shell wall thickness, torsion warping and constrained warping. The membership functions of material properties are introduced to model the uncertainties of material properties of composites and are determined based on the stochastic behaviors obtained from experimental studies.

It is observed from the numerical studies that the fuzzy membership function approach results in reliable representation of uncertainty quantification of thin walled composite beams. The propagation of uncertainties is also demonstrated in the estimation of structural responses of composite beams.

This work demonstrates the use of fuzzy approach to incorporate uncertainties in the responses analytically, in turn improving computational efficiency drastically as compared to the Monte‐Carlo method.

This paper aims to present a shape sensing method and feedback control strategy based on fiber Bragg grating (FBG) sensor to improve the control accuracy of the robot and ensure the safety of the cardiac interventional surgery.

To theoretically describe the shape of the catheter robot, the kinematic model is established by the geometric analysis method. And to obtain the actual shape, a large curvature assemble sensor based on FBG is adopted and a novel simple shape reconstruction model is proposed, which can provide the shape curve and distal position. In addition, the influence of external load on the bending deformation is investigated by experiments. To improve the shape accuracy of the robot, a shape feedback control method is presented to control the catheter robot, which can control the robot to bend into the pre-given desired shape.

Experiment results verify the effectiveness of the shape sensing method and the reconstruction model, and the correlation coefficients of three sets of curve in different coordinate directions are 0.9986, 0.9992 and 0.9999. Results of the shape feedback experiment show that the curvature error and direction angle error are 1.42% and 10.3%, respectively. The continuum catheter robot can be controlled to achieve the desired bending shape.

The shape reconstruction method and feedback control strategy proposed in this paper can improve the control accuracy of the robot to avoid the risk of the collision with the surrounding blood vessels, the tissues and organs.