Search

In this paper, a residual-type a posteriori error estimator is proposed and analyzed for a weak Galerkin finite element method for solving linear elasticity problems. The error estimator is proven to be both reliable and efficient, and be used for adaptive refinement. Numerical experiments are presented to illustrate the effectiveness of this error estimator. [ABSTRACT FROM AUTHOR]

In the free-bending process, the tube undergoes bending and deformation due to the action of a guide mechanism and bending die. The plastic deformation zone of the bent tube is less constrained by the die, and the quality of the formed tube is significantly affected by the friction between the tube and the die. To assess the impact of friction between tube and die on the formability of the bent tube, the theoretical modeling that considers the friction coefficient is conducted. Afterward, the free-bending experiments and finite element simulations are performed using Cr12MoV and ceramic bushing. The theoretical and experimental results are compared with those obtained from finite element simulation under different friction conditions to confirm the validity of finite element simulation. The influence of friction on the arc radius, wall thickness variation, and cross-section deformation of the curved tube is explored and discussed. With the increase of friction coefficient, the arc radius decreases gradually, the wall thickness thickens more obviously, and the cross-sectional distortion becomes more serious. Furthermore, the effect of different bushing materials on the surface quality of aluminum alloy and stainless-steel bent tubes is experimentally investigated. Those findings expand our understanding of the influence of tube-die friction on deformation behavior and it is necessary to first determine the friction condition during the actual free-bending forming process. [Display omitted] • The increase of friction coefficient introduces the improvement of axial force. • Shift of strain-neutral layer is verified by simulation and theoretical deduction. • The bending radius of bent tube decreases with increasing friction coefficient. • The surface quality of bent tube is improved by using the ceramic bushing. [ABSTRACT FROM AUTHOR]

With the advancement of 'Industrial 4.0', industrial robots are becoming increasingly widespread. Thus, this study proposes a novel robot-based tube bending forming technology (RTBF) to increase the flexibility of manufacturing thin-walled complex-shaped tubes and to improve their quality. The forming mechanism and characteristics of the proposed technology are investigated using finite element modelling. Besides, the theoretical models for calculating the tube's inner and outer sides' equivalent stress are also presented. The obtained results showed that the bending die feeds in the tube axis direction while rotating in the novel robot-based tube bending forming, and the axial tensile stress T on the tube during the bending process is reduced. Comparing these results with the traditional rotary draw bending (RDB), the tensile stress and strain on the outer side of the bent tube and the thinning wall rate are both lower. On the other hand, the compressive stress and strain on the inner side of the bent tube and the wall thickening rate are higher in the robot-based tube bending process. The maximum cross-sectional distortion of a bent tube in the robot-based tube bending forming process remains unchanged with increasing bending angle and is always smaller than in the RDB process: the larger the bending angle, the more noticeable the difference. In summary, the robot-based tube bending forming technology significantly reduces the small diameter tube's wall thickness and cross-sectional distortion. [ABSTRACT FROM AUTHOR]

Undesired wall thickness distribution and flanging cracking easily occur in reverse drawing--flanging combined processes of steel spokes when improper process parameters are used. Thus, based on GRA (grey relational analysis) and FEM (finite element method), a GRA model for a reverse drawing--flanging combined process for high strength steel B550CL spoke was established and validated. The results show that: (1) the most significant factors affecting uneven wall thickness distribution and excessive thinning in the mounting zone and center hole cracking are the friction coefficient and the shape of punch, respectively; (2) the non-uniformity of wall thickness U increases with the increase of the friction coefficient. The conical punch has a lower thinning ratio T, the spherical punch has a lower value of damage D; (3) considering synthetically the indexes of uneven wall thickness distribution, the excessive thinning in the mounting zone and center hole cracking, optimal results for the process parameters are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we investigate error estimates and superconvergence of a mixed finite element method for elliptic optimal control problems. The gradient for our method belongs to the square integrable space instead of the classical H ( div ; Ω ) space. The state and co-state are approximated by the P 0 2 – P 1 (velocity–pressure) pair and the control variable is approximated by piecewise constant functions. First, we derive a priori error estimates in H 1 -norm for the state and the co-state scalar functions, a priori error estimates in ( L 2 ) 2 -norm for the state and the co-state vector functions and a priori error estimates in L 2 -norm for the control function. Then, using postprocessing projection operator, we derive a superconvergence result for the control variable. Next, we get a priori error estimates in L 2 -norm for the state and the co-state scalar functions. Finally, a numerical example is given to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

Cross-sectional deformation of the double-ridged rectangular tube inevitably occurs in the rotary draw bending process. It has serious effect on the characteristic of microwave transmission and restricts the quality and performance of tube. Different mandrels play different roles in the bending process, so the rigid and polyvinyl chloride (PVC) mandrels are applied in the E-typed and H-typed rotary draw bending of double-ridged rectangular tube to study their influence on the cross-sectional deformation. Based on the platform of ABAQUS/Explicit, the three-dimensional finite element models for E-typed and H-typed rotary draw bending of H96 brass double-ridged rectangular tube with rigid and PVC mandrels have been established and validated by experiment. Results show that whether in the E-typed or H-typed bending, the PVC mandrel has better inhibitory effect on the cross-sectional long-side deformation δ , short-side deformation δ , and spacing deformation between the bottom of ridge grooves δ of the tube. And the PVC mandrel can be more helpful to reduce the width deformation of ridge grooves of the tube in H-typed bending. The rigid mandrel can restrain the width expansion deformation of outer ridge groove of the tube more effectively in E-typed bending. However, whether using the rigid or PVC mandrel, the width shrinkage deformation of inner ridge groove of the tube in E-typed bending is less affected by the type of mandrels. And the width of two ridge grooves on sidewalls of the tube in H-typed bending also has the obvious shrinkage deformation. [ABSTRACT FROM AUTHOR]

Cross-sectional deformation is one of the critical factors that affect the forming accuracy of double-ridged rectangular tube (DRRT) in E-typed rotary draw bending (RDB). In the forming process, springback is inevitable and it has a direct impact on the cross-sectional deformation. Based on ABAQUS platform, three-dimensional finite element (3D-FE) models for bending and springback of H96 brass DRRT in E-typed RDB were established. With the models, the impact of springback on the cross-sectional deformation was studied. Results show that after springback, the deformation of cross-sectional height and two ridge grooves spacing increase in cores-support zone while decrease in no-cores-support zone. The impact of springback on width deformation is not significant. The maximum values of cross-sectional height deformation and two ridge grooves spacing deformation from 0° to 30° become larger after springback, while the change rules of these two from 30° to 90° are reversed. What's more, the maximum value of width deformation from 0° to 60° becomes larger after springback while that of outer ridge groove width deformation becomes smaller, and these two from 60° to 90° both have the reversed change rules as well. [ABSTRACT FROM AUTHOR]

This paper introduces an adaptive finite element method (AFEM) using the newest vertex bisection and marking exclusively according to the error estimator without special treatment of oscillation. By the combination of the global lower bound and the localized upper bound of the posteriori error estimator, perturbation of oscillation, and cardinality of the marked element set, it is proved that the AFEM is quasi-optimal for linear elasticity problems in two dimensions, and this conclusion is verified by the numerical examples. [ABSTRACT FROM AUTHOR]

Abstract: Numerical simulation for flow, heat transfer and thermal stress for a 3in. diameter liquid-encapsulated float zone growth of single-crystal InP is conducted by using the finite-element method under zero gravity condition. The results show that the crystal and feed rod rotation rate has a notable influence on the flow pattern in the melt. It also shows that the melt/crystal interface shape becomes more convex and the maximum value of thermal stress in the crystal reduces with increasing encapsulant thickness, decreasing pulling rate and decreasing the length of the melting zone. [Copyright &y& Elsevier]

An Adaptive Edge Finite Element Method (AEFEM) for three-dimensional indefinite time-harmonic Maxwell equations with variable coefficients is proved to be convergent and arbitrary order Nédélec edge elements are considered. A posteriori upper bound, quasi-orthogonality and the contraction of the error estimator are provided to prove the contraction of the sum of the energy error and the scaled error estimator between two consecutive adaptive loops. Numerical experiments are presented to support the theoretical results. [ABSTRACT FROM AUTHOR]