Element Removal Method Research Articles

Robust well-balanced method with flow resistance terms for accurate wetting and drying modeling in shallow water simulations

Hydrodynamic simulations in shallow water environments require careful consideration of the Wetting and Drying (WD) processes, which poses challenges to accurately modeling moving boundaries. This study introduces a novel method called the flow resistance method (FRM), which builds upon the foundation of the Negative-Depth Method (NDM) to tackle the intricacies of the moving boundary problem. Inspired by the Navier-Stokes/Brinkman (NSB) model from porous media theory, FRM incorporates a continuous function related to additional flow resistance that is proportional to the flow velocity. This approach facilitates a seamless transition between the exposed bed and fluid area wherein the additional flow resistance becomes 0 within the fluid area and approaches infinity in the exposed bed. Consequently, FRM adeptly and implicitly manages the moving boundary problem, causing a rapid decay of flow velocity to 0 in the exposed bed. In order to test the performance of FRM, four typical numerical experiments were conducted, along with an examination of a real-life case. Accuracy, robustness, and computational efficiency were assessed as key performance indicators. The simulations demonstrate that FRM adeptly tracks the moving water front, yielding precise results. Furthermore, when compared to established methods such as the Element Removal Method (ERM) and NDM, FRM exhibits broader applicability and achieves significant enhancements in the key performance indicators. These findings underscore the promising potential and broad applications of FRM in the field.

유한요소 해석을 이용한 소형 무인항공기 암의 최적화 설계

The usability of drones is largely related to their performance, and among them, lightening is a very important factor in increasing flight distance and flight time by mounting a larger battery as a flight object and enabling low power flight. In this paper, finite element analysis was used to optimize the design aimed at reducing the weight and improving the strength of a 1 kgf class drone arm with a leg-type landing gear. o this end, finite element stress analysis and optimization design were performed step by step, and a method of modifying design variables using a combination of methods such as element removal method was used to realize the optimal structure. As a result of the stepwise optimal design performed in this paper, the optimization of the drone arm was achieved, which reduces the maximum effective stress by 0.04% while reducing the mass by 12.38%.

Graph-based element removal method for topology synthesis of beam based ground structures

This note proposes a novel element removal method for ground structured based topology optimization that utilizes a double-filtering scheme based on a graph representation of the topology. Two types of systems: planar resonators and compliant mechanisms, are used to illustrate the method.

Optimum bracing design under wind load by using topology optimization

Seismic and wind load performances of buildings are commonly improved by using bracing systems. In practice, standard bracing systems, such as X, Y, V, and K types are used. To determine the appropriate bracing type, the designer uses trial & error method among the standard bracings to obtain better results. However, using topology optimization yields more efficient bracing systems or new bracing can be developed depending on building and loading types. Determination of optimum bracing type for minimum deformation on a building under the effect of wind load is given in this study. A new bracing system is developed by using topology optimization. Element removal method is used to determine and remove the comparatively inefficient materials. Optimized bracing is compared with proposed bracing types available in the related literature. Maximum deformation value of building is used as performance indicator to compare effectiveness of different bracings to resist wind loads. The proposed bracing, yielded 99%, deformation reduction compared to the unbraced building.

Novel Bracing Type Against Seismic Loading: KX Type

In this study, a new bracing system is proposed which is named as KX type. Element removal method is used to obtain this new bracing. KX type optimized bracing is compared with V, and K type bracings under seismic loading. Maximum deformation value is used as performance indicator to compare effectiveness of V, K, and proposed KX type bracings to resist seismic loads. The proposed KX type bracing, yielded 99.72%, 93% and 88% reduced deformation with respect to unbraced, K type, and V type bracings respectively.

Neutron diffraction and finite element modeling to study the weld residual stress relaxation induced by cutting

Temperature and residual stresses were thermo-mechanically modeled in a 1000mm long welding plate based on the simplified variable length heat source. The stress relaxations were simulated as a function of the plate length after cutting the initial weld specimen by using an element removal method and treating the prior stress field as the next cutting origins. Meanwhile residual stresses were sequentially measured in a weld with the length of 300mm and cut welds having 150, 10mm lengths for comparison using neutron diffraction. Residual stresses from both the modeling and experimental results exponentially decrease from about 370 to 0MPa as the total weld plate length decreases from 300mm to 10mm. Such stress relaxation by the cutting length is correlated to the exponential decrease law based on the St. Venant’s principle. It suggests that the minimum cutting length about 300mm is necessary to prevent the stress relaxation less than 3% of the initial stresses in a high-strength steel weld.

A Finite Element Removal Method for 3D Topology Optimization

Topology optimization provides great convenience to designers during the designing stage in many industrial applications. With this method, designers can obtain a rough model of any part at the beginning of a designing stage by defining loading and boundary conditions. At the same time the optimization can be used for the modification of a product which is being used. Lengthy solution time is a disadvantage of this method. Therefore, the method cannot be widespread. In order to eliminate this disadvantage, an element removal algorithm has been developed for topology optimization. In this study, the element removal algorithm is applied on 3-dimensional parts, and the results are compared with the ones available in the related literature. In addition, the effects of the method on solution times are investigated.

Numerical Simulation of Liquid-Solid Extrusion Process Based on the Mechanical Model Coupled with Solidification

Liquid-solid extrusion process is a combined process of casting and extrusion which can be used to form tubes or bars directly from liquid metal. The performance of products is enhanced through the large deformation and the solidification under pressure with less shrinkage cavity or porosity. Numerical simulation of this process is hard to run for it involves mechanical modeling of the dynamic transition from liquid phase to solid phase. The liquid zone and solid zone were modeled independently for reasons of their different characteristics of deformation. The deformation of liquid zone was described according to the principle of element removal method which eliminates the elemental distortion during the simulation. The solidified zone under elevated temperature was modeled through the hyperbolic sine constitutive equation. The dynamic transitions from liquid phase to solid phase were determined based on the results of thermal analysis. The mechanical model coupled with solidification proposed in this paper was verified through the experiments of liquid-solid extrusion of LY12 alloy.

Study on High Reduction Face Gears (1st Report, Meshing Analysis)

An analyzing method for applying to various types of face gears is proposed. Equations to calculate the profile of the face gear generated by the pinion as a profile on a cylinder are derived, and the tooth surface of the face gear was expressed by a series of profiles on each cylinder with a different radius. The envelope curve was calculated using the element removal method that simulates a metal removal process by a tool. The obtained results as follows : (1) A meshing condition diagram that reveals a whole aspect of meshing of the face gears with consideration of two kinds of interferences and tip pointing caused on the gear flanks is proposed. (2) Face gear pairs can be designed in compact size by an appropriate offset between the pinion and gear shafts. (3) By using a worm-like pinion under an appropriate offset, there is some possibility of designing the high reduction face gear pair.

Study on Finishing of Pinion Cutters by Form Grinding. 2nd Report. Finishing of Tooth Flanks by Multiple Motions.

This report describes a new method to finish tooth flanks of pinion cutters by form grinding with multiple relieving motions, which are the approaching motion between the grinding wheel and the pinion cutter, the rotational motion of the pinion cutter and the shifting motion of the grinding wheel. The method can successfully finish the whole depth of the cutting edge of the pinion cutter with an arbitrary profile by one-pass grinding for each tooth flank. The motions were decided as to minimize the cutting edge errors at two regrinding positions. As an example of profile calculation and the finishing test, the involute helical pinion cutter with a protuberance was selected. The profile of grinding wheel was calculated by applying the element removal method. The finishing test was conducted on the NC form gear-grinding machine and the pinion cutter with almost no profile error and a small regrinding error was obtained.

An improved element removal method for evolutionary structural optimization

The purpose of this study was to develop a new element removal method for ESO (Evolutionary Structural Optimization), which is one of the topology optimization methods, ESO starts with the maximum allowable design space and the optimal topology emerges by a process of removal of lowly stressed elements. The element removal ratio of ESO is fixed throughout topology optimization at 1 or 2%. BESO (bidirectional ESO) starts with either the least number of elements connecting the loads to the supports, or an initial design domain that fits within the maximum allowable domain, and the optimal topology evolves by adding or subtracting elements. But the convergence rate of BESO is also very slow. In this paper, a new element removal method for ESO was developed for improvement of the convergence rate. Then it was applied to the same problems as those in papers published previously. From the results, it was verified that the convergence rate was significantly improved compared with ESO as well as BESO.

Sharpening of Hob Cutting Edges with Helical Flutes.

Sharpening of a hob with helical flutes is a difficult problem in the gear production field because interference between a grinding wheel and hob rake face is apt to occur. In this paper, mechanism of interference in hob sharpening is analyzed and the condition without interference that causes a trouble is shown by means of the figure. Then, the profile of grinding wheel for sharpening the hob with helical flutes is calculated using the element removal method in the same way as form grinding of the helical gear with a profile of straight line. Also, the relation between the depth of hob flute and the tooth height of hob rake face being finished is shown by means of the figure. The sharpening test of the involute worm hob(mn=5, N=3, γ=23.917°)was conducted using the CNC gear form grinding machine. The radial alignment of hob rake face after sharpening was less than 5μm.

Relief Grinding of Worm Hobs with a Pencil Wheel.

A new method for calculating the profile of a pencil-type grinding wheel to finish worm hobs is proposed using the element removal method. The method realizes the finishing of worm hobs with an arbitrary profile and a large lead angle, without depending on the experience and perception of an expert. In this paper, a worm hob (mn=5 mm, Nh=3, rh=18.5 mm) is used as an example of profile calculation and finishing tests. The regrinding errors of the cutting edge profiles of the hobs to be finished with the pencil wheel and disk wheel are discussed by calculating the changes in the rack profiles expressed by the hob cutting edges after regrinding. To show the usefulness of the proposed method, the finishing tests of the worm hob were conducted on the CNC relief grinding machine with the pencil wheel attachment made by the authors. The accuracy of the finished worm hob was in the zero class of JIS.

ELEMENT REMOVAL METHOD FOR SINGULAR MINIMIZERS IN PROBLEMS OF HYPERELASTICITY

A numerical method called element removal method is applied to calculate singular minimizers in problems of hyperelasticity. The method overcomes the difficulty in finite element approximations caused by restrictions, such as det (I+∇u)>0, on admissible functions and can avoid Lavrentiev phenomenon if it does occur in the problem. The convergence of the method is proved.

Element removal method for singular minimizers in variational problems involving Lavrentiev phenomenon

A numerical method called element removal method is designed to calculate singular minimizers which cannot be approximated by simple applications of standard numerical methods because of the so-called Lavrentiev phenomenon. The convergence of the method is proved. The results of numerical experiments show that the method is effective.

Design and Manufacture of Pinion Cutters for Finishing Gears with an Arbitrary Profile.

A new method of calculating grinding-wheel profiles for finishing pinion cutters to shape spur and helical gears with an arbitrary profile is developed using the theory of the element removal method (ERM) previously proposed by the authors. In order to show the usefulness of this method, the profiles of the grinding wheel for finishing the pinion cutter (mn = 3) for Novikov gears with concave teeth are calculated numerically, and then the profiles of the pinion cutter finished by the grinding wheel are calculated. The difference (calculation error) between the given and the calculated profile of the pinion cutter was less than O.1 μm before regrinding. Profile errors of the cutting edges after regrinding are shown in terms of the number of teeth, the helix and rake angles and the regrinding stock. The effective clearance angles of cutting edges, which produce some broblems in gear finishing, are calculated from changes in the profiles of the cutting edges before and after regrinding.

Design and manufacture of pinion cutters for finishing gears with an arbitrary profile.

A new method of calculating grinding-wheel profiles for finishing pinion cutters to shape spur and helical gears with an arbitrary profile is developed using the theory of the element removal method (ERM) previously proposed by the authors. In order to show the usefulness of this method, the profiles of the grinding wheel for finishing the pinion cutter (mn=3) for Novikov gears with concave teeth are calculated numerically, and then the profiles of the pinion cutter finished by the grinding wheel are calculated. The difference (calculation error) between the given and the calculated profile of the pinion cutter was in the range of about 0.1μm before regrinding. Profile errors of the cutting edges after regrinding are shown in terms of the number of teeth, the helix and rake angles and the regrinding stock. The effective clearance angles of cutting edges, which produce some problems in gear finishing, are calculated from changes in the profiles of the cutting edges before and after regrinding.

Design and manufacture of gear cutting tools and gears with an arbitrary profile.

The authors introduced a new method (element removal method) for calculating the profiles of the tools (hob, form grinding wheel, etc.) used for finishing gears with an arbitrary tooth profile. Because this method simulates exactly the metal removing process in the gear tooth profile generation, it is possible to calculate the generated tooth profile when interference occurs between the cutting edge and the finished tooth profile. Using this method, the authors calculated the exact wheel profile which can produce and involute tooth profile with a tip relief at a transverse section of the involute helical gears. The wheel profile was generated by a single point diamond dresser using a universal NC milling machine with an attachment made by the authors. The tooth flank and root of test gears were ground at the same time to prevent a step (notch), which is apt to be produced at the boundary of ground and unground surfaces. The accuracy of the form ground test gears was in the zero class of JIS and the surface roughness was in the range of 0.5 to 1.0 μm Rmax.

Experimental study of residual stresses in thin-walled rotational shells made of composite materials by means of the annular element removal method

Experimental study of residual stresses in thin-walled rotational shells made of composite materials by means of the annular element removal method