Sub-problem Method Research Articles

Sizing optimisation of steel truss based on algorithms

Computational methods enable mathematical discretisation in structural design. Thus, thanks to the algorithmic design, the obtained results matrix presents various structurally efficient load-bearing elements. The main aim of this paper is to address the topic of material optimisation in truss bar structures with different approaches. The paper analyses and compares steel truss optimisation based on two software optimisation algorithms (MS Excel and Ansys Mechanical) using gradient and sub-problem methods. The key findings present how effective each method is in structural optimisation and concludes the present study with a roadmap to efficient structural designing of the load-bearing truss elements.

Structural design and dynamics optimization for heald frame made by carbon fiber reinforced composites

For improving the performance defects of traditional heald frame, the carbon fiber reinforced composites was applied to technical upgrading of the heald frame. On the basis of the theory analysis of composites laminates, the symmetrical ply scheme suitable for manufacturing of the heald frame in overall laminated was constructed, and a type of parametric program for finite element modeling was developed by ANSYS Parametric Design Language (APDL). The optimal mathematical model of the composites heald frame was proposed, and then the thickness parameter ( t) and direction parameters (α, θ) of fiber layer were dynamic optimized by using of Sub-problem method. The work increased the fundamental frequency (ω1) of the heald frame by 10.38%. Besides, the harmonic response frequency was also increased from 48.41 Hz to 53.77 Hz, which conductive to further improve dynamics properties of the composites heald frame. This paper provides technical guidance for innovative design of new heald frame, and is helpful to solve the problem of speed matching between heald frame and high-speed loom.

Modeling and compensation of volumetric errors for a six-axis automated fiber placement machine based on screw theory

This paper presents a novel modeling and compensation method for the volumetric errors of a six-axis gantry automated fiber placement (AFP) machine. Based on the screw theory, the forward and inverse kinematics models of the AFP machine are established. In order to improve the accuracy of the inverse kinematics solution, the Paden-Kahan sub-problem method is used to perform the inverse kinematics solution for the simplified topology of the rotary axes. Using error motion twist to establish a volumetric error transfer model for 54 geometric errors. According to the measurement data of a laser tracker and the Levenberg-Marquardt method to identify the geometric error parameters. The explicit formula of the inverse kinematics solution is used to obtain the error compensation of each motion axis, and the G code of the laying path is modified by the iterative method to realize the compensation of the volumetric errors. By comparing the positions of the tool center point before and after the error compensation, the practicability of the volumetric error modeling and iterative compensation methods are verified, and the geometric accuracy of the AFP machine can be effectively improved.

Improved error of electromagnetic shielding problems by a two-process coupling subproblem technique

Introduction: The direct application of the classcial finite element method for dealing with magnetodynamic problems consisting of thin regions is extremely difficult or even not possible. Many authors have been recently developed a thin shell model in order to overcome this drawback. However, this development generally neglects inaccuracies around edges and corners of thin shell, that lead to inaccuracies of the magnetic fields, eddy currents and joule power losses, specially increasing with the thickness.
 Methods: In this article, we propose a two-process coupling subproblem technique for improving the errors that overcome thin shell assumptions. This technique is based on the subproblem method to couple SPs in two-processes. The first scenario is an initial problem solved with coils/stranded inductors together with thin region models. The obtained solutions are then considered as volume sources for the second scenario including actual volume improvements that scope with the thin shell assumptions. The final solution is sum up of the subproblem solutions achieved from both the scenarios. The extended method is approached for the h-conformal magnetic formulation.
 Results: The obtained results of the method are checked/compared to be close to the reference solutions computed from the classcial finite element method and the measured results. This can be pointed out a very good agreement.
 Conclusion: The extended method has been also successfully applied to the practical problem (TEAM workshop problem 21, model B).

Two-way coupling of thin shell finite element magnetic models via an iterative subproblem method

PurposeThe purpose of this paper is to deal with the correction of the inaccuracies near edges and corners arising from thin shell models by means of an iterative finite element subproblem method. Classical thin shell approximations of conducting and/or magnetic regions replace the thin regions with impedance-type transmission conditions across surfaces, which introduce errors in the computation of the field distribution and Joule losses near edges and corners.Design/methodology/approachIn the proposed approach local corrections around edges and corners are coupled to the thin shell models in an iterative procedure (each subproblem being influenced by the others), allowing to combine the efficiency of the thin shell approach with the accuracy of the full modelling of edge and corner effects.FindingsThe method is based on a thin shell solution in a complete problem, where conductive thin regions have been extracted and replaced by surfaces but strongly neglect errors on computation of the field distribution and Joule losses near edges and corners.Research limitations/implicationsThis model is only limited to thin shell models by means of an iterative finite element subproblem method.Originality/valueThe developed method is considered to couple subproblems in two-way coupling correction, where each solution is influenced by all the others. This means that an iterative procedure between the subproblems must be required to obtain an accurate (convergence) solution that defines as a series of corrections.

OPUS-Fold: An Open-Source Protein Folding Framework Based on Torsion-Angle Sampling.

In this article, we propose a protein folding framework, named OPUS-Fold, which can integrate various methods for subproblems in protein structure prediction to contribute to folding. OPUS-Fold is based on torsion-angle sampling. After each sampling step, it reconstructs the structure and estimates the model quality with an energy function that is formed by combining many different constraining terms designed either by ourselves or by others in the literature. OPUS-Fold balances accuracy and efficiency, delivers good results in a short time, and leaves more space for including the results of other subproblem methods. Moreover, OPUS-Fold also contains a fast side-chain modeling method OPUS-Rota2 (J. Chem. Theory Comput. 2019, 15 (9), 5154-5160), which enables a speedy construction of all-atom atomic models during the folding process that allows the usage of all-atom-required subproblem methods. In summary, OPUS-Fold provides a protein folding platform for incorporating the results from various subproblem methods, including those containing nondifferentiable information such as partial experimental data. The source code of OPUS-Fold can be downloaded from https://github.com/thuxugang/opus_fold.

Using edge elements for modeling of 3-D magnetodynamic problem via a subproblem method

Introduction: The mathematical modeling of electromagnetic problems in electrical devices are often presented by Maxwell’s equations and constitutive material laws. These equations are partial differential equations linked to fields and their sources. In order to solve these equations and simulate the distribution of magnetic fields and eddy current losses of electromagnetic problems, a subproblem method for modeling a 3-D magnetodymic problem with the b-conformal formulation is proposed.
 Methods: In this paper, the subproblem method with using edge finite elements is proposed for coupling subproblems via several steps to treat and deal with some troubles regarding to electromagnetic problems that gets quite difficulties when directly applying a finite element method. In the strategy subproblem method, it allows a complete problem to define into several subproblems with adapted dimensions. Each subproblem can be solved on its independent domain and mesh without performing in whole domain or mesh. This easily supports meshing and decreases computing time.
 Results: The obtained results, the subproblem method with edge elements indicates magnetic flux densities and the eddy current losses in the conducting region. The computed results is also compared with the measured results done by other authors. This can be shown that there is a very good agreement.
 Conclusion: The validated method has been successfully applied to a practical test problem (TEAM Problem 7).

An Energy and SLA-Aware Resource Management Strategy in Cloud Data Centers

Reducing energy consumption of data centers is an important way for cloud providers to improve their investment yield, but they must also ensure that the services delivered meet the various requirements of consumers. In this paper, we propose a resource management strategy to reduce both energy consumption and Service Level Agreement (SLA) violations in cloud data centers. It contains three improved methods for subproblems in dynamic virtual machine (VM) consolidation. For making hosts detection more effective and improving the VM selection results, first, the overloaded hosts detecting method sets a dynamic independent saturation threshold for each host, respectively, which takes the CPU utilization trend into consideration; second, the underutilized hosts detecting method uses multiple factors besides CPU utilization and the Naive Bayesian classifier to calculate the combined weights of hosts in prioritization step; and third, the VM selection method considers both current CPU usage and future growth space of CPU demand of VMs. To evaluate the performance of the proposed strategy, it is simulated in CloudSim and compared with five existing energy–saving strategies using real-world workload traces. The experimental results show that our strategy outperforms others with minimum energy consumption and SLA violation.

Progressive Current Source Models in Magnetic Vector Potential Finite-Element Formulations

Progressive refinements of the current sources in magnetic vector potential finite-element (FE) formulations are done with a subproblem method. The sources are first considered through magnetomotive force or Biot-Savart models up to their volume FE models, from statics to dynamics. A novel way to define the source fields is proposed to lighten the computational efforts, through the conversion of the common volume sources to surface sources, without the need for any preresolution. Accuracy improvements can then be obtained for local currents and fields, and global quantities, i.e., inductances, resistances, Joule losses, and forces.

Improved Inverse Kinematics Algorithm Using Screw Theory for a Six-DOF Robot Manipulator

Based on screw theory, a novel improved inverse-kinematics approach for a type of six-DOF serial robot, “Qianjiang I”, is proposed in this paper. The common kinematics model of the robot is based on the Denavit-Hartenberg (D-H) notation method while its inverse kinematics has inefficient calculation and complicated solution, which cannot meet the demands of online real-time application. To solve this problem, this paper presents a new method to improve the efficiency of the inverse kinematics solution by introducing the screw theory. Unlike other methods, the proposed method only establishes two coordinates, namely the inertial coordinate and the tool coordinate; the screw motion of each link is carried out based on the inertial coordinate, ensuring definite geometric meaning. Furthermore, we adopt a new inverse kinematics algorithm, developing an improved sub-problem method along with Paden-Kahan sub-problems. This method has high efficiency and can be applied in real-time industrial operation. It is convenient to select the desired solutions directly from among multiple solutions by examining clear geometric meaning. Finally, the effectiveness and reliability performance of the new algorithm are analysed and verified in comparative experiments carried out on the six-DOF serial robot “Qianjiang I”.

Progressive inductor modeling via a finite element subproblem method

Purpose – The purpose of this paper is to develop a subproblem method (SPM) for progressive modeling of inductors, with model refinements of both source conductors and magnetic cores. Design/methodology/approach – The modeling of inductors is split into a sequence of progressive finite element (FE) SPs. The source fields (SFs) generated by the source conductors alone are calculated at first via either the Biot-Savart (BS) law or FEs. With a novel general way to define the SFs via interface conditions (ICs), to lighten their evaluation process, the associated reaction fields for each added or modified region, mainly the magnetic cores, and in return for the source conductor regions themselves when massive, are then calculated with FE models. Changes of magnetic regions go from perfect magnetic properties up to volume linear and nonlinear properties, and from statics to dynamics. Findings – For any added or modified region, the novel proposed ICs to define the SFs appear of general usefulness, which opens the method to a wide range of model improvements. Originality/value – The resulting SPM allows efficient solving of parameterized analyses thanks to a proper mesh for each SP and the reuse of previous solutions to be locally corrected, in association with novel SF ICs that strongly lighten the quantity of BS evaluations. Significant corrections are progressively obtained for the fields, up to nonlinear magnetic core properties and skin and proximity effects in conductors, and for the related inductances and resistances.

Subproblem Finite-Element Refinement of Inductors From Wire to Static and Dynamic Volume Models

Progressive refinements of inductors are done with a subproblem method, from their wire or filament representations with Biot-Savart models up to their volume finite-element models, from statics to dynamics. The reaction fields of additional magnetic and/or conducting regions are also considered. Accuracy improvements are efficiently obtained for local fields and global quantities, i.e., inductances, resistances, Joule losses, and forces.

Increasing bending strength in spur gears using shape optimisation of cutting tool profile

The geometrical shape of gear tooth fillet profile, usually cut out by the cutter tip, plays a significant role in the evaluation of the gear bending stress. In order to improve the teeth bending strength, a novel curve (quadratic rational Bezier curve) is introduced to describe the cutter tip. The gear tooth finite element models are founded by APDL in the ANSYS software. With the maximum bending stress (von Mises stress) as the objective function, SUB-PROBLEM and FIRST-ORDER optimisation methods in ANSYS are used to optimise the cutter tip. Single-tooth bending test is also conducted to prove the optimisation result. The study reveals that the relationship between the design variable and tooth root bending stress is non-linear, and the gear cut by the optimised cutter exhibits higher bending strength rather than the gear cut by standard cutting tool.

Progressive eddy current modeling via a finite element subproblem method

The modeling of eddy currents in conductors is split into a sequence of progressive finite element subproblems. The source fields generated by the inductors alone are calculated at first via either the Biot- Savart law or finite elements. The associated reaction fields for each added conductive region, and in return for the source regions themselves when massive, are then calculated with finite element models, possibly with initial perfect conductor and/or impedance boundary conditions to be further corrected. The resulting subproblem method allows efficient solving of parameterized analyses thanks to a proper mesh for each subproblem and the reuse of previous solutions to be locally corrected.

Design of UHVDC Wall Bushing and its Electric Field Simulation

Reviewing and analyzing insulation mechanism of high voltage wall bushing, the structure of 1100kV UHVDC wall bushing and its key technical parameters are designed according to work conditions. Insulation structure and electric field of key bushing parts are simulated by ANSYS11.0. And the solution is optimized by SubProblem method based on the DC field theory. The result indicated that the parameters of designed solution could meet the needs of 1100kV UHVDC power transmission project.

Perfect Conductor and Impedance Boundary Condition Corrections via a Finite Element Subproblem Method

A finite element subproblem method is developed to correct the inaccuracies proper to perfect conductor and impedance boundary condition models, particularly near edges and corners of the conductors, for a large range of conductivities and frequencies. Successive local corrections, supported by fine local meshes, can be obtained from each model to a more accurate one, allowing efficient extensions of their domains of validity.

Hybrid Sampling/Spectral Method for Solving Stochastic Coupled Problems

In this paper, we present a hybrid method that combines Monte Carlo sampling and spectral methods for solving stochastic coupled problems. After partitioning the stochastic coupled problem into subsidiary subproblems, the proposed hybrid method entails iterating between these subproblems in a way that enables the use of the Monte Carlo sampling method for subproblems that depend on a very large number of uncertain parameters and the use of spectral methods for subproblems that depend on only a small or moderate number of uncertain parameters. To facilitate communication between the subproblems, the proposed hybrid method shares between the subproblems a reference representation of all the solution random variables in the form of an ensemble of samples; for each subproblem solved by a spectral method, it uses a dimension-reduction technique to transform this reference representation into a subproblem-specific reduced-dimensional representation to facilitate a computationally efficient solution in a reduced...

최적화 해석기법을 이용한 샌드위치 복합재와 알루미늄 압출재 하이브리드 모듈화 차체구조물의 경량 설계 연구

본 논문은 위상최적화와 치수최적화 해석기법을 이용한 샌드위치 복합재와 알루미늄 압출재로 구성되는 하이브리드 철도차량 차체 구조물의 경량 모듈화 설계에 관한 연구이다. 위상최적설계는 초기설계단계에 차체 구조물의 최적의 재료적용부위를 선정하기 위해 사용되었으며, 치수최적화설계는 하이브리드 차체 구조물의 최적 설계 변수를 찾기 위해 사용되었다. 이때, 최적화해석은 일계법과 부분문제근사법을 사용하였다. 위상최적설계해석을 통해 차체 구조물의 강성 및 제작성을 향상시키기 위한 언더프레임, 로우 사이드 패널 모듈에 1차 부재인 알루미늄 압출재의 적용이 적절하고, 샌드위치 복합재는 무게를 최소화하기 위한 2차 부재로서 루프 및 미들 사이드 패널 모듈에 적용이 적합하다는 결론을 얻었다. 또한, 알루미늄 압출재와 샌드위치 복합재로 구성되는 하이브리드 차체 구조물의 무게는 샌드위치 복합재로만 만들어진 차체 구조물과 비교하여 최대 17.7%까지의 경량화 효과를 얻을 수 있음을 확인하였다.

A Finite Element Subproblem Method for Position Change Conductor Systems

Analyses of magnetic systems with position changes of both massive and stranded conductors are performed via a finite element subproblem method. A complete problem is split into subproblems associated with each conductor and the magnetic regions. Each complete solution is then expressed as the sum of subproblem solutions supported by different meshes. The subproblem procedure simplifies both meshing and solving processes, with no need of remeshing, and accurately quantifies the effect of the position changes of conductors on both local fields, e.g., skin and proximity effects, and global quantities, e.g., inductances and forces. Applications covering parameterized analyses on conductor positions to moving conductor systems can benefit from the developed approach.

A study on size optimization of rocket motor case using the modified 2D axisymmetric finite element model

In this study, we evaluated the structural integrity and weight of a rocket motor with a torispherical dome by size optimal design. Size optimal design was achieved by first-order and sub-problem methods, using the Ansys Parametric Design Language (APDL). For rapid design verification, a modified 2D axisymmetric finite-element model was used, and the bolt pre-tension load was expressed as function of the ratio of the cross-sectional area. The thickness of the dome and the cylindrical part of the rocket motor were selected as the design parameters. Our results showed that the weight and structural integrity of the rocket motor at the initial design stage could be determined more rapidly and accurately with the modified 2D axisymmetric finite-element model than with the 3D finite-element model. Further, the weight of the rocket motor could be saved to maximum of 17.6% within safety limit.