Submodeling Method Research Articles

Structural optimization design and numerical analysis of in-vessel magnetic compression coils

An FRC (field reversed configuration) device HUST-FRC (HFRC) is under construction at Huazhong University of Science and Technology, and the magnetic compression experiments will be investigated. 22 compression coils installed inside the metal vacuum chamber are designed with a peak current of about 110 kA rising within 50 μs. The coils are subjected to large electromagnetic forces during the compression process, which will challenge the structural stability of the coils. Therefore, it is necessary to estimate the structural stability of the compression coils during the compression progress. The compression process involves complex physical problems such as the coupling of circuit-electromagnetic-thermal-mechanical and non-linear contacts between adjacent coil components. It is also a challenge to calculate the coil current, electromagnetic load, and structure stress. To solve these problems, a joint analysis method is developed based on a two-dimensional (2-D) circuit-electromagnetic-thermal model and a three-dimensional (3-D) electromagnetic-mechanical model. The submodeling method is employed in mechanical simulations to improve the efficiency of coil optimization design. The electromagnetic and mechanical results confirm that the design of the compression coils is valid and feasible.

Evaluating the in Vitro Mechanical Responses of Stem Cell Under Fluid Perfusion in Different Porous Scaffolds

Abstract A suitable scaffold architecture is always desirable to get a favorable tissue response for bone tissue engineering. In this regard, a fluid-structure interaction analysis was carried out on different porous scaffolds to observe the in vitro mechanical responses due to fluid flow, followed by a submodeling method to obtain the cellular deformation and strain. Different types of scaffolds were designed based on different porosity and architecture. The cell was modelled with cytoplasm, nucleus, cell membrane, and cytoskeletons. The main objective of the study is to examine the variation of cellular responses due to different porosity and architecture of the scaffold. The results of this study highlight that permeability is higher in the case of gyroid structure and wall shear stress (WSS) is higher in the case of diamond structure. The permeability of all scaffolds increases with the increase of porosity. The opposite trend is shown in the case of WSS within scaffolds. The cell is showing higher deformation when it is placed on the front position of the scaffold towards the direction of fluid flow. This study will guide us in predicting an ideal scaffold for better cell growth.

The sloshing effects on the crack instability of the spherical tank under the simultaneous effect of internal pressure and earthquake

Spherical tanks have an important function in the industry due to the internal pressure of their contents. Also, the supporting structure of the spherical tank controls stability and damage to the tank One of the damages that can lead to a critical situation is an unstable crack in the column-vessel joint. In this study, the sloshing effects on the instability of 10 mm and 20 mm long semi-elliptical cracks with three aspect ratios in the connection zones of the supporting structure under the effect of internal pressure and eleven earthquakes have been investigated. Furthermore, using the finite element sub-modeling method around the crack area and part of the structure, the effect of fluid–structure interaction has been considered for three liquid levels to calculate the stress intensity factors along the crack front. Since the tank is under the simultaneous effect of internal pressure, earthquake, and sloshing motion, a three-dimensional mixed-mode stress intensity factor needed to be considered to study the crack instability. The results show that earthquakes and sloshing motions can have various effects on the equivalent stress intensity factors. For almost two-thirds of the studied cases, the equivalent stress intensity factor for the 50% filled vessel was 10%–70% greater than the 98% filled vessel. This finding shows that the crack located in the connection zones of the supporting structure under the simultaneous effect of internal pressure, earthquake, and sloshing motion, could lead to failure.

High-Dimensional Uncertainty Quantification in a Hybrid Data + Model-Based Submodeling Method for Refined Response Estimation at Critical Locations

AbstractThis study presents frameworks to build nonintrusive polynomial chaos expansion (PCE) models with regression and Smolyak sparse-grid quadrature to perform high-dimensional uncertainty propa...

Submodeling method to study the residual stress of TBCs near the interfacial asperity on a vane

Modeling the residual stress of TBCs near the interfacial asperity on turbine component tends to encounter numerical cumbersomeness ordinarily due to huge computational scale and complex mechanical behavior. This paper proposed a numerical method named submodeling method to simulate the local stress near the asperity by a partition model (named submodel) of a coated vane, based on the submodeling technique of ABAQUS code. First a global mechanical analysis about the coated vane was carried lasting three thermal cycles without considering interface asperities. Then a submodel was established with asperity and divided into three unique zones with proper mesh density according to their functions. Finally the local mechanical analysis was separately processed by submodeling method, based on interpolation of the solution from the global analysis onto the outer zone of the submodel. The results show that the stress level of TC near the asperity is relatively low after 3 thermal cycles. The normal stress and the shear stress of BC near the asperity are concentrated in the peak and nearby the trough, respectively. These stress concentrations may lead to TGO/BC interfacial crack. The stress values and distribution feature of BC near the asperity is quite agreement with former results. These may prove that submodeling method can be applicable for local stress modeling and failure prediction.

Hybrid data + model‐based submodeling method for a refined response estimation at critical locations

Hybrid data + model‐based submodeling method for a refined response estimation at critical locations

РАСЧЕТ ПЛОТНОСТИ ПОТОКА ТЕПЛОВЫХ НЕЙТРОНОВ В РАДИАЦИОННОЙ ЗАЩИТЕ ПО ПРОГРАММЕ FRIGATE С ПРИМЕНЕНИЕМ МЕТОДА СУБМОДЕЛИРОВАНИЯ

Using the example of calculating the thermal neutron flux density in an ionization chamber, where a methodically correct solution is required to be obtained only within a fragment of the computational model, and particle transport from the source to the studied region can be carried out in a more rough approximation, the use of DSN-DSN schemes discrete ordinate method on grids with a completely heterogeneous structure in combination with the submodeling method. The paper presents the results of calculating the thermal neutron flux density and the number of fission reactions in the sensitive part of an ionization chamber located in a concrete radiation protection shaft using the FRIGATE program (DSN method using the submodeling method) and cross-validation with the TDMCC program (Monte-Carlo method). The work continued the study, aimed at verifying the method of submodeling by spatial, angular, and energy variables, recommended for use in radiation protection calculations by deterministic codes. Cross-verification was performed using the FRIGATE DSN program and the TDMCC Monte Carlo code using the example of calculating the thermal neutron flux density and the number of fission reactions in the sensitive part of the fission ionization chamber. Verification results showed good agreement between the considered functionals (constant methodological discrepancy within 25 %). The obtained results confirm the effectiveness of using DSN programs in combination with irregular grids and the submodeling method in radiation protection calculations.

A boundary-condition-transfer method for shell-to-solid submodeling and its application in high-speed trains

The boundary-condition-transfer method for a shell-to-solid submodeling is fundamental for analyzing local or weak regions of a complex structure accurately. In this paper, a novel method is presented for transferring displacement boundaries based on hypothetical nodes. By considering the invariable volume of an element as a constraint, the interpolation through conventional methods using 6-degrees-of-freedom (DOFs) nodal translations and rotations is converted into a 3-DOF translational interpolation at the cut boundary of a submodel. To demonstrate this method, a radial basis function (RBF) was employed for interpolation. For validating the accuracy of the proposed method, a square plate with a hole under tensile and bending load were designed as examples. By considering global and local errors, three typical kernel functions with respect to mesh density ratios were analyzed to fix the optimal parameter in RBF. The examples showed that the proposed method significantly improves the accuracy in shell-to-solid submodeling problems compared to conventional solutions such as ANSYS. For structural analysis of a high-speed train car body under combined mechanical and aerodynamic loads, the submodeling method was implemented on the solid-element-based local model with a welding seam, with which a more detailed stress state was obtained compared with that computed by shell elements. The accurate and reliable results illustrate that the proposed method is the core for the global–local analysis of large complex structures, which also is used for the design and evaluation of the mechanical properties.

Coupled Thermo-Mechanical Analysis of 3D ICs Based on an Equivalent Modeling Methodology With Sub-Modeling

The coupled thermo-mechanical field analysis of three-dimensional (3D) stacked integrated circuits (ICs) is evaluated by an efficient and accurate simulation strategy that combines equivalent homogenization modeling methodology and sub-modeling technique. The thermal field is first investigated using the proposed approach, and based on which the structural field is also examined through the calculation of warpage. The utilization of sub-modeling method reveals the local temperature and warpage distributions, which is lost or ignored by the conventional homogenization method. To validate the proposed method, the simulation results of a five-layer stacked integrated circuits are compared against true 3D results of the detailed model, where the maximum deviation for temperature and warpage is as low as 1.62% and 4.89%, respectively, which are greatly improved compared to 8.23% and 7.83% using traditional homogenization method. In addition, the total computation time is reduced by 76.7% in contrast to true 3D finite element analysis (FEA) simulation. Furthermore, the impacts of through-silicon-via (TSV) geometries, underfill and μ -bump parameters on the temperature and warpage distributions are also studied to guide the design of 3D ICs with high performance and reliability.

Reliability of the Rubber Tube of Automotive Hydraulic Braking System Under Fatigue Failures Considering Random Variation of Load and the Process of Aging of Material

This paper presents the approach for the assessing of the operational reliability of a multi-layer thick-walled tube made of rubber with textile reinforcement. The analysis of the fatigue accumulation process is carried out within the framework of the concept of the continuum mechanics of damage. The mathematical model, which takes into account the accumulation of damages in case of a random spread of the strength characteristics of the material, as well as the process of stochastic aging for the elastomeric matrix of the composite and possible random variation of the workload has been developed. In this case, the aging process is modelled as a reduction of the endurance limit of the material. In this paper, the mean equivalent strains of the tube and their possible statistical variation in operation have been investigated on the basis of the finite element method. To solve the above problems, a submodeling method has been employed in this work. The probability of non-failure operation of the tube has been determined using the methods and models proposed. The influence of the rate of the aging process on the life-time of the tube has been estimated.

Application of Submodeling Technique in Numerical Modeling of Mechanized Tunnel Excavation

This research proposes a novel methodology of applying submodeling technique in the numerical simulation of mechanized tunnel excavation. A submodel is a smaller scale cut out of the full scale model (global model) in which the more in detail simulations along with higher degree of precision are conducted. Apparently, the submodel should include the near field around the TBM that is significantly affected by tunneling process and the region of interest such as ground surface where the model responses have to be surveyed. The appropriate size of the submodel is found by evaluation of the strain energy distribution in the domain while the energy gradient has to fulfill the predefined criterion. To analyze the submodel, the nodal displacements are derived from the global model and applied to the boundaries of the submodel. Using the proposed submodeling technique in the tunneling, the computational costs are reduced, while the submodel provides realistic prediction of the deformations in the system and lining forces. Finally, the proposed submodeling method is applied in both 2D and 3D tunneling simulations while two types of submodeling strategy (“fixed submodel” and “moving submodel”) are adopted for the 3D simulations. The results indicate that both approaches are adequate for predicting the lining forces and ground movements.

Numerical simulation of fatigue behavior for cable-stayed orthotropic steel deck bridges using mixed-dimensional coupling method

Effective methods and technologies in fatigue behavior and assessment for cable-stayed orthotropic steel deck bridges are critical to ensure their safety and serviceability. In this study, a mixed-dimensional finite element coupling method is used for structural fatigue assessment. A general framework of the Mix-dimensional Coupling (MDC) method is constructed on the basis of a compromise between simplicity and efficiency as compared to conventional sub-modeling or substructure method. Fatigue details and performance at welded joints have been investigated through the MDC method. Efficiency of the MDC method is demonstrated by a comparison with the simplified Bridge-deck-system (BDS) method. Besides the benefits of the saving time, the numerical simulation also indicated that the MDC method can effectively capture the global behavior for better fatigue prediction, that be ignored in the conventional BDS method as expected. Findings suggest that the MDC method is a cost-effective alternative for fatigue behavior and fatigue assessment of large-span orthotropic steel deck bridges.

Analysis of Ultimate Load-Bearing Capacity for Dowel Bar System in Rigid Pavement Based on XFEM

In order to analyze the premature damage of dowel bar system in jointed concrete pavement, the eXtended finite element method (short for XFEM) coupled with submodeling method were employed to simulate the fracture process of concrete around the dowel bar under loading. This coupling method is based on 3-D finite element analysis for the whole concrete pavement structure. The initialization and evolution of the cracks on the concrete had been monitored in model simulation. The results demonstrate that the XFEM coupled with submodeling method is an efficient and accurate method to calculate the ultimate bearing capacity of dowel bar. Furthermore, the critical axle load could be back-calculated based on the former analyzing results. This study is expected to provide a valuable numerical analysis method to simulate the fracture process in stresses concentration region of the concrete structure.

Analysis of Ultimate Load-Bearing Capacity for Dowel Bar System in Rigid Pavement Based on XFEM

In order to analyze the premature damage of dowel bar system in jointed concrete pavement, the eXtended finite element method (short for XFEM) coupled with submodeling method were employed to simulate the fracture process of concrete around the dowel bar under loading. This coupling method is based on 3-D finite element analysis for the whole concrete pavement structure. The initialization and evolution of the cracks on the concrete had been monitored in model simulation. The results demonstrate that the XFEM coupled with submodeling method is an efficient and accurate method to calculate the ultimate bearing capacity of dowel bar. Furthermore, the critical axle load could be back-calculated based on the former analyzing results. This study is expected to provide a valuable numerical analysis method to simulate the fracture process in stresses concentration region of the concrete structure.

서브모델링 기법을 이용한 철도차량 복합재 대차프레임의 금속재 체결부 볼트 위치 최적화 해석 연구

This paper describes the optimum design of bolt locations for metal joint parts of railway bogie frame made of glass fiber/epoxy 4-harness satin woven laminate composite and PVC foam core. The optimum design analysis was done by sub-problem approximation method using Ansys Parameter Design Language(APDL). The sub-modeling method was introduced to conduct the detailed recalculation for the only target parts and reduce calculating time. The structural analysis for composite bogie frame was performed according to JIS E 4207. The results showed that the optimum design analysis using sub-modeling method was able to obtain faster and more precise results than that of the entire model by the control of mesh size for the target parts, and the maximum Von-Mises stress has been reduced in comparison with its original dimensions due to the optimum design of bolt locations.

Accurate Stress Analysis on Steel Box Girder of Long Span Suspension Bridges Based on Multi-Scale Submodeling Method

The streamline flat steel box girder is broadly used in long span cable-supported bridges all over the world. As one of the most important part of the bridges, its stress level and distribution under various dynamic loads are especially concerned. However, it is difficult to obtain the accurate stress of the steel box girder by common finite element (FE) calculation. The Runyang Suspension Bridge (RSB) is taken as an example. To increase the accuracy of results, a 3-dimensional FE full model for the RSB is created by ANSYS and a spatial submodel of the steel box girder is particularly built with greater detail. Submodeling method is then employed as a connection technique to link different scale models. After the global analysis and connecting process, the local stress of the steel box girder under various vehicle loads is obtained by submodel analysis. The composite action between the full model and the submodel is analyzed, and the reasonable mesh size for the submodel is specially investigated. The numerical results are proved to be accurate by the field test results. This study demonstrates the reliability and efficiency of the submodeling method; and can provide references for accurately analyzing and designing the steel box girders of other long span bridges.

A finite element analysis of fretting fatigue crack growth behavior in Ti–6Al–4V

There is a need for methodology(ies) to analyze the crack growth behavior under fretting fatigue condition since its experimental determination is a challenging task. A finite element sub-modeling method was used to estimate the crack propagation life in titanium alloy, Ti–6Al–4V specimens. Two contact geometries, cylinder-on-flat and flat-on-flat, were analyzed. The computed crack propagation lives were combined with the results of an experimental study where total fatigue lives were measured. The combined numerical–experimental approach provided the crack initiation lives. The crack propagation life increased with increasing applied cyclic bulk stress in similar manner for both contact geometries. Almost 90% of the fretting fatigue life was spent during the crack nucleation and initiation phases in the high cycle fatigue regime. A parametric study was also conducted to investigate the effects of contact load, coefficient of friction and tangential force on the crack growth behavior. The crack propagation life decreased with increase of these three parameters. This decrease was similar for the contact load and the tangential force in both contact geometries, however, the decrease in the case of coefficient of friction was relatively more in the cylindrical pad than in the flat pad.

多層サブミクロン薄膜における界面コーナー部はく離発生条件の破壊力学的評価

This paper aims at the evaluation of crack initiation along the interface between sub-micron films. The stress singularity field in the vicinity of the edge due to the mismatch of deformations of films governs the crack initiation. Especially, a crack initiates at the corner point where singularity filed of stresses appears strongly, but it is not easy to clarify its mechanism because of the difficulty of controlling the crack initiation and the complication of the structure of the corner. In this paper, the specimen and loading system for interface cracking at the corner point are proposed and the interface strength between Si3N4 and Cu films in multi-layered films on the silicon substrate for an advanced LSI is measured. By using a three-dimensional finite element analysis with sub-modeling method, the stress singularity field in the vicinity of the corner of interface where the crack initiates is revealed. The interface strength of crack initiation can be measured on the basis of fracture mechanics concept and the criterion of mixed-mode interface fracture at the edge or corner is examined.

1115 多層サブミクロン膜のコーナー部からのはく離発生条件

The effect of three-dimensional structure on the interface strength at the edge point between submicron films was examined. The test was carried out for the test piece in which the effect of the three-dimensional shape appeared strongly for opening mode testing method. The interface cracking initiates at the point of the edge between Si_3N_4 and Cu films. By using sub-modeling method of FEM, the singularity field in the vicinity of the corner point is revealed. On the basis of fracture mechanics concept, the interface fracture toughness is determined. By the effect of the three-dimensional shape, the possibility in which the fracture mode changed was shown.