Constant Geometry Research Articles

Acceleration of 3D pin-by-pin calculations based on the heterogeneous variational nodal method

The pin-by-pin method with homogenization performed at the pin cell level is of considerable interest in thermal reactor physics calculations. However, significant computational costs are required in pin-by-pin calculations due to the fine spatial meshes. To resolve this issue, we present in this paper the three-dimensional (3D) heterogeneous variational nodal method (VNM), along with dedicated acceleration methods. The combined methods can be utilized to perform pin-by-pin diffusion calculations more efficiently. 3D response matrix (RM) equations are formulated, allowing for incorporation of multiple pin cells into one coarse node without altering the original pin cell configuration. Within the nodes, finite elements in the x-y plane and orthogonal polynomials in the axial direction are employed to describe the piecewise constant heterogeneous geometry. On the nodal interfaces, orthogonal polynomials in the x-y interfaces and piecewise constants in the axial interfaces are adopted to approximate neutron current distributions. The resulting RM equations are solved by the standard Red-Black Gauss-Seidel (RBGS) iteration. Matrix reordering (MR) acceleration and parallelization tailored to the RM formation are incorporated. The coarse nodes acceleration (CNA) is investigated by combining homogenized pin cell nodes into larger heterogeneous nodes. A series of meshing schemes are examined with a small modular reactor core problem. Results show that the implementation of MR and parallelization effectively reduces the RM formation time. Besides, with sufficient radial interface expansion order, CNA is able to reproduce the results obtained with fine node calculations. Furthermore, it is demonstrated that judicious choice of coarse nodes substantially accelerate the RBGS iteration. The combined acceleration schemes achieve favorable accuracy-efficiency trade-off.

Impact of near-surface fault geometry on secular slip rate assessment derived from uplifted river terraces: implications for convergence accommodation across the frontal thrust in southern Central Bhutan

Vertical velocities obtained from uplifted river terrace dating near mountain fronts are commonly converted into overthrusting slip rates assuming simple geometry of the fault at depth. However, the lack of information on the dip angle of these shallow structures can lead to misinterpretation in the accommodation of convergence, and thus to erroneous conclusions on the transfer of shortening to the emergent thrust faults. Here, to assess the impact of fault geometry, we focus on the eastern Himalayan region in the south Central Bhutan, where the topographic frontal thrust (TFT) has been already documented by GPS, paleoseismic, geomorphic and geological studies. This study is based on high-resolution near-surface geophysical investigations, including electrical resistivity, seismic and gravity measurements. Using a similar stochastic inversion approach for all data sets, new quantitative constraints on both fault geometry and petrophysical parameters are obtained to image shallow depths, in the upper ca. 80 m. The combined results from both surface observations and geophysical measurement provide a TFT geometry that is dipping northwards with a shallow angle at the top (0–5 m), steeply dipping in the middle (5–40 m) and flattening at deeper depths (>40 m). Together, our new constraints on the fault geometry allow us to estimate a minimum overthrusting slip rate of 10 ± 2 mm yr−1, which is only a part of the ca. 17 mm yr−1 GPS convergence. This suggests that, in the study area, significant deformation partitioning on several faults including TFT and the Main Boundary Thrust cannot be ruled out. More importantly, assuming constant slip rate, the obtained dip angle variations lead to uplift rate changes with distance to the TFT. This underlines that taking into account uplift rate from terrace dating only at the front location and assuming a constant dip angle fault geometry based on surface observations may significantly bias the slip rate estimates.

Design and evaluation of ZMesh topology for on-chip interconnection networks

This article presents the design and evaluation of a scalable and energy efficient Network-on-Chip topology with diagonal links, called ZMesh. A heuristic technique for mapping applications onto the ZMesh topology has been proposed. Further, a mapping technique based on particle swarm optimization combined with simulated annealing has also been considered for a fair comparison of the performance of ZMesh with that of other topologies. Experimental evaluation shows that ZMesh when compared with baseline Mesh, shows an average improvement of up to 1.25× and 1.20× in energy consumption and execution time, respectively while running real application traces. Compared to the state-of-the-art topologies such as DMesh, ZMesh shows an average improvement of up to 2.39× in terms of energy consumption, while suffering a degradation of up to 9.37% in execution time, for running real application traces. For the synthetic as well as real applications with more uniform traffic pattern, such as constant geometry algorithms, ZMesh achieves better energy efficiency than the other considered topologies. Evaluation of ZMesh for multicast kind of traffic using a proposed multicast routing algorithm shows improvement in link energy consumption by up to 55%, for the considered scenarios, as compared to unicast-based multicast routing.

Acceleration of within group iteration for pin-by-pin calculations

In thermal reactor physics fine mesh neutron diffusion calculations in which homogenization is only at the pin cell level are of considerable interest. However, the slow convergence of iterations on fine-mesh spatial grids limits their applicability to practical problems. We present here an efficient way to accelerate the within-group iterations for pin-by-pin calculations based on a two-dimensional heterogeneous variational nodal method (VNM). Response matrix (RM) equations are formulated that incorporate multiple pins within each node. Within the nodes, finite elements in the x-y plane are employed to describe the piecewise constant heterogeneous geometry. On the nodal interfaces orthogonal polynomials are employed to approximate current distributions. The RM equations are solved using the Red-Black Gauss-Seidel (RBGS) iteration. Investigations on the coarse nodes acceleration (CNA) by combining homogenized pin cell nodes into larger heterogeneous nodes are performed. A series of meshing schemes are examined with a 2D small modular reactor core problem. With sufficient interface expansion order, CNA do not cause significant errors to either eigenvalues or fission rate distributions compared with fine mesh calculations. It is demonstrated that CNA accelerate the RBGS iteration significantly and achieves favorable accuracy-efficiency trade-off.

Experimental investigation of work hardening, residual stress and microstructure during machining Inconel 718

The influence of high-speed machining under different cutting conditions with different tool materials on microstructure, residual stresses and work hardening of Inconel 718 super alloy has been investigated. The cutting/turning was performed using three different tool materials namely carbide, ceramic, and cBN with constant tool geometry under three different cutting environments such as dry machining, minimum quantity lubrication, and flood cooling cutting condition. Subsurface micro-structural changes, grain refinement, and deformation were observed by using CARL ZIESS optical microscope having 50 X to 1500 X magnification, equipped with Clemex vision professional edition image analysis software. The nature induced residual stresses were measured and analysed using X-ray diffraction technique. Micro-hardness on surface and subsurface was measured by using Vickers micro-hardness tester. An attempt has been made to understand the correlation between work hardening, residual stresses and microstructural alteration.

A diatom record of CO2 decline since the late Miocene

Extratropical sea surface temperature records from alkenones record a dramatic cooling of up to 17 °C over the last ∼14 Ma, but the relationship between this cooling and greenhouse gas forcing has been elusive due to sparse and contrasting reconstructions of atmospheric CO2 for the time period. Alkenone carbon isotopic fractionation during photosynthesis has previously been used to estimate changes in pCO2 over this interval, but is complicated by significant changes in cell size of the alkenone-producing coccolithophorids over this time period. In this study, we reconstruct carbon isotopic fractionation during photosynthesis (εp) using organic compounds trapped within the frustules of pennate diatoms in sediments from the Eastern Equatorial Pacific Ocean at Ocean Drilling Program Site 846 over the last ∼13 Ma. Physical separation of pennate diatoms prior to measuring carbon isotopic fractionation enables us to obtain a record with constant cell geometry, eliminating this factor of uncertainty in our pCO2 reconstruction. In the past ∼11 Ma, εp declines from 15.5 to 10.3‰. Using the classic diffusive model and taking into account variations in opal content, alkenone concentration and coccolith Sr/Ca as indicators of past productivity and growth rate, and sea surface temperature records from the site, we estimate a decline in pCO2 from 454 (+/−41) to 250 (+/−15) ppmv between ∼11 and 6 Ma. Models accounting for changing the significance of active carbon uptake for photosynthesis, which likely produce more accurate CO2 estimates, suggest a significant larger pCO2 decline of up to twice that shown by the classic diffusive model (in average from 794 (+/−233) ppmv at ∼11 Ma to 288 (+/−25) ppmv at ∼6 Ma, considering growth rates varying between 0.5 and 1.7 day−1). Large uncertainties in the pCO2 estimated between ∼8 and 11 Ma using the active uptake model are related to the growth rate used for calculations. Together, these results suggest CO2 forcing for this period of steep decline in temperatures.

Duality structures and discrete conformal variations of piecewise constant curvature surfaces

A piecewise constant curvature manifold is a triangulated manifold that is assigned a geometry by specifying lengths of edges and stipulating the simplex has an isometric embedding into a constant curvature background geometry (Euclidean, hyperbolic, or spherical) with the specified edge lengths. Additional geometric structure leads to a notion of discrete conformal structure, generalizing circle packings and their generalizations as studied by Thurston and others. We analyze discrete conformal variations of piecewise constant curvature 2-manifolds, giving particular attention to the variation of angles. Formulas are derived for the derivatives of angles in each background geometry, which yield formulas for the derivatives of curvatures and to curvature functionals. Finally, we provide a complete classification of possible definitions of discrete conformal structures in each of the background geometries.

UAV CAMERAS: OVERVIEW AND GEOMETRIC CALIBRATION BENCHMARK

Abstract. Different UAV platforms and sensors are used in mapping already, many of them equipped with (sometimes) modified cameras as known from the consumer market. Even though these systems normally fulfil their requested mapping accuracy, the question arises, which system performs best? This asks for a benchmark, to check selected UAV based camera systems in well-defined, reproducible environments. Such benchmark is tried within this work here. Nine different cameras used on UAV platforms, representing typical camera classes, are considered. The focus is laid on the geometry here, which is tightly linked to the process of geometrical calibration of the system. In most applications the calibration is performed in-situ, i.e. calibration parameters are obtained as part of the project data itself. This is often motivated because consumer cameras do not keep constant geometry, thus, cannot be seen as metric cameras. Still, some of the commercial systems are quite stable over time, as it was proven from repeated (terrestrial) calibrations runs. Already (pre-)calibrated systems may offer advantages, especially when the block geometry of the project does not allow for a stable and sufficient in-situ calibration. Especially for such scenario close to metric UAV cameras may have advantages. Empirical airborne test flights in a calibration field have shown how block geometry influences the estimated calibration parameters and how consistent the parameters from lab calibration can be reproduced.

Tool Wear Assessment During Machining of Inconel 718

Machining of superalloy Inconel 718 would have established some issues like, inability of the tool materials to sustain for a longer duration due to the work hardening effect and very high cutting forces causes metallurgical damage on the work pieces. This research paper focuses on the tool life issues of different tool materials associated with the turning of Inconel 718 under different cutting conditions. Further, it is significant to identify the parameters that cause the machining characteristics, in particular the flank wear and to understand the relationship they have with the different controllable parameters. Turning experiments on Inconel – 718 were investigated under different cutting conditions using three controllable parameters namely feed rate, cutting speed and depth of cut. Three different cutting tools such as PVD TiAlN coated carbide inserts, Al2O3 – TiC Ceramic and cBN inserts with constant tool geometry were used for all experimental trials. The flank wear occurred on the inserts during every trail are measured and recorded using CARL ZIESS Optical Microscope having 50 X to 1500 X magnification, equipped with Clemex Vision Professional Edition Image Analysis Software. Scanning Electron Microscope (SEM) observations were made to understand the wear pattern encountered by different tool materials. Analysis of Variance (ANOVA) was performed to understand the percentage influence of all the cutting parameters on the flank wear.

Influence of Pleat Deformation on Pressure Drop for a High-Efficiency Particulate Air Filter: A Small-Scale Experimental Approach

For industrial or domestic applications, the wide range of use of pleated filters makes the understanding of their airflow behavior a major issue for designer and users. In all industrial installations dealing with radioactive matter, the containment of pollutants must be ensured. High-efficiency particulate air (HEPA) filters are used as the last purification stage before the air is rejected in the environment. These filters can be used either alone, in the case of nonsensible installation, or coupled with other filtration devices disposed before it where contamination level could be important. The prediction of their pressure drop is very important in nuclear safety to be able to anticipate any dysfunction or rupture of these devices. It has been observed that geometry of the medium has an influence on the pressure drop of a pleated filter. In the case of HEPA filters, no convincing explanation has been brought to explain their airflow behavior. The pressure drop evolution of the filter during the clogging remains difficult to explain by assuming constant pleat geometry. Some studies show that deformation occurs during the filter use, which could induce an increase of the available volume in the pleat and a reduction of the efficient filtration surface. The increase in computation capacity introduces nowadays the possibility to perform complex simulation, taking into account the effect of fluids on sensible devices. This can be the case for simple structural analysis or for more complex analysis such as vibration induced by gas or fluid flow. It is mostly applied to avoid breaking or deformation of safety devices, and this can also be applied to anticipate the fluid behavior of some special devices such as filters. In classical filtration application, properties of the filter are coupled with particle deposition (e.g., changes in geometry and permeability depend on the thickness of the deposit). The studies concerning mechanical properties of filters are mainly performed for liquid filtration and clean filters. For pleated filters, the complexity of this kind of analysis remains the modification of the link between geometry, pressure drop, mechanical strength, and particle transport and accumulation inside the pleat. As a first approach, it has been chosen to combine an experimental and a numerical approach to improve the understanding of filter behavior. In this paper, the pleat deformation will be investigated using a direct nonintrusive laser measurement performed on a single pleat experiment. The rate of filtration surface lost will be estimated using these data and taken into account to evaluate the pressure drop against the filtration velocity. Results obtained show that the pleat deformation is an important parameter, which influences the geometry of the pleat.

Probabilistic biomechanical finite element simulations: whole-model classical hypothesis testing based on upcrossing geometry

Statistical analyses of biomechanical finite element (FE) simulations are frequently conducted on scalar metrics extracted from anatomically homologous regions, like maximum von Mises stresses from demarcated bone areas. The advantages of this approach are numerical tabulability and statistical simplicity, but disadvantages include region demarcation subjectivity, spatial resolution reduction, and results interpretation complexity when attempting to mentally map tabulated results to original anatomy. This study proposes a method which abandons the two aforementioned advantages to overcome these three limitations. The method is inspired by parametric random field theory (RFT), but instead uses a non-parametric analogue to RFT which permits flexible model-wide statistical analyses through non-parametrically constructed probability densities regarding volumetric upcrossing geometry. We illustrate method fundamentals using basic 1D and 2D models, then use a public model of hip cartilage compression to highlight how the concepts can extend to practical biomechanical modeling. The ultimate whole-volume results are easy to interpret, and for constant model geometry the method is simple to implement. Moreover, our analyses demonstrate that the method can yield biomechanical insights which are difficult to infer from single simulations or tabulated multi-simulation results. Generalizability to non-constant geometry including subject-specific anatomy is discussed.

Stable propagation of mechanical signals in soft media using stored elastic energy

Soft structures with rationally designed architectures capable of large, nonlinear deformation present opportunities for unprecedented, highly tunable devices and machines. However, the highly dissipative nature of soft materials intrinsically limits or prevents certain functions, such as the propagation of mechanical signals. Here we present an architected soft system composed of elastomeric bistable beam elements connected by elastomeric linear springs. The dissipative nature of the polymer readily damps linear waves, preventing propagation of any mechanical signal beyond a short distance, as expected. However, the unique architecture of the system enables propagation of stable, nonlinear solitary transition waves with constant, controllable velocity and pulse geometry over arbitrary distances. Because the high damping of the material removes all other linear, small-amplitude excitations, the desired pulse propagates with high fidelity and controllability. This phenomenon can be used to control signals, as demonstrated by the design of soft mechanical diodes and logic gates.

Influence of relative permeability on injection pressure and plume configuration during CO2 injections in a mafic reservoir

Carbon capture and sequestration projects have traditionally targeted deep sedimentary basins; however, mafic reservoirs may also be attractive targets for CO2 disposal on the basis of permanent mineral trapping over relatively short time scales (101 to 102yr). Nevertheless, CCS development in mafic reservoirs is hampered by substantial uncertainty in fracture-controlled reservoir characteristics, particularly with respect to the effects of multi-phase fluid flow, e.g., relative permeability and capillary pressure. The present study quantifies uncertainty surrounding relative permeability effects in a basalt reservoir by developing a numerical modeling experiment on the basis of site characterization data from the Slack Canyon #2 flow top, which is one of three flow tops comprising the injection zone at the Wallula Basalt Sequestration Pilot Project in southeast Washington State. This numerical modeling experiment controls for the effects of curvature in the relative permeability models by performing an ensemble of 399 CO2 injection simulations with constant geometry and reservoir properties, while systematically varying the phase interference parameter (λ) and residual CO2 saturation (Sgr), which govern wetting and non-wetting phase relative permeability, respectively. The relative permeability parameter space is defined by selecting combinations of λ and Sgr that cover a wide range of experimental laboratory measurements. For each simulation, CO2 is injected into the reservoir for 10 years at a constant rate of 2.78kgs−1 (87,856metrictons(MT)yr−1), which is 10% of the annual injection rate proposed for one injection scenario at the Wallula Site. Results from the ensemble of simulations show that relative permeability alone can account for >50MPa of variability in the injection pressure and a two-fold difference in lateral CO2 plume migration. Additionally, this work shows that curvature in the wetting phase relative permeability model is the stronger influence on reservoir pressure accumulation, while curvature in the non-wetting phase relative permeability model strongly governs CO2 plume geometry.

Assessment of combined Noise-Air quality and combined exposure to Noise-Air pollution at the curbside open-air microenvironment of Kolkata city, India

A four year long research programme divided into four phases has been designed for the first time to assess the combined Noise-Air quality and combined exposure to Noise-Air pollution at the curbside open-air microenvironment of Kolkata city, India. The results and the findings of the different phases of study had already been published. The objective of the review work is to fuse the findings of the different phases of studies; to identify the factor(s) influences the degree of correlation between concentration of the air pollutant(s) and traffic noise level at the microenvironment of the city. Incidence of moderate to very strong positive Pearson’s correlation coefficients between concentration of the air pollutant(s) and traffic noise level indicated chances of correlated exposure to these environmental stressors at the microenvironment of the city. Average combined Noise-Air quality and combined exposure to Noise-Air pollution of the microenvironment of the city was very poor (0.17) to fair (0.50) and poor (-0.06) to excellent (3.33) respectively. The best combined Noise-Air quality and the best level of combined exposure to Noise-Air pollution at the microenvironment of the city was prominently evidenced in after-noon, in summer and under variable road geometry. However, the worst combined Noise-Air quality and the worst level of combined exposure to Noise-Air pollution at the microenvironment of the city was prominently evidenced in evening, in winter and under constant road geometry. A principal component analysis revealed that intensity of wind determines the degree of correlation between the environmental stressors at the microenvironment.

Deformation inside a paleosubduction channel – Insights from microstructures and crystallographic preferred orientations of eclogites and metasediments from the Tauern Window, Austria

The Eclogite Zone, of the Tauern Window is an exhumed subduction channel comprising eclogites with different grades of retrogression in a matrix of high-pressure metasediments. The rocks were exposed to 600 °C and 20–25 kbars, and then retrogressed during their exhumation, first under blueschist facies and later under amphibolite facies metamorphism. To gain insights into the deformation within the subduction channel during subduction and exhumation, both fresh and retrogressed eclogites, as well as the surrounding metasediments were investigated with respect to their deformation microstructures and crystallographic preferred orientations (CPOs). Pristine and retrogressed eclogites show grain boundary migration and subgrain rotation recrystallization microstructures in omphacite. A misorientation axes analysis reveals the activity of complementary deformation mechanisms including grain boundary sliding and dislocation creep. The omphacite CPOs of the eclogites correspond to dominant SL-fabrics characteristic of plane strain deformation, though there are local variations towards flattening or constriction within the paleosubduction channel. The glaucophane CPOs in retrogressed eclogites match those of omphacite, suggesting that a constant strain geometry persisted during exhumation at blueschist facies conditions. Plastic deformation of the host high-pressure metasediments outlasted that of the eclogites, as indicated by white mica fabrics and quartz CPO. The latter is consistently asymmetric, pointing to the operation of non-coaxial deformation. The microstructures and CPO data indicate a continuous plastic deformation cycle with eclogite and blueschist facies metamorphism related to subduction and exhumation of the different rock units.

Modelling reactive diffusion in clays with two-phase-informed pore networks

Development of pore network models for reactive diffusion of various species in clays is presented. Networks are constructed using experimentally measured pore-space and solid-phase characteristics. This way incomplete experimental information for the topological (pore connectivity) and the geometrical (inter-pore distances) properties of a given pore system can be balanced by known solid-phase properties. Opalinus Clay (OPA) is selected to demonstrate the application and validate the proposed model. OPA is modelled as anisotropic porous medium, reflecting preferential orientation of meso-porosity along clay bedding direction. Bulk diffusivities of various species (HTO, Cl− and I−) are calculated to investigate the effects of pore structure, anion exclusion and adsorption. Adsorption is simulated by changing the pore space, which is more realistic compared to existing reactive transport models with assumed constant pore geometry. Anion exclusion effects are simulated by introducing diffuse double layer (DDL) in the model. Results agree well with experimentally measured diffusion coefficients for transport parallel and perpendicular to the bedding direction. The proposed model is applicable to a large class of geo-materials and suitable for linking to lattice models for deformation and damage.

Variable width based stepped MEMS cantilevers for micro or pico level biosensing and effective switching

High performance and sensitivity of a microcantilever beam is much demanded in biosensing and needs accurate measurement of tip deflection under very low range of analyte adhesion. Constant geometry based rectangular microcantilevers are not good enough for micro or pico level triglyceride (TG) and glucose detection. With the same surface area, length and thickness, the proposed variable width based stepped microcantilever beams exhibit nearly twice or thrice more tip deflection corresponding to the same TG and glucose molecular pressure. With the less pull-in voltage requirement, such proposed stepped microcantilever beam based switches can be utilized in RF reconfigurable antenna for altering its operating frequency and radiation properties. Several configurations of proposed microcantilevers have been studied and analyzed for finding the optimal design with better deflection sensitivity. This paper also encompasses the mathematical modeling of proposed single and double stepped microcantilever beam, which exhibits good agreement with the simulation.

Reconfigurable data parallel constant geometry fast Fourier transform architectures on Network-on-Chip

This paper reports the design and development of reconfigurable (up to 8192-point), data parallel, constant geometry fast Fourier transform (CG-FFT) architectures based on Network-on-Chip (NoC) paradigm. Twiddle factor multiplications have been realized using pipelined CORDIC rotators in the proposed architecture in order to ensure its high throughput. Mapping of FFT functions to cores has been done by considering the proposed signal flow graph (SFG) for CG-FFT architecture, which helps in optimizing the design of network components (routers and network interfaces) and reducing the latency of FFT computation. The proposed input-size aware architecture can withstand faults in other processing elements (PEs) as it can accomplish the entire FFT computation using only one PE as well. When mapped onto mesh based NoC, the proposed architectures could achieve reduction in latency by 5×, compared to several existing FFT architectures on NoC. Hardware realization of the PE and the network components of the proposed architectures have been done using Xilinx Kintex-7 family field-programmable gate array (FPGA) device. The maximum operating frequency of a PE in the proposed architecture has been found to be 184.010 MHz, which meets the timing specifications of several application standards, such as DVB-T/H, DAB, 802.11a/n and UWB. In addition to the FPGA-prototype, the proposed architectures have also been synthesized in ASIC design flow to obtain area and power results.

Axisymmetric flow over a backward‐facing step in an annular pipe

AbstractThe incompressible flow of a Newtonian fluid over a backward‐facing step is investigated numerically. The geometry is an annular pipe in which the radius of the inner cylinder decreases suddenly. Keeping the radial expansion ratio fixed axisymmetric flows are computed for outlet radius ratios from 0.1 to 1 (ratio of the inner to the outer outlet radius). The Reynolds number at which the flow separates from the outer cylinder decreases as the outlet radius ratio decreases for constant inlet geometry. The growth with Reynolds number of the recirculation zone on the inner outlet cylinder just behind the step is strongly reduced when the recirculation zone on the outer cylinder is established. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Study on reducing edge effects by using assistant force in laser forming

The laser forming process, in which a bending deformation of a metal plate is produced by nonuniform thermal stress coming from nonlinear laser-heating cycles, is a promising technology for the rapid production of metallic shaping components. In laser forming, except for the desirable bending deformation, the bending angle varies along the laser-heating line. This undesirable deformation, or edge effect, exists because the forming process is asymmetrical, which leads to the forming accuracy failing to reach the design requirement. To reduce the edge effect, a method with various assistant forces is proposed and the effects of these different forces on forming accuracy have been studied. The results show that the forming accuracy can be improved under the action of two unequal concentrated forces. The relative variation of the value of the bending angle decreases by about 80% compared with that of the pure laser forming when the proper external forces are chosen. The laser process parameters also play an important role in the bending angle variations under constant geometry, material, and assistant forces. The final shapes of a forming part may be controlled to a desirable accuracy by selecting the proper assistant forces and process parameters.