Topology optimization of turbine disk considering maximum stress prediction and constraints

For the stress-constrained topology optimization of a turbine disk under centrifugal loads,the jagged boundaries of the mesh and the gray densities on the solid/void interfaces could make the calculated stress field inconsistent with the actual value.It may result in overestimating the maximum stress and thus affect the effectiveness of stress constraints.This paper proposes a new method for predicting the maximum stress to overcome the difficulty.In the process,a predicted density is newly defined to obtain stable boundaries with thin layers of gray elements,a transition factor is innovatively proposed to evaluate the effects of intermediate-density elements,two different stiffness penalty schemes are flexibly used to calculate the elastic modulus of elements,and a linear stress penalty is further adopted to relax the stress field of the structure.The proposed approach for predicting the maximum stress value is verified by the analysis of a structure with smooth boundaries and the topology optimization of a turbine disk.An updating scheme of the stress constraint in the topology optimization is also developed using the predicted maximum stress.Some key ingredients affecting the optimization results are discussed in detail.The results prove the effectiveness and efficacy of the proposed maximum stress prediction and developed stress constraint methods.

Microstructural image based convolutional neural networks for efficient prediction of full-field stress maps in short fiber polymer composites

The increased demand for superior materials has highlighted the need of investigating the mechanical properties of composites to achieve enhanced constitutive relationships.Fiber-reinforced polymer composites have emerged as an integral part of materials development with tailored mechanical properties.However,the complexity and heterogeneity of such composites make it considerably more challenging to have precise quantification of properties and attain an optimal design of structures through experimental and computational approaches.In order to avoid the complex,cumbersome,and labor-intensive experimental and numerical modeling approaches,a machine learning(ML)model is proposed here such that it takes the microstructural image as input with a different range of Young’s modulus of carbon fibers and neat epoxy,and obtains output as visualization of the stress component S11(principal stress in the x-direction).For obtaining the training data of the ML model,a short carbon fiberfilled specimen under quasi-static tension is modeled based on 2D Representative Area Element(RAE)using finite element analysis.The composite is inclusive of short carbon fibers with an aspect ratio of 7.5that are infilled in the epoxy systems at various random orientations and positions generated using the Simple Sequential Inhibition(SSI)process.The study reveals that the pix2pix deep learning Convolutional Neural Network(CNN)model is robust enough to predict the stress fields in the composite for a given arrangement of short fibers filled in epoxy over the specified range of Young’s modulus with high accuracy.The CNN model achieves a correlation score of about 0.999 and L2 norm of less than 0.005 for a majority of the samples in the design spectrum,indicating excellent prediction capability.In this paper,we have focused on the stage-wise chronological development of the CNN model with optimized performance for predicting the full-field stress maps of the fiber-reinforced composite specimens.The development of such a robust and efficient algorithm would significantly reduce the amount of time and cost required to study and design new composite materials through the elimination of numerical inputs by direct microstructural images.

PREDICTION OF FLOW STRESS OF HIGH-SPEED STEEL DURING HOT DEFORMATION BY USING BP ARTIFICIAL NEURAL NETWORK

The hot deformation behavior of TI (18W-4Cr-1V) high-speed steel was investigated by means of continuous compression tests performed on Gleeble 1500 thermomechan- ical simulator in a wide range of tempemtures (950℃-1150℃) with strain rotes of 0.001s-1-10s-1 and true strains of 0-0. 7. The flow stress at the above hot defor- mation conditions is predicted by using BP artificial neural network. The architecture of network includes there are three input parameters:strain rate,temperature T and true strain , and just one output parameter, the flow stress ,2 hidden layers are adopted, the first hidden layer includes 9 neurons and second 10 negroes. It has been verified that BP artificial neural network with 3-9-10-1 architecture can predict flow stress of high-speed steel during hot deformation very well. Compared with the prediction method of flow stress by using Zaped-Holloman parumeter and hyperbolic sine stress function, the prediction method by using BP artificial neurul network has higher efficiency and accuracy.

3D numerical simulation of heterogeneous in situ stress field in low-permeability reservoirs

Analysis of the in situ stress orientation and magnitude in the No.4 Structure of Nanpu Sag was performed on the basis of data obtained from borehole breakout and acoustic emission measurements.On the basis of mechanical experiments,logging interpretation,and seismic data,a 3 D geological model and heterogeneous rock mechanics field of the reservoir were constructed.Finite element simulation techniques were then used for the detailed prediction of the 3 D stress field.The results indicated that the maximum horizontal stress orientation in the study area was generally NEE-SWW trending,with significant changes in the in situ stress orientation within and between fault blocks.Along surfaces and profiles,stress magnitudes were discrete and the in situ stress belonged to theⅠa-type.Observed inter-strata differences were characterized as five different types of in situ stress profile.Faults were the most important factor causing large distributional differences in the stress field of reservoirs within the complex fault blocks.The next important influence on the stress field was the reservoir’s rock mechanics parameters,which impacted on the magnitudes of in situ stress magnitudes.This technique provided a theoretical basis for more efficient exploration and development of low-permeability reservoirs within complex fault blocks.

Predicting the present-day in situ stress distribution within the Yanchang Formation Chang 7 shale oil reservoir of Ordos Basin, central China

The Yanchang Formation Chang 7 oil-bearing layer of the Ordos Basin is important in China for producing shale oil.The present-day in situ stress state is of practical implications for the exploration and development of shale oil;however,few studies are focused on stress distributions within the Chang 7 reservoir.In this study,the present-day in situ stress distribution within the Chang 7 reservoir was predicted using the combined spring model based on well logs and measured stress data.The results indicate that stress magnitudes increase with burial depth within the Chang 7 reservoir.Overall,the horizontal maximum principal stress(SHmax),horizontal minimum principal stress(Shmin) and vertical stress(Sv) follow the relationship of Sv≥SHmax>Shmin,indicating a dominant normal faulting stress regime within the Chang 7 reservoir of Ordos Basin.Laterally,high stress values are mainly distributed in the northwestern parts of the studied region,while low stress values are found in the southeastern parts.Factors influencing stress distributions are also analyzed.Stress magnitudes within the Chang 7 reservoir show a positive linear relationship with burial depth.A larger value of Young's modulus results in higher stress magnitudes,and the differential horizontal stress becomes higher when the rock Young's modulus grows larger.

The environment shear stress field for the 1976 Tangshan earthquake sequence

The environment shear stress of Tangshan main earthquake and 38 great aftershocks have been calculated by the acceleration data of Tangshan earthquake sequence. The environment shear stress for 52 smaller aftershocks from July of 1982 to July of 1984 have also been calculated by use of the digital data of the Sino-American cooperation recorded by the instrumental arrays in Tangshan. The results represent that the environment shear stress τ0 values have a weak dependence on the seismic moment, only the small and moderate earthquakes will be able to occur in the region with smaller τ0 value and the large earthquakes are only in the region with greater τ0 value. The peak acceleration, velocity and displacement will be larger for the earthquakes occurred in the region with greater τ0 value, Therefore, the measurement of environment shear stress τ0 value for the significant region will play an important role in earthquske prediction and engineering shock-proof. The environment shear stress values for the great aftershocks occurred in the two ends of the main fault are often higher than that for the main shock. This case may represent the stress concentration in the two ends of the fault. This phenomenon provides the references for the place where the great aftershock will occur.