Infiltration,runoff,and slope stability behaviors of infinite slope with macropores based on an improved Green–Ampt model

Infiltration–runoff–slope instability mechanism of macropore slope under heavy rainfall is unclear.This paper studied its instability mechanism with an improved Green–Ampt(GA)model considering the dual-porosity(i.e.,matrix and macropore)and ponding condition,and proposed the infiltration equations,infiltration–runoff coupled model,and safety factor calculation method.Results show that the infiltration processes of macropore slope can be divided into three stages,and the proposed model is rational by a comparative analysis.The wetting front depth of the traditional unsaturated slope is 17.2%larger than that of the macropore slope in the early rainfall stage and 27%smaller than that of the macropore slope in the late rainfall stage.Then,macropores benefit the slope stability in the early rainfall but not in the latter.Macropore flow does not occur initially but becomes pronounced with increasing rainfall duration.The equal depth of the wetting front in the two domains is regarded as the onset criteria of macropore flow.Parameter analysis shows that macropore flow is delayed by increasing proportion of macropore domain(ω_(f)),whereas promoted by increasing ratio of saturated permeability coefficients between the two domains(μ).The increasing trend of ponding depth is sharp at first and then grows slowly.Finally,when rainfall duration is less than 3 h,ωf andμhave no significant effect on the safety factor,whereas it decreases with increasingωf and increases with increasingμunder longer duration(≥3 h).With the increase ofω_(f),the slope maximum instability time advances by 10.5 h,and with the increase ofμ,the slope maximum instability time delays by 3.1 h.

A Subdivision-Based Combined Shape and Topology Optimization in Acoustics

We propose a combined shape and topology optimization approach in this research for 3D acoustics by using the isogeometric boundary element method with subdivision surfaces.The existing structural optimization methods mainly contain shape and topology schemes,with the former changing the surface geometric profile of the structure and the latter changing thematerial distribution topology or hole topology of the structure.In the present acoustic performance optimization,the coordinates of the control points in the subdivision surfaces fine mesh are selected as the shape design parameters of the structure,the artificial density of the sound absorbing material covered on the structure surface is set as the topology design parameter,and the combined topology and shape optimization approach is established through the sound field analysis of the subdivision surfaces boundary element method as a bridge.The topology and shape sensitivities of the approach are calculated using the adjoint variable method,which ensures the efficiency of the optimization.The geometric jaggedness and material distribution discontinuities that appear in the optimization process are overcome to a certain degree by the multiresolution method and solid isotropic material with penalization.Numerical examples are given to validate the effectiveness of the presented optimization approach.

A Deep Learning Approach to Shape Optimization Problems for Flexoelectric Materials Using the Isogeometric Finite Element Method

A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization problems.To improve the fitting ability of the neural network,we use the idea of pre-training to determine the structure of the neural network and combine different optimizers for training.The isogeometric analysis-finite element method(IGA-FEM)is used to discretize the flexural theoretical formulas and obtain samples,which helps ANN to build a proxy model from the model shape to the target value.The effectiveness of the proposed method is verified through two numerical examples of parameter optimization and one numerical example of shape optimization.

Machine Learning Enhanced Boundary Element Method:Prediction of Gaussian Quadrature Points

This paper applies a machine learning technique to find a general and efficient numerical integration scheme for boundary element methods.A model based on the neural network multi-classification algorithmis constructed to find the minimum number of Gaussian quadrature points satisfying the given accuracy.The constructed model is trained by using a large amount of data calculated in the traditional boundary element method and the optimal network architecture is selected.The two-dimensional potential problem of a circular structure is tested and analyzed based on the determined model,and the accuracy of the model is about 90%.Finally,by incorporating the predicted Gaussian quadrature points into the boundary element analysis,we find that the numerical solution and the analytical solution are in good agreement,which verifies the robustness of the proposed method.

Subdivision Surface-Based Isogeometric Boundary Element Method for Steady Heat Conduction Problems with Variable Coefficient

The present work couples isogeometric analysis(IGA)and boundary element methods(BEM)for three dimensional steady heat conduction problems with variable coefficients.The Computer-Aided Design(CAD)geometries are built by subdivision surfaces,and meantime the basis functions of subdivision surfaces are employed to discretize the boundary integral equations for heat conduction analysis.Moreover,the radial integration method is adopted to transform the additional domain integrals caused by variable coefficients to the boundary integrals.Several numerical examples are provided to demonstrate the correctness and advantages of the proposed algorithm in the integration of CAD and numerical analysis.

Isogeometric Boundary Element Method for Two-Dimensional Steady-State Non-Homogeneous Heat Conduction Problem

The isogeometric boundary element technique(IGABEM)is presented in this study for steady-state inhomogeneous heat conduction analysis.The physical unknowns in the boundary integral formulations of the governing equations are discretized using non-uniform rational B-spline(NURBS)basis functions,which are utilized to build the geometry of the structures.To speed up the assessment of NURBS basis functions,the Bezier extraction´approach is used.To solve the extra domain integrals,we use a radial integration approach.The numerical examples show the potential of IGABEM for dimension reduction and smooth integration of CAD and numerical analysis.