Comparison of perfectly matched layer and multi-transmitting formula artificial boundary condition based on hybrid finite element formulation

The theory of perfectly matched layer （PML） artificial boundary condition （ABC）, which is characterized by absorption any wave motions with arbitrary frequency and arbitrarily incident angle, is introduced. The construction process of PML boundary based on elastodynamic partial differential equation （PDE） system is developed. Combining with velocity-stress hybrid finite element formulation, the applicability of PML boundary is investigated and the numerical reflection of PML boundary is estimated. The reflectivity of PML and multi-transmitting formula （MTF） boundary is then compared based on body wave and surface wave simulations. The results show that although PML boundary yields some reflection, its absorption performance is superior to MTF boundary in the numerical simulations of near-fault wave propagation, especially in comer and large angle grazing incidence situations. The PML boundary does not arise any unstable phenomenon and the stability of PML boundary is better than MTF boundary in hybrid finite element method. For a specified problem and analysis tolerance, the computational efficiency of PML boundary is only a little lower than MTF boundary.

Differential quadrature time element method for structural dynamics

An accurate and efficient differential quadrature time element method （DQTEM） is proposed for solving ordi- nary differential equations （ODEs）, the numerical dissipation and dispersion of DQTEM is much smaller than that of the direct integration method of single/multi steps. Two methods of imposing initial conditions are given, which avoids the tediousness when derivative initial conditions are imposed, and the numerical comparisons indicate that the first method, in which the analog equations of initial displacements and velocities are used to directly replace the differential quadra- ture （DQ） analog equations of ODEs at the first and the last sampling points, respectively, is much more accurate than the second method, in which the DQ analog equations of initial conditions are used to directly replace the DQ analog equations of ODEs at the first two sampling points. On the contrary to the conventional step-by-step direct integration schemes, the solutions at all sampling points can be obtained simultaneously by DQTEM, and generally, one differential quadrature time element may be enough for the whole time domain. Extensive numerical comparisons validate the effi- ciency and accuracy of the proposed method.

An Artificial Neural Network-Based Response Surface Method for Reliability Analyses of c-φ Slopes with Spatially Variable Soil

This paper presents an artificial neural network（ANN）-based response surface method that can be used to predict the failure probability of c-φslopes with spatially variable soil.In this method,the Latin hypercube sampling technique is adopted to generate input datasets for establishing an ANN model;the random finite element method is then utilized to calculate the corresponding output datasets considering the spatial variability of soil properties;and finally,an ANN model is trained to construct the response surface of failure probability and obtain an approximate function that incorporates the relevant variables.The results of the illustrated example indicate that the proposed method provides credible and accurate estimations of failure probability.As a result,the obtained approximate function can be used as an alternative to the specific analysis process in c-φslope reliability analyses.

Modeling effects of alloying elements and heat treatment parameters on mechanical properties of hot die steel with back-propagation artificial neural network

Materials data deep-excavation is very important in materials genome exploration.In order to carry out materials data deep-excavation in hot die steels and obtain the relationships among alloying elements,heat treatment parameters and materials properties,a 11×12×12×4 back-propagation（BP）artificial neural network（ANN）was set up.Alloying element contents,quenching and tempering temperatures were selected as input;hardness,tensile and yield strength were set as output parameters.The ANN shows a high fitting precision.The effects of alloying elements and heat treatment parameters on the properties of hot die steel were studied using this model.The results indicate that high temperature hardness increases with increasing alloying element content of C,Si,Mo,W,Ni,V and Cr to a maximum value and decreases with further increase in alloying element content.The ANN also predicts that the high temperature hardness will decrease with increasing quenching temperature,and possess an optimal value with increasing tempering temperature.This model provides a new tool for novel hot die steel design.

Precise output loads control of load-diffusion components with topology optimization

The purpose of this paper is to present a novel topology optimization approach to control precisely the output loads under static loads and harmonic excitations.We introduce the Artificial Bar Element(ABE)at the designated output positions,where the output loads are equivalently measured and constrained with the nodal displacements of ABE.Optimization model is then formulated considering the output load constraints as well as the minimization of strain energy and dynamic displacement responses respectively under the static and dynamic conditions.The influences of the ABEs stiffness,different material usages of the design domain,widths of the output loads constraint intervals and variation ratios of output loads are discussed in detail.The proposed method is verified with several numerical examples with clear and reasonable load transfer paths.