A stable implicit nodal integration-based particle finite element method(N-PFEM)for modelling saturated soil dynamics

In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.

Structural Integrity Analysis of Containers Lost at Sea Using Finite Element Method

Unlike traditional transportation,container transportation is a relatively new logistics transportation mode.Shipping containers lost at sea have raised safety concerns.In this study,finite element analysis of containers subjected to hydrostatic pressure,using commercial software ANSYS APDL was performed.A computer model that can reasonably predict the state of an ISO cargo shipping container was developed.The von Mises stress distribution of the container was determined and the yield strength was adopted as the failure criterion.Numerical investigations showed that the conventional ship container cannot withstand hydrostatic pressure in deep water conditions.A strengthened container option was considered for the container to retain its structural integrity in water conditions.

Evaluation of mixed-mode stress intensity factors by extended finite element method

Extended finite element method （XFEM） implementation of the interaction integral methodology for evaluating the stress intensity factors （SIF） of the mixed-mode crack problem is presented. A discontinuous function and the near-tip asymptotic function are added to the classic finite element approximation to model the crack behavior. Two-state integral by the superposition of actual and auxiliary fields is derived to calculate the SIFs. Applications of the proposed technique to the inclined centre crack plate with inclined angle from 0° to 90° and slant edge crack plate with slant angle 45°, 67.5° and 90° are presented, and comparisons are made with closed form solutions. The results show that the proposed method is convenient, accurate and computationallv efficient.

SPACE-TIME FINITE ELEMENT METHOD FOR SCHRDINGER EQUATION AND ITS CONSERVATION

Energy conservation of nonlinear Schrodinger ordinary differential equation was proved through using continuous finite element methods of ordinary differential equation; Energy integration conservation was proved through using space-time continuous fully discrete finite element methods and the electron nearly conservation with higher order error was obtained through using time discontinuous only space continuous finite element methods of nonlinear Schrodinger partial equation. The numerical results are in accordance with the theory.

Research of the Higher-order Finite Element Arithmetic for Radiation Exchange

With the development of aeronautic and astronautic techniques, radiation becomes much more significant while the structure is exposed to the higher and higher temperature. Most of the current finite element software packages treat it using the net-radiation method or absorbed radiation method based on the assumption of isothermal surface with uniform radiation heat flux, which brings the conflict between the precision and the quantity of grids. Using integral method to compute the variable radiation heat flux in higher-order finite element, the precision can be improved greatly while using the same quantity of grids, because it is more consistent with the distribution of real temperature. In this paper, the integral is only processed on the same integral points as those used for solving the finite element equations, so it may be of high efficiency. In an academic testing model, the result is contrast to which get in ANSYS, proving the high precision of the method. Then an actual sandwich panel used in the thermal protection system is analyzed with the method, and the error is comparatively low to the analytical answer while the computation being of high efficiency.

EQUIVALENT BOUNDARY INTEGRAL EQUATIONS WITH INDIRECT UNKNOWNS FOR THIN ELASTIC PLATE BENDING THEORY

Equivalent Boundary Integral Equations (EBIE) with indirect unknowns for thin elastic plate bending theory, which is equivalent to the original boundary value problem, is established rigorously by mathematical technique of non-analytic continuation and is fully proved by means of the variational principle. The previous three kinds of boundary integral equations with indirect unknowns are discussed thoroughly and it is shown that all previous results are not EBIE.

Method to analyze wrinkled membranes with zero shear modulus and equivalent stiffness

To solve the problems of divergence,low accuracy and project application of membrane wrinkling analysis,an analysis method of zero shear modulus and equivalent stiffness was proposed.This method is an improvement to the previous method (Method I) of local coordinate transposition and stiffness equivalence.The new method is derived and the feasibility is theoretically proved.A small-scale membrane structure is analyzed by the two methods,and the results show that the computational efficiency of the new method (Method II) is approximately 23 times that of Method I.When Method II is applied to a large-scale membrane stadium structure,it is found that this new method can quickly make the second principal stress of one way wrinkled elements zero,and make the two principal stresses of two-way wrinkled elements zero as well.It could attain the correct load responses right after the appearance of wrinkled elements,which indicates that Method II can be applied to wrinkling analysis of large-scale membrane structures.

ELEMENT－BY－ELEMENT MATRIX DECOMPOSITION ANDSTEP－BY－STEP INTEGRATION METHOD FOR TRANSIENTDYNAMIC PROBLEMS

In this paper a general matrix decomposition scheme as well as an element-by-clement relaxation algorithm combined with step-by -step integration method is presented for transient dynamic problems thus the finite element method can be fromforming global stiffness matrix global mass matrix as well as solyin large scale sparse equations Theory analysis and numerical results show that the presented matrix decomposition scheme is the optimal one The presented algoithm has else physicalmeaning and can be busily applied to finite element codes

On the Total Dynamic Response of Soil-Structure Interaction System in Time Domain Using Elastodynamic Infinite Elements with Scaling Modified Bessel Shape Functions

This paper is devoted to a new approach—the dynamic response of Soil-Structure System (SSS), the far field of which is discretized by decay or mapped elastodynamic infinite elements, based on scaling modified Bessel shape functions are to be calculated. These elements are appropriate for Soil-Structure Interaction problems, solved in time or frequency domain and can be treated as a new form of the recently proposed elastodynamic infinite elements with united shape functions (EIEUSF) infinite elements. Here the time domain form of the equations of motion is demonstrated and used in the numerical example. In the paper only the formulation of 2D horizontal type infinite elements (HIE) is used, but by similar techniques 2D vertical (VIE) and 2D corner (CIE) infinite elements can also be added. Continuity along the artificial boundary (the line between finite and infinite elements) is discussed as well and the application of the proposed elastodynamical infinite elements in the Finite element method is explained in brief. A numerical example shows the computational efficiency and accuracy of the proposed infinite elements, based on scaling Bessel shape functions.

Design and Development of Small Modular Courses for“Education-Training Integration”in Vocational Colleges:A Case Study

Vocational education plays a vital role in the development of skilled technical professionals and the advancement of the economy.However,the emphasis on campus education often neglects the importance of external training,hindering the overall development of vocational education.This study aims to address this issue by exploring the design and development of small modular courses that integrate training and education in vocational colleges,focusing on the mechanics course as a case study.The research methods employed in this study include an in-depth analysis of enterprise training needs,the development of digital teaching resources utilizing the finite element method(FEM),and the implementation of a small modular course integrating education and training.The data analysis reveals positive outcomes in terms of learners’comprehension and engagement with complex mechanics formulas through the use of stress nephograms and other digital resources.This research provides a new perspective on curriculum design and offers insights into the integration of training and education in vocational colleges.The findings underscore the significance of incorporating innovative teaching methodologies and digital resources in enhancing the quality and relevance of vocational education,ultimately contributing to the cultivation of skilled professionals and the growth of the vocational education sector.

Finite element analysis of stresses and interface crack in TBC systems

Thermal barrier coatings have been used on high temperature components. Due to high stresses leading to unpredictable failure, a transient thermal-structural finite element solution was employed to analyze the stress distribution and J-integral at the interface between the bond coating and thermally growing oxide(TGO) in the EB-PVD thermal barrier coatings subjected to thermal loadings. The effects of some environmental and material parameters were studied, such as thermal convection coefficient, ceramic elastic modulus and TGO thickness. The results show that the stresses and J-integral values are impacted by these parameters.

CHARACTERISTIC GALERKIN METHOD FOR CONVECTION-DIFFUSION EQUATIONS AND IMPLICIT ALGORITHM USING PRECISE INTEGRATION

This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using precise integration method. With the operator splitting procedure, the precise integration method is introduced to determine the material derivative in the convection-diffusion equation, consequently, the physical quantities of material points. An implicit algorithm with a combination of both the precise and the traditional numerical integration procedures in time domain in the Lagrange coordinates for the characteristic Galerkin method is formulated. The stability analysis of the algorithm shows that the unconditional stability of present implicit algorithm is enhanced as compared with that of the traditional implicit numerical integration procedure. The numerical results validate the presented method in solving convection-diffusion equations. As compared with SUPG method and explicit characteristic Galerkin method, the present method gives the results with higher accuracy and better stability.

Analysis of multiple interfacial cracks in three-dimensional bimaterials using hypersingular integro-differential equation method

By using the concept of finite-part integral, a set of hypersingular integro-differential equations for multiple interracial cracks in a three-dimensional infinite bimaterial subjected to arbitrary loads is derived. In the numerical analysis, unknown displacement discontinuities are approximated with the products of the fundamental density functions and power series. The fundamental functions are chosen to express a two-dimensional interface crack rigorously. As illustrative examples, the stress intensity factors for two rectangular interface cracks are calculated for various spacing, crack shape and elastic constants. It is shown that the stress intensity factors decrease with the crack spacing.

The Numerical Integration of Discrete Functions on a Triangular Element

With the application of Hammer integral formulas of a continuous function on a triangular element, the numerical integral formulas of some discrete functions on the element are derived by means of decomposition and recombination of base functions. Hammer integral formulas are the special examples of those of the paper.

A New Iterative Method for Multi-Moving Boundary Problems Based Boundary Integral Method

The present paper deals with very important practical problems of wide range of applications. The main target of the present paper is to track all moving boundaries that appear throughout the whole process when dealing with multi-moving boundary problems continuously with time up to the end of the process with high accuracy and minimum number of iterations. A new numerical iterative scheme based the boundary integral equation method is developed to track the moving boundaries as well as compute all unknowns in the problem. Three practical applications, one for vaporization and two for ablation were solved and their results were compared with finite element, heat balance integral and the source and sink results and a good agreement were obtained.

Integrity and Failure Analysis of Cement Sheath Subjected to Coalbed Methane Fracturing

Perforation and fracturing are typically associated with the development of coalbed methane wells.As the cement sheath is prone to failure during this process,in this work,the effects of the casing pressure,elastic modulus of the cement,elastic modulus of the formation,and casing eccentricity on the resulting stresses are analyzed in the frame of a finite element method.Subsequently,sensitivity response curves of the cement sheath stress are plotted by normalizing all factors.The results show that the maximum circumferential stress and Mises stress of the cement sheath increase with the casing internal pressure,elastic modulus of the cement and casing eccentricity.As the elastic modulus of the formation increases,the maximum circumferential stress of the cement sheath decreases,and its maximum Mises stress increases slightly.The cement sheath undergoes tensile failure during coalbed methane fracturing.The stress sensitivity of the cement sheath to the influential parameters is in the following order:casing internal pressure>elastic modulus of cement sheath>casing eccentricity>elastic modulus of formation.

Design of Rotor Magnetic Barrier Structure of Built-in Permanent Magnet Motor Based on Taguchi Method

In this paper,a 20kW vehicle built-in permanent magnet synchronous motor is taken as an example,and a magnetic barrier structure is added to the rotor of the motor to solve the uneven saturation problem of the rotor side magnetic bridge.This structure improves the air-gap flux density waveform of the motor by influencing the internal magnetic flux path of the motor rotor,thus improving the sine of the no-load back EMF waveform of the motor and reducing the torque ripple of the motor.At the same time,Taguchi method is used to optimize the structural parameters of the added magnetic barrier.In order to facilitate the analysis of its uneven saturation phenomenon and improve the optimization effect,a simple equivalent magnetic network(EMN)model considering the uneven saturation of rotor magnetic bridge is established in this paper,and the initial values of optimization factors are selected based on this model.Finally,the no-load back EMF waveform distortion rate,torque ripple and output torque of the optimized motor are compared and analyzed,and the influence of magnetic barrier structure parameters on the electromagnetic performance of the motor is also analyzed.The results show that the optimized motor can not change the output torque of the motor as much as possible on the basis of reducing the waveform distortion rate of no-load back EMF and torque ripple.

三维可变形圆化多面体离散单元法

为真实模拟岩体的变形特性与运动形态,将圆化多面体离散元法与有限单元法结合,提出一种三维可变形圆化多面体离散单元法。该方法既能真实表征块体的不规则特征,又降低了接触判断的难度,同时能准确反映块体的变形特性。在求解切向接触力时,将接触判断对象从接触对简化为单元整体,显著提高了计算效率。为分析块体变形特性,在块体离散单元内部划分有限元网格,将最外层有限元网格作为最小接触单元。采用直接平均法,将接触力转化为等效节点力,并采用非线性有限单元法实现对单元变形特性的精确模拟,克服了圆化多面体无法反映单元变形的缺陷。通过5个算例论证了新方法在捕捉单元变形、运动形态以及其力学特征等方面的准确性和高效性。

超大跨劲性骨架拱桥缩尺模型试验方案设计研究

为对超大跨劲性骨架拱桥缩尺模型试验方案进行合理设计,以计算跨径600 m的劲性骨架拱桥——天峨龙滩特大桥为背景,围绕模型缩尺比、结构设计、材料及加载系统等关键环节,开展主拱圈缩尺模型试验方案设计研究。最终确定模型拱缩尺比为1∶10,劲性钢骨架采用单肋形式,采用与实桥主拱圈性能相近、便于施工的材料,采用阵列式滑轮组加载系统实现模型拱和实桥主拱圈的应力等效,还原外包混凝土分环分段浇筑施工,并简化劲性钢骨架与管内混凝土施工。将模型拱外包混凝土应力实测值、ANSYS建模计算得到的模型拱理论值及实桥主拱圈理论值进行对比,结果表明:模型拱和实桥主拱圈外包混凝土在施工阶段的应力变化趋势基本相同,最大绝对误差在2 MPa以内,模型拱应力实测值和理论值也吻合较好,缩尺模型试验方案设计合理。

仿生平面三角形单元积分声场的波函数构造

波叠加法在求解声源外部辐射声场时,需要对所有离散单元进行数值积分计算导致计算效率较低,而等效源法由于过度简化单元始终存在较大的积分近似误差.针对以上缺陷,利用Helmholtz方程在球坐标系下的解构造了一种与单元积分等效且无需积分的波函数.受仿生复合材料三角形缝合结构启发,以适用范围最广的平面三角形单元为例,构造了波函数的一般形式和内推形式.最后,通过数值仿真对比了两种波函数与直接积分的计算声场的精度和效率.结果表明,两种波函数与直接积分的计算误差低于0.5%,且内推波函数的计算效率约为直接积分的6倍.