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.

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 computationally efficient.

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.

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.

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.

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.

Theory and Calculation of the J-Integral for Coupled Chemo-Mechanical Fracture Mechanics

In this paper,by introducing a chemical field,the J-integral formulation is presented for the chemo-mechanical coupled medium based on the laws of thermodynamics.A finite element implementation of the J-integral was performed to study the mode I chemo-mechanical coupled fracture problem.For derivation of the coupled J-integral,the equivalent domain integral(EDI)method was applied to obtain the mode I J-integral,with expression of the area integrals based on constitutive relationships of a linear elastic small deformation for chemo-mechanical coupling,instead of the finite deformation problem.A finite element procedure is developed to compute the mode I J-integral,and numerical simulation of the y-direction stress field is studied by a subroutine UEL(User defined element)developed in ABAQUS software.Accuracy of the numerical results obtained using the mode I J-integral was verified by comparing them to a well-established model based on linear elastic fracture mechanics(LEFM).Furthermore,a numerical example was presented to illustrate path-independence of the formulated J-integral for a chemo-mechanical coupled specimen under different boundary conditions,showing a high accuracy and reliability of the present method.The variation laws of J-integral and the y-direction stress field with external chemical,mechanical loading and time are revealed.The J-integral value increases with larger external concentration loading in the same integral domain.The extent of diffusion is much greater with larger concentration,which leads to a stronger coupling effect due to the chemical field.This work provides new insights into the fracture mechanics for the chemo-mechanical coupled medium.

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.

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

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.

Extraction of Stress Intensity Factors by Using the P-Version Finite Element Method and Contour Integral Method

The stress intensity factors(SIFs)for two-dimensional cracks are extracted using the p-version finite element method(P-FEM)and the contour integral method.Several numerical experiments,e.g.,crack initiating from the edge of a circular hole under an unidirectional uniform tension and two equal-length,unequal-length hole-edge cracks,respectively,at a rectangular plate,an inclined centered crack under uniaxial tension at a square plate and a pipeline crack model,are used to demonstrate the accuracy and effectiveness of the approaches.SIFs are presented for the effects of various crack lengths and length-width ratio.Numerical results are analyzed and compared with reference solutions and results obtained by the Voronoi cell finite element method,boundary element method,high-order extended finite element method(high-order XFEM)and commercial finite element software ABAQUS in the available literature.Numerical results are in good agreement with the benchmark problems and show faster convergence rate,higher accuracy and better numerical stability.

基于交互作用积分的异种金属焊接区域裂纹扩展模拟方法

核电厂中存在大量的异种金属焊接区域,该区域内裂纹扩展的合理评价与核电厂安全运行密切相关。由于焊接区域材料具有显著的非均匀特点,传统的J积分理论在该区域不再具有守恒性,同时大量的运行经验反馈表明,在焊接区域裂纹扩展呈现出明显的偏折现象,传统基于Ⅰ型裂纹扩展的分析方法不再适用。为解决上述问题,本文建立了基于交互作用积分理论的异种金属焊接区域裂纹扩展模拟方法。通过交互作用积分的引入,能够准确计算焊接区域复合型裂纹的应力强度因子,采用最大周向应力等裂纹扩展准则后,能够快速实现裂纹扩展路径的预测。通过将本文方法与实验结果和解析解进行对比分析,验证了当前方法的精度和有效性。该方法的建立对焊接区域裂纹扩展模拟及核电设备安全分析评价具有重要意义。

平面多裂纹相互影响分析

为研究含多裂纹的工程结构在服役过程中的不确定性问题,通过改变多裂纹之间的相对位置,采用有限元数值方法计算主裂纹尖端的J积分值,分析多裂纹之间的相互影响规律。结果表明:当裂纹之间有重叠区域时,干扰裂纹会减缓主裂纹的扩展;当裂纹之间无重叠区域时,干扰裂纹会加快主裂纹的扩展,且干扰裂纹与主裂纹的夹角越小,干扰裂纹对主裂纹的影响越大。当水平间距比大于9或垂直间距比大于±3时,干扰裂纹对主裂纹无影响。若从安全角度考虑,两条干扰裂纹对主裂纹影响的效果可视为两条干扰裂纹单独存在时对主裂纹影响的效果的叠加。

车载一体化配料装置上臂架结构优化设计研究

以某重点项目的车载一体化配料装置上臂架为研究对象,针对其轻量化、稳定性好、翻转可靠的性能要求,对其进行结构拓扑优化及尺寸优化。根据优化后的结果确定了臂架侧面腹杆以及底面连杆的具体布局和截面尺寸参数,然后把优化结果和实际市场主流尺寸规格相结合重新构建上臂架模型。最后数值分析表明:在保证上臂架力学特性的前提下,该优化方法减重147kg,节约了21%的材料,满足轻量化要求,最大变形量降低6mm,增强了结构的稳定性,最终实现优化的目标。

基于扩展有限元法的传热管贯穿裂纹应力强度因子计算

蒸汽发生器作为压水堆的重要压力边界,其传热管是否破损直接关系到反应堆的运行安全。为解决蒸汽发生器中传热管疲劳裂纹扩展数字孪生中裂纹长度的预测问题,本文通过ABAQUS软件,对已存在贯穿裂纹的传热管进行建模,比较其自带的围线积分法和扩展有限元法(extended finite element method,XFEM)计算应力强度因子(stress intensity factor,SIF)的准确性。在裂纹尺寸a/W>0.5时,XFEM与公式解结果相差较小。因此,采用XFEM计算其在不同应力下的应力强度因子,发现随着裂纹尺寸、载荷的增大,应力强度因子也随着增大,应力值与应力强度因子成正比关系。

基于等效线性化隔震结构设计周期折减系数研究

《建筑隔震设计标准》提出的隔震设计是基于复振型分解反应谱等效线性化的一体化直接设计方法,但未提及隔震结构周期折减系数如何取值。基于此,根据刚度串联关系推导等效单自由度隔震体系周期折减系数简化计算公式,探讨隔震结构周期折减系数因素的影响规律,建立不同填充材料、不同填充率的有限元数值模型,并利用数值模拟结果验证隔震结构周期折减系数简化计算公式。结果表明:隔震结构周期折减系数与名义周期比、非隔震结构周期折减系数存在函数关系;墙体开洞与通高墙体的隔震结构的周期折减系数均随着填充率的增大而减小,当填充率相同时,呈现出随填充材料弹性模量增大而减小的趋势,墙体开洞会增大隔震结构周期折减系数,且隔震结构的周期折减系数的取值范围相对较窄,为0.915~0.965;数值有限元模拟与理论结果偏差小于3%,吻合度高,以验证隔震结构周期折减系数简化计算公式的正确性,说明该简化计算方法对隔震工程设计具有一定指导意义。