PARTITION OF UNITY FINITE ELEMENT METHOD FOR SHORT WAVE PROPAGATION IN SOLIDS

A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency.

PARTITION OF UNITY FINITE ELEMENT METHOD FOR SHORT WAVE PROPAGATION IN SOLIDS

A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency.

Conversion between solid and beam element solutions of finite element method based on meta-modeling theory:development and application to a ramp tunnel structure

In this study, a new method for conversion of solid finite element solution to beam finite element solution is developed based on the meta-modeling theory which constructs a model consistent with continuum mechanics. The proposed method is rigorous and efficient compared to a typical conversion method which merely computes surface integration of solid element nodal stresses to obtain cross-sectional forces. The meta-modeling theory ensures the rigorousness of proposed method by defining a proper distance between beam element and solid element solutions in a function space of continuum mechanics. Results of numerical verification test that is conducted with a simple cantilever beam are used to find the proper distance function for this conversion. Time history analysis of the main tunnel structure of a real ramp tunnel is considered as a numerical example for the proposed conversion method. It is shown that cross-sectional forces are readily computed for solid element solution of the main tunnel structure when it is converted to a beam element solution using the proposed method. Further, envelopes of resultant forces which are of primary importance for the purpose of design, are developed for a given ground motion at the end.

Treatment of discontinuous interface in liquid-solid forming with extended finite element method

Extended finite element method(XFEM) is proposed to simulate the discontinuous interface in the liquid-solid forming process.The discontinuous interface is an important phenomenon happening in the liquid-solid forming processes and it is difficult to be simulated accurately with conventional finite element method(CFEM) because it involves solid phase and liquid phase simultaneously.XFEM is becoming more and more popular with the need of solving the discontinuous problem happening in engineering field.The implementation method of XFEM is proposed on Abaqus code by using UEL(user element) with the flowchart.The key is to modify the element stiffness in the proposed method by using UEL on the platform of Abaqus code.In contrast to XFEM used in the simulation of solidification,the geometrical and physical properties of elements were modified at the same time in our method that is beneficial to getting smooth interface transition and precise analysis results.The analysis is simplified significantly with XFEM.

Quantifying Uncertainty in Dielectric Solids’ Mechanical Properties Using Isogeometric Analysis and Conditional Generative Adversarial Networks

Accurate quantification of the uncertainty in the mechanical characteristics of dielectric solids is crucial for advancing their application in high-precision technological domains,necessitating the development of robust com-putational methods.This paper introduces a Conditional Generation Adversarial Network Isogeometric Analysis(CGAN-IGA)to assess the uncertainty of dielectric solids’mechanical characteristics.IGA is utilized for the precise computation of electric potentials in dielectric,piezoelectric,and flexoelectric materials,leveraging its advantage of integrating seamlessly with Computer-Aided Design(CAD)models to maintain exact geometrical fidelity.The CGAN method is highly efficient in generating models for piezoelectric and flexoelectric materials,specifically adapting to targeted design requirements and constraints.Then,the CGAN-IGA is adopted to calculate the electric potential of optimum models with different parameters to accelerate uncertainty quantification processes.The accuracy and feasibility of this method are verified through numerical experiments presented herein.

Fractional four-step finite element method for analysis of thermally coupled fluid-solid interaction problems

An integrated fluid-thermal-structural analysis approach is presented. In this approach, the heat conduction in a solid is coupled with the heat convection in the viscous flow of the fluid resulting in the thermal stress in the solid. The fractional four-step finite element method and the streamline upwind Petrov-Galerkin （SUPG） method are used to analyze the viscous thermal flow in the fluid. Analyses of the heat transfer and the thermal stress in the solid axe performed by the Galerkin method. The second-order semi- implicit Crank-Nicolson scheme is used for the time integration. The resulting nonlinear equations are lineaxized to improve the computational efficiency. The integrated analysis method uses a three-node triangular element with equal-order interpolation functions for the fluid velocity components, the pressure, the temperature, and the solid displacements to simplify the overall finite element formulation. The main advantage of the present method is to consistently couple the heat transfer along the fluid-solid interface. Results of several tested problems show effectiveness of the present finite element method, which provides insight into the integrated fluid-thermal-structural interaction phenomena.

Coupling of discrete-element method and smoothed particle hydrodynamics for liquid-solid flows

Particle based methods can be used for both the simulations of solid and fluid phases in multiphase medium, such as the discrete-element method for solid phase and the smoothed particle hydrodynamics for fluid phase. This paper presents a computational method combining these two methods for solid-liquid medium. The two phases are coupled by using an improved model from a reported Lagrangian-Eulerian method. The technique is verified by simulating liquid-solid flows in a two-dimensional lid-driven cavity.

Tensile Shock Physics in Compressible Thermoviscoelastic Solid Medium

This paper addresses tensile shock physics in thermoviscoelastic (TVE) solids without memory. The mathematical model is derived using conservation and balance laws (CBL) of classical continuum mechanics (CCM), incorporating the contravariant second Piola-Kirchhoff stress tensor, the covariant Green’s strain tensor, and its rates up to order n. This mathematical model permits the study of finite deformation and finite strain compressible deformation physics with an ordered rate dissipation mechanism. Constitutive theories are derived using conjugate pairs in entropy inequality and the representation theorem. The resulting mathematical model is both thermodynamically and mathematically consistent and has closure. The solution of the initial value problems (IVPs) describing evolutions is obtained using a variationally consistent space-time coupled finite element method, derived using space-time residual functional in which the local approximations are in hpk higher-order scalar product spaces. This permits accurate description problem physics over the discretization and also permits precise a posteriori computation of the space-time residual functional, an accurate measure of the accuracy of the computed solution. Model problem studies are presented to demonstrate tensile shock formation, propagation, reflection, and interaction. A unique feature of this research is that tensile shocks can only exist in solid matter, as their existence requires a medium to be elastic (presence of strain), which is only possible in a solid medium. In tensile shock physics, a decrease in the density of the medium caused by tensile waves leads to shock formation ahead of the wave. In contrast, in compressive shocks, an increase in density and the corresponding compressive waves result in the formation of compression shocks behind of the wave. Although these are two similar phenomena, they are inherently different in nature. To our knowledge, this work has not been reported in the published literature.

Approach of technical decision-making by element flow analysis and Monte-Carlo simulation of municipal solid waste stream

This paper deals with the procedure and methodology which can be used to select the optimal treatment and disposal technology of municipal solid waste （MSW）, and to provide practical and effective technical support to policy-making, on the basis of study on solid waste management status and development trend in China and abroad. Focusing on various treatment and disposal technologies and processes of MSW, this study established a Monte-Carlo mathematical model of cost minimization for MSW handling subjected to environmental constraints. A new method of element stream （such as C, H, O, N, S） analysis in combination with economic stream analysis of MSW was developed. By following the streams of different treatment processes consisting of various techniques from generation, separation, transfer, transport, treatment, recycling and disposal of the wastes, the element constitution as well as its economic distribution in terms of possibility functions was identified. Every technique step was evaluated economically. The Mont-Carlo method was then conducted for model calibration. Sensitivity analysis was also carried out to identify the most sensitive factors. Model calibration indicated that landfill with power generation of landfill gas was economically the optimal technology at the present stage under the condition of more than 58% of C, H, O, N, S going to landfill. Whether or not to generate electricity was the most sensitive factor. If landfilling cost increases, MSW separation treatment was recommended by screening first followed with incinerating partially and composting partially with residue landfilling. The possibility of incineration model selection as the optimal technology was affected by the city scale. For big cities and metropolitans with large MSW generation, possibility for constructing large-scale incineration facilities increases, whereas, for middle and small cities, the effectiveness of incinerating waste decreases.

Numerical simulation of coal-bed methane transfer with finite element method

The mathematical model and the numerical simulation for the transfer of coal bed methane were established based on the combination of the porous flow theory and elastic plastic mechanics theory and the numerical solution was given, together with the consideration of the fluid solid interaction between the coal bed gas and coal framework. Then the dispersion for the equation of gas porous flow and coal seam distortion was carried out and the functional analysis equation was obtained. Finally, the coupling solution was educed and calculated by finite element method(FEM) on a model example.

A boundary element method for the simulation of non-spherical bubbles and their interactions near a free surface

The basic principle and numerical technique for simulating two three-dimensional bubbles near a free surface are studied in detail by using boundary element method. The singularities of influence coefficient matrix are eliminated using coordinate transformation and so-called 4π rule. The solid angle for the open surface is treated in direct method based on its definition. Several kinds of configurations for the bubbles and free surface have been investigated. The pressure contours during the evolution of bubbles are obtained in our model and can better illuminate the mechanism underlying the motions of bubbles and free surface. The bubble dynamics and their interactions have close relation with the standoff distances, buoyancy parameters and initial sizes of bubbles. Completely different bubble shapes, free surface motions, jetting patterns and pressure distributions under different parameters can be observed in our model, as demon- strated in our calculation results.

A Cell-Based Linear Smoothed Finite Element Method for Polygonal Topology Optimization

The aim of this work is to employ a modified cell-based smoothed finite element method(S-FEM)for topology optimization with the domain discretized with arbitrary polygons.In the present work,the linear polynomial basis function is used as the weight function instead of the constant weight function used in the standard S-FEM.This improves the accuracy and yields an optimal convergence rate.The gradients are smoothed over each smoothing domain,then used to compute the stiffness matrix.Within the proposed scheme,an optimum topology procedure is conducted over the smoothing domains.Structural materials are distributed over each smoothing domain and the filtering scheme relies on the smoothing domain.Numerical tests are carried out to pursue the performance of the proposed optimization by comparing convergence,efficiency and accuracy.

Theoretical calculation of tidal Love numbers of the Moon with a new spectral element method

The tidal Love numbers of the Moon are a set of nondimensional parameters that describe the deformation responses of the Moon to the tidal forces of external celestial bodies.They play an important role in the theoretical calculation of the Moon’s tidal deformation and the inversion of its internal structure.In this study,we introduce the basic theory for the theoretical calculation of the tidal Love numbers and propose a new method of solving the tidal Love numbers:the spectral element method.Moreover,we explain the mathematical theory and advantages of this method.On the basis of this new method,using 10 published lunar internal structure reference models,the lunar surface and lunar internal tidal Love numbers were calculated,and the influence of different lunar models on the calculated Love numbers was analyzed.Results of the calculation showed that the difference in the second-degree lunar surface Love numbers among different lunar models was within 8.5%,the influence on the maximum vertical displacement on the lunar surface could reach±8.5 mm,and the influence on the maximum gravity change could reach±6μGal.Regarding the influence on the Love numbers inside the Moon,different lunar models had a greater impact on the Love numbers h_(2) and l_(2) than on k_(2) in the lower lunar mantle and core.

Cup-drawing formation of steel sheet with nickel coating by finite element method

The finite element method(FEM) simulation of deep-drawing of steel sheet with nickel coating based on the solid element and dynamic explicit method was reported. Penalty function method was used to treat the contact algorithm. The friction between the punch and coating sheet was based on a Coulomb formulation. The combination of coating and substrate was defined as tied with failure contact. The results of the simulation illustrate that the steel sheet and the nickel coating do not delaminate at the interface. The stress field of the nickel coating is more complicated than that of the steel substrate. Furthermore,it is found that the punch-nose radius is the most unsubstantial part for the intensity of the entire deep-drawing part and the thinnest part,it is a dangerous zone for the break. At this zone,the thickness thinning of the steel sheet and the nickel coating are up to 4.8% and 6.7%,respectively. Meanwhile,it is found that the curve of the variable blankholder force(VBHF) designed can improve the formability of sheet.

A method for 3D simulation of internal gas effects on thermal-mechanical behaviors in nuclear fuel elements

A new method for three-dimensional simulation of the interaction between the gas and the solid around is developed.The effects of the gas on the thermal-mechanical behaviors within the surrounded solid are performed by replacing the internal gas with an equivalent solid in the modeling,which can make it convenient to simulate the thermal-mechanical coupling effects in the solid research objects with gases in them.The applied thermal expansion coefficient,Young's modulus and Poisson's ratio of the equivalent solid material are derived.A series of tests have been conducted;and the proposed equivalent solid method to simulate the gas effects is validated.

基于微观流固耦合的超深层致密砂岩气藏应力敏感性分析

超深层致密砂岩气藏具有强应力敏感性,目前常用的研究方法包括压力脉冲实验法和实时在线CT扫描法两种,压力脉冲实验法不能揭示产生应力敏感性的微观机理,而实时在线CT扫描法也无法模拟深部地层高压、高应力的条件。为解决应力敏感性实验研究的不足,基于离散单元法与管道网络模型建立了微观流固耦合算法,编制了模拟器,并对模拟器力学计算和流固耦合模块的正确性进行了验证,分析了应力大小、加载方向和孔隙压力对岩心渗透率的影响,最后从微观上揭示了超深层致密砂岩气藏的应力敏感性机理。研究结果表明:①应力通过增加与之垂直方向上喉道两侧的法向压力,减小喉道的水力半径,进而降低储层的渗透率;②较高的孔隙压力能够阻碍岩石颗粒在应力作用下的移动,从而减缓了孔隙和喉道的变形,使模型保持较高的渗透率;③致密砂岩气藏的渗透率受到应力和地层压力的共同控制,并且具有各向异性,在垂直于最小主应力方向上形成渗透率较大的优势通道;④异常高压阻碍了地应力的压实作用,有利于保护储层孔隙,使地层有较好的储集性能和较高的渗透率。结论认为,根据离散元法结合孔隙网络模型建立的流固耦合方法可为理解超深层致密砂岩应力敏感性提供理论参考,并为超深层致密砂岩气藏的科学高效开发提供指导。

后摆心潜入式喷管柔性接头力学特性数值仿真

针对后摆心潜入式喷管柔性接头在燃气压力与摆动联合载荷下,弹性件与增强件的力学特性计算问题,建立了对称刚体-柔性体结合的几何模型;采用了有限元方法,获取了柔性接头在燃气压力、摆动载荷及联合载荷下应力、弹性比力矩分布规律。研究表明:随着燃气压力增大,弹性比力矩降低;随摆角增大,弹性比力矩增大。文中的数值仿真方法,可以应用于柔性接头力学特性的计算,为柔性接头强度的安全性评估提供指导。

固体发动机喷管热结构耦合数值仿真研究

针对在热载荷与内压联合作用下,固体火箭发动机潜入式喷管的热结构耦合数值仿真问题,采用流体仿真软件与结构计算软件,展开了数值模拟。在流体仿真软件中,计算了潜入式喷管工作过程的内部稳态流场,提取了高温燃气流动参数与固体壁面对流换热系数。在有限元结构计算平台内,编写了非均布壁面压力载荷与非均布对流换热系数子程序,耦合求解了喷管热结构耦合问题,获取了热防护材料内部温度场与应力场分布。研究表明,热载荷是引起喉衬应力的主要原因。喉衬环向压应力与拉应力随时间呈现先增大后减小的过程。经地面喷管结构完整性热试车试验验证,该热结构耦合数值仿真方法可用于喷管结构完整性与安全性分析,为喷管结构设计提供合理指导。

Sm^(3+)掺杂LaOF荧光粉的制备及光学性能

以LaOF晶体为基质,利用水热辅助固相法制备出一系列Sm^(3+)掺杂LaOF荧光粉。采用XRD、TEM、荧光光谱仪等测试手段对所制得的样品的相结构、微观形貌及光学性能进行表征。结果表明,LaOF在不同煅烧温度下会产生四方相和斜方六面体两种不同晶相。此外,由于受跃迁概率和局域对称性的影响,Sm^(3+)掺杂四方相LaOF发光强度更大,其各浓度样品在405 nm光激发下,于567 nm、605 nm、651 nm和710 nm等处均出现了Sm^(3+)的特征发射峰,并且随着Sm^(3+)掺杂量的增加,其发光强度呈现先增大后减小的趋势,且当Sm^(3+)掺杂量为3.0%(摩尔分数,下同)时,La_(1-x)Sm_(x)OF样品发光强度达最大值。此外,所得样品的色纯度极高,其多个激发峰均位于商用近紫外和蓝光LED芯片的发射波长附近,可实现多种波长激发下的可见橙光发射。

非均匀装药的复杂燃面退移与内弹道性能预示

非均匀装药的复杂燃面退移与内弹道性能预示是固体火箭发动机设计的核心问题。建立非均匀装药燃烧的燃面退移数学模型,提出一种采用有限元法通过求解泊松方程逼近程函方程黏滞解的新方法(PEF)。所提方法可将燃面退移问题转化为特殊的稳态热传导问题,实现对几何形状不规则且燃速分布复杂的三维装药燃面退移的计算。考虑燃烧室压力变化等实际因素,在平衡压力假设下,形成了内弹道性能预示的4种计算模型。完成了二维星型装药、三维翼柱型装药和含金属丝的双推进剂装药的计算。计算结果表明:所提方法不仅可以高精度地适应多种推进剂构成的复杂交界面,而且可以直接在商业有限元软件的稳态热传导模块上应用和求解,充分利用商业有限元软件成熟的计算机辅助设计(CAD)建模、前处理、后处理及二次开发能力,实现了复杂燃面退移与内弹道性能预示方法的通用化和实用化。