三维热权函数法和多虚拟裂纹扩展技术

热权函数法直接利用温度场与热权函数的乘积的积分来求应力强度因子(SIF)的过渡过程，它可以免除对每一时刻进行热弹性力学有限元或边界元应力分析，计算效率大大提高。本文给出了三维热权函数法的基本方程，并提出了求解三维热权函数法基本方程的多虚拟裂纹扩展法(MVCE法)。在MVCE法中，可以引入无穷多个虚拟裂纹扩展模式；虚拟裂纹扩展模式与应力强度因子的插值直接相联系，所得到的方程组的系数矩阵是一个三对角矩阵，具有良好的计算性能。它对于裂纹前缘SIF分布急剧变化的情况，有良好的数值模拟能力。实例计算表明，MVCE法具有权高的计算效率，并具有很高的计算精度。     

Crack propagation in a functionally graded plate under thermal shock

Summary Thermal cracking in a ceramic/metal functionally graded plate is discussed. When a functionally graded plate is cooled from high temperature, curved or straight crack paths are experimentally observed on the ceramic surface. One of the reasons that make the crack paths to differ are the thermal or mechanical conditions. In order to clarify the influence of these conditions on the crack path, the crack propagation is simulated using finite element method. Received 29 September 1998; accepted for publication 2 August 1999     

Bending of Timoshenko beam with effect of crack gap based on equivalent spring model

Considering the effect of crack gap,the bending deformation of the Timoshenko beam with switching cracks is studied.To represent a crack with gap as a nonlinear unidirectional rotational spring,the equivalent flexural rigidity of the cracked beam is derived with the generalized Dirac delta function.A closed-form general solution is obtained for bending of a Timoshenko beam with an arbitrary number of switching cracks.Three examples of bending of the Timoshenko beam are presented.The influence of the beam’s slenderness ratio,the crack’s depth,and the external load on the crack state and bending performances of the cracked beam is analyzed.It is revealed that a cusp exists on the deflection curve,and a jump on the rotation angle curve occurs at a crack location.The relation between the beam’s deflection and load is bilinear,each part corresponding to an open or closed state of crack,respectively.When the crack is open,flexibility of the cracked beam decreases with the increase of the beam’s slenderness ratio and the decrease of the crack depth.The results are useful in identifying non-destructive cracks on a beam.     

Dynamic thermal shock in a layered cylinder with initial interface pressure

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本构模型对复合材料中X射线热击波数值模拟结果的影响

以碳酚醛靶中的一维应变热击波为例,讨论本构模型对热击波数值模拟结果的影响.数值模拟采用3种本构模型,即各向同性理想弹塑性本构模型、各向异性理想弹塑性本构模型及各向异性动态弹塑性本构模型.结果表明:与各向同性理想弹塑性、各向异性理想弹塑性本构模型相比,利用各向异性动态弹塑性本构模型获得的热击波应力峰值较小、应力峰值衰减较...     

THE PRECISE AND NEW ANALYSIS FOR A MODE Ⅲ GROWING CRACK IN AN ELASTIC-PERFECTLY PLASTIC SOLID

The near crack line field analysis method has been used to investigate into ModeⅢ quasistatically propagating crack in an elastic-perfectly plastic material.Thesignificance of this paper is that the usual small scale yielding theory has been brokenthrough.By obtaining the general solutions of the stresses and the displacement rate ofthe near crack line plastic region,and by matching the general solutions with theprecise elastic fields(not the usual elastic K-dominant fields)at the elastic-plasticboundary,the precise and new solutions of the stress and deformation fields,the sizeof the plastic region and the unit normal vector of the elastic-plastic boundary havebeen obtained near the crack line.The solutions of this paper are sufficiently precisenear the crack line region because the roughly qualitative assumptions of the smallscale yielding theory have not been used and no other roughly qualitative assumptionshave been taken,either.The analysis of this paper shows that the assumingly“steady-state cas     

Study on the thermal protection performance of superalloy honeycomb panels in high-speed thermal shock environments

The thermal protection performance of superalloy honeycomb structure in high-temperature environments are important for thermal protection design of high-speed aircrafts. By using a self-developed transient aerodynamic thermal simulation system, the thermal protection performance of superalloy honeycomb panel was tested in this paper at different transient heating rates ranging from 5°C/s to 30°C/s, with the maximum instantaneous temperature reaching 950°C. Furthermore, the thermal protection performance of superalloy honeycomb structure under simulated thermal environments was computed for different high heating rates by using 3D finite element method, and a comparison between calculational and experimental results was carried out. The results of this research provide an important reference for the design of thermal protection systems comprising superalloy honeycomb panel.     

Hamilton体系下功能梯度梁的热冲击动力屈曲分析

在Hamilton体系下,基于Euler梁理论研究了功能梯度材料梁受热冲击载荷作用时的动力屈曲问题;将非均匀功能梯度复合材料的物性参数假设为厚度坐标的幂函数形式,采用Laplace变换法和幂级数法解析求得热冲击下功能梯度梁内的动态温度场:首先将功能梯度梁的屈曲问题归结为辛空间中系统的零本征值问题,梁的屈曲载荷与屈曲模态分别对应于Hamilton体系下的辛本征值和本征解问题,由分叉条件求得屈曲模态和屈曲热轴力,根据屈曲热轴力求解临界屈曲升温载荷。给出了热冲击载荷作用下一类非均匀梯度材料梁屈曲特性的辛方法研究过程,讨论了材料的梯度特性、结构几何参数和热冲击载荷参数对临界温度的影响。     

I-II复合型裂缝断裂角的分层剪滞模型与分析

采用修正的剪滞理论建立了岩石、混凝土等准脆性材料的I-II复合型裂缝在单向拉伸荷载作用下的计算模型,得到了与实验相吻合且优于传统S判据的断裂角。通过对远场应力、斜裂缝区应力以及子层位移的合理简化,得到了求解剪滞分析模型的边界条件,进而得到了含斜裂缝的各子层位移分布函数。引入最大应力集中因子,对I-II复合型裂缝前缘应力场进行简化;基于斜裂缝沿最大应力集中因子方向扩展,得到裂缝的断裂角。根据斜裂缝的应力分布,设置不同的子层分区,得到了更为细化的位移分布模式。通过对计算数据的分析,针对单向拉伸荷载作用下的I-II复合型裂缝,建立了按应力场分区设置子层的分层剪滞模型,得到更为精确的斜裂缝断裂角。     

The dynamic thermal stresses in hollow cylinder by thermal shock simultaneous with mechanical shock acting on the inner movable boundary

The transient temperature fields and dynamic thermal stress fields in gun barrel are studied in this paper, which are problems of interior ballistics.The high blast temperature and pressure act simultaneously on the inner surface of the barrel behind projectile moving in the barrel during shooting. Under this boundary condition, the governing equations of the thermoelastic problems of hollow cylinder are given, the corresponding functional is studied and the numerical results calculated by the finite element method are obtained.     

微惯性传感器建模及冲击响应分析

研究了微惯性传感器在冲击环境下的可靠性问题，重点分析了微惯性传感器在冲击载荷作用下的冲击响应问题。根据微惯性传感器结构部件主要由质量块、支承梁、衬底组成的特点，建立了微惯性传感器结构部件的集总参数模型，得出了微加速度计和微陀螺在半周正弦加速度冲击载荷作用下的冲击响应解析解，并采用有限元分析软件ANSYS验证了该解析解的正确性。此冲击响应解析解对预测微惯性传感器在冲击环境下的可靠性具有重要作用。     

屈服后表面裂纹与穿透裂纹的等效裂纹长度换算

在较小范围屈服条件下，将D-M模型和弹塑性线弹簧模型相结合，建立了屈服后一般扁壳表面裂纹的计算模型，导出了其控制方程和相应的COD计算公式。在此基础上，提出了屈服后一般扁壳表面裂纹与平板穿透裂纹的等COD换算方法。通过各种影响因素的分析并去除次要因素，最终给出了该等效换算关系的简单拟合公式。计算结果表明，该分析方法简便且有足够的工程精度，适应于在役压力容器等结构的现场快速断裂评定。     

液压减振器随机热力学模型与油温变化研究

为了获得具有更多信息和更加接近工程实际的液压减振器油温热力学模型,将随机不确定性理论引入到液压减振器油温传统热力学模型中进行研究。将液压油密度、导热系数、比热容和运动粘度作为随机变量,运用求解函数数字特征的代数综合法建立减振器随机热力学模型,进而获得油液传热过程规律。将油温随机热力学模型研究结果和传统模型的计算结果与实验结果进行比较,证明随机不确定性理论的引入可行且随机热力学模型比传统模型更加优越。     

Variational formula for a body with a crack and its applications (review)

A review is made of studies on the variational formula for a body with a crack, asymptotic expansions, weight functions, and displacements of crack faces __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 8, pp. 30–46, August 2007.     

新型路基同心筒热冲击机理与热环境影响因子

针对新型同心筒自力发射高速热冲击载荷下热环境评估与影响因子决策问题,结合弹性变形和域动分层结合的动网格技术,求解了二维轴对称Navier-Stokes方程,分析了新型路基同心筒流场机理与热冲击特性,并确定了热环境评价指标;通过建立以优化拉丁超立方试验设计和径向基神经网络为理论基础的近似数学模型,解决了CFD自动建模困难、计算量大的难点;结合径向基神经网络训练方法,对导弹热环境的影响因子进行了智能决策研究。分析表明:倒吸进入新型同心筒内筒的低温气体有力改善了同心筒热环境;建立的近似模型精度较高,满足工程需求;对导弹热环境的影响因子从大到小依次为筒底导流板直径、筒底导流板长度、导流器高度;为导弹热环境多学科优化设计提供参考。     

Surface and thermal effects on vibration of embedded alumina nanobeams based on novel Timoshenko beam model

This paper deals with the free vibration analysis of circular alumina （Al2O3） nanobeams in the presence of surface and thermal effects resting on a Pasternak foun- dation. The system of motion equations is derived using Hamilton＇s principle under the assumptions of the classical Timoshenko beam theory. The effects of the transverse shear deformation and rotary inertia are also considered within the framework of the mentioned theory. The separation of variables approach is employed to discretize the governing equa- tions which are then solved by an analytical method to obtain the natural frequencies of the alumina nanobeams. The results show that the surface effects lead to an increase in the natural frequency of nanobeams as compared with the classical Timoshenko beam model. In addition, for nanobeams with large diameters, the surface effects may increase the natural frequencies by increasing the thermal effects. Moreover, with regard to the Pasternak elastic foundation, the natural frequencies are increased slightly. The results of the present model are compared with the literature, showing that the present model can capture correctly the surface effects in thermal vibration of nanobeams.     

Singular perturbation analysis of dynamic fields in a thermoelastic solid with a small surface-breaking crack

An asymptotic analysis is presented for a dynamic problem of a semi-infinite isotropic thermoelastic solid with a small surface breaking crack. The exterior surface of the solid is subjected to a series of short thermal pulses. The crack surface is traction free and an ideal thermal contact is assumed across the crack. The stress intensity factor is asymptotically evaluated as a function of the crack depth and time. The effect of a boundary layer associated with the diffusive term is identified. The theoretical model is supplied with numerical simulations.     

激波在带扩容室的变截面管中传播和消波效果的数值分析

在利用实验结果验证程序的基础上,对激波在具有复杂结构管道内的传播特性进行了数值模拟,比较了不同入射激波条件和特征尺寸对扩容室消波效应的影响,并考虑了二维(轴对称、平面)模型和三维模型的影响。计算结果表明,同一尺寸的扩容室对不同马赫数入射激波的消波效果是相近的,扩容室特征尺寸不同则消波效果差别很大。     

Analytical solutions for thermal forcing vortices in boundary layer and its applications

Using the Boussinesq approximation, the vortex in the boundary layer is assumed to be axisymmetrical and thermal-wind balanced system forced by diabatic heating and friction, and is solved as an initial-value problem of linearized vortex equation set in cylindrical coordinates. The impacts of thermal forcing on the flow field structure of vortex are analyzed. It is found that thermal forcing has significant impacts on the flow field structure, and the material representative forms of these impacts are closely related to the radial distribution of heating. The discussion for the analytical solutions for the vortex in the boundary layer can explain some main structures of the vortex over the Tibetan Plateau.     

裂缝分析的比例边界有限元与有限元耦合的虚拟结构面模型

比例边界有限元法SBFEM(Scaled Boundary Finite Element Method)是一种半解析数值方法,在裂缝分析特别是强度因子计算上具有相当高的精度。本文提出了一种用于裂缝分析的基于虚拟结构面的SBFEM与常规FEM的耦合分析方法。首先选取裂缝周边一定范围的计算域,并将结构分成不含裂缝区域和含裂缝区域两部分。然后,对不含裂缝区域,采用FEM进行网格离散;对含裂缝区域,采用SBFEM进行网格离散;两者相互独立,在这两个域内,分别采用各自相应的位移模式。最后通过在SBFEM网格的外边界设置虚拟耦合结构面的模式,实现有限元网格和比例边界有限元网格的耦合。通过两个经典的含裂缝平板的算例研究,探讨了本文方法在I型开裂和混合型开裂分析中,影响应力强度因子精度的因素。算例表明,SBFEM具有的降维和半解析性质,使本文方法在裂缝分析中的前处理简单易行,且计算结果具有相当高的计算精度。