【作者】 钱秀清；

【导师】 姚振汉；

【作者基本信息】 清华大学 ， 力学， 2005， 博士

【摘要】 工程中很多重要的问题属于反问题,如结构中残余应力的确定,材料参数及其它参数的识别等等。与正问题相比,反问题的求解比较困难,因此经常采用数值计算方法求解,有时还需要与实验数据相接合。本文研究了两种反问题:一是利用较少的实验数据构造平面与轴对称残余应力场;二是利用球形压头压入实验提取延性材料的塑性特性。基于固有应变的概念,利用边界元方法,将残余应力场的构造问题,归结为引起残余应力的固有应变识别的反问题,建立了一种满足平面自平衡条件的残余应力场。为了增加反问题解的稳定性,将固有应变用光滑基函数表达;为了保持边界元法的优势,采用双重互易边界元法(DRBEM)将域内积分转化为边界积分,可以得到灵敏度矩阵的显式表达,更加有效地构造残余应力场。数值算例验证了本方法的有效性。利用相似的方法建立了轴对称残余应力场的构造方案。推导了轴对称平衡方程的伽辽金矢量形式以及位移的伽辽金矢量表达式,采用DRBEM将域内积分转换为边界积分,导出了灵敏度矩阵的显式表达,提高了反分析的效率。基于量纲分析原理和有限元计算,提出了一种利用球形压头压入实验基于能量的反方法确定延性材料的塑性特性。研究发现,对于给定的压入深度和压头半径的比值,通过定义依赖能量变化的表征应变,可以得到表征应力与可直接测量的量之间的解析表达式;根据两个不同压入深度与压头半径的比值的表征应变和表征应力,可以唯一地确定材料的塑性特性。数值算例显示目前的方法可适用于多种材料,包括高弹性材料和高塑性材料;分析了目前算法的存在性、唯一性和稳定性。利用相似的方法,提出考虑摩擦的影响时,用球形压头压入提取延性材料的塑性特性的方法,并讨论了一些决定摩擦对压入响应影响的关键因素。研究发现,摩擦的影响和压入过程中弹性功与总功的比值有密切关系;弹性功与总功的比值越大,摩擦对压入的影响越小,当弹性功与总功的比值大于0.65时,摩擦的影响可以忽略。更多还原

【Abstract】 Many significant problems in engineering are well known as inverse problems,including the determination of residual stresses in structure, the identification ofmaterial characteristics and other parameters, and so on. Because the inverseproblems are much difficult to solve than corresponding direct problems, numericalmethods become the main powerful tools to treat them, and sometimes incombination with experimental tests. In this thesis a number of inverse approachesare presented, related to constructing residual stress field in planar and axisymmetricstructures based on fewer testing data, and extracting the plastic properties of ductilematerials from spherical indentation tests.An inverse approach based on the inherent strain method using BEM ispresented for constructing the planar residual stresses field, which meets theself-equilibrium conditions. To enhance the stability of the inverse analysis, theinherent strain field is approximately expressed as a series of smooth basis functions.In order to preserve the advantage of the BEM, the domain integral in integralequation is transformed into boundary integral by means of the dual reciprocityboundary element method (DRBEM). In this way the explicit expression of thesensitivity matrix can be obtained and the distribution of residual stresses can beconstructed efficiently. Numerical examples show the applicability of the presentedscheme.A similar approach is proposed for constructing residual stress field inaxisymmetric structure. After the equilibrium equations with body forces in terms ofGalerkin-Papkovich vectors and the displacement expressions usingGalerkin-Papkovich vectors are deduced, corresponding domain integral can betransformed into boundary integral by means of the DRBEM. The explicit expressionof the sensitivity matrix can be obtained and the distribution of residual stresses canbe constructed efficiently.An energy based inverse approach for extracting plastic properties of ductilematerials from spherical indentation tests is presented, based on dimensional analysisand finite element computations. By defining a representative strain dependent on theenergy, for a given ratio of the indentation depth to indenter radius, a closed-fromexpression of the relationship between the directly measurable quantities and therepresentative stress was obtained. Based on the representative strains and stressescorresponding to two different ratios of the indentation depth to indenter radius, theplastic properties of materials are uniquely determined. Numerical examples andfurther theoretical analysis show that the present method is robust for a wide range ofmaterials, including both highly plastic and highly elastic materials. The existence,uniqueness and especially the stability of the solution of the present algorithm havebeen proved.A similar approach is proposed for extracting plastic properties of ductilematerials by taking the effect of friction into consideration and the key factors indetermining the effect of friction on the indentation response is discussed. It is shownthat the effect of friction is closely related to a directly measurable quantity, i.e., theratio between the reversible work and the total work done by the indenter. The biggerthe ratio of the reversible work to the total work is, the smaller the effect of friction is,and the effect of friction can be neglected provided the ratio of the reversible work tothe total work is bigger than 0.65.更多还原