谈拉格朗日中值定理在高等数学课程教学中的应用

拉格朗日中值定理是微分学的基础定理之一,是连接函数及其导数之间关系的桥梁,有着广泛的应用。文章用七个例题,从三大方面总结了拉格朗日中值定理的灵活应用。这对于正确的理解和掌握拉格朗日中值定理,以及以后进一步学习数学具有重要的作用和深远的意义。     

油田站外单管集油辅助工艺对比

为了解决部分油井无法单管输送的问题,采用PIPESIM模拟软件对不同含水率、不同集输半径和不同产液量油井的集输管线进行计算分析,同时结合各油田单管集输设计经验,得出中质原油站外系统单管集油工艺改造的技术界限,而对于达不到技术界限的油井,可以通过辅助措施实现单管集油,通过对比电磁加热器、空气源热泵、管道内置电伴热、井口气电加热器、油井保温隔热油管、地热、太阳能光热技术及井口加药等单管辅助措施的原理及工艺特点,最终确定在不同工况条件下的辅助单管集输措施,为油田站外单管集输工艺选择和优化提供了理论依据。     

Prediction of forming limit in hydro-mechanical deep drawing of steel sheets using ductile fracture criterion

It has been observed that the forming limit curve at fracture (FLCF) of steel sheets, with a relatively higher ductility limit have linear shapes, similar to those of a bulk forming process. In contrast, the FLCF of sheets with a relatively lower ductility limit have rather complex shapes approaching the forming limit curve at neck (FLCN) towards the equi-biaxial strain paths. In this study, the FLCFs of steel sheets were measured and compared with the fracture strains predicted from specific ductile fracture criteria, including a criterion suggested by the authors, which can accurately describe FLCFs with both linear and complex shapes. To predict the forming limit for hydro-mechanical deep drawing of steel sheets, the ductile fracture criteria were integrated into a finite element simulation. The simulation, results based on the criterion suggested by authors accurately predicted the experimetal, fracture limits of steel sheets for the hydro-mechanical deep drawing process.     

板料双向加压液压胀形数值模拟

应用商用有限元软件ANSYS/LS-DYNA,对板料的双向加压液压胀形过程进行了数值模拟.并利用韧性断裂准则作为胀形高度极限的判断依据,将模拟得到的必要数据代入到准则中.对两种材料、不同初始液体压力条件下的模拟结果表明,随着初始液体压力的升高,胀形的极限高度也相应的增加,当初始压力与板料的强度相当时,极限高度提高的更明显.     

双剪统一强度理论在厚壁圆筒分析中的应用

运用双剪统一强度理论对厚壁圆筒进行了屈服应力函数和极限载荷的分析,得到了一系列公式,而这一理论可以运用在挤压凹模的塑性分析中。在这些计算公式中,当拉压异性系数α和中间主应力影响系数b取不同值时,可以简化成按不同的屈服准则分析的计算结果。运用双剪统一强度理论可以更好地发挥材料的强度潜力,取得更大的经济效益。     

High temperature oxidation mechanism of dilute copper aluminium alloys

Dilute copper-aluminium alloys were oxidized in air from 700 to 1000 °C. Two distinctive behaviours were observed: alloys with at least 3 wt% aluminium showed excellent oxidation resistance in the whole temperature range. Alloys with 2 wt% or less aluminium exhibited good oxidation resistance up to 800 °C; but as the temperature was further increased, the oxidation rate of these alloys increased and became comparable to that of pure copper. A kinetic model was developed to explain the oxidation behaviour and indirectly determine the amount of dissolved oxygen in the alloys tested. It was found that the oxygen dissolved in alloys with up to 2 wt% Al exceeded its solubility limit in copper, whereas the dissolved oxygen in alloys with higher aluminium contents was below the solubility limit. This difference may account for the significantly different oxidation resistance.     

圆锥形零件冲压成形极限的确定

圆锥形零件极限变形程度可用极限拉深系数［ｍｚｄ］＝［ｄ２／Ｄ０］来表示。根据圆锥形零件与圆筒形零件的内在联系，经力学分析得出了便于实用的圆锥形零件极限拉深系数［ｍｚｄ］的计算表达式，并由此给出了用［ｍｚｄ］所表示的成形极限曲线和第一次拉深时的极限拉深系数。经实验验证表明所确定的成形极限是准确和可靠的。     

调制波长对Cu／Ni金属多层膜力学性能的影响

用电沉积法在低碳钢基体上制备了具有不同调制波长(一个调制波长等于单层Cu膜与单层Ni膜厚度之和)的Cu/Ni金属多层膜，研究了多层膜硬度与其中单层膜厚度之间的关系。结果表明，当膜厚在亚微米范围内时，Cu/Ni多层膜的屈服强度(为硬度值的1/3)与单层膜厚之间符合基于位错塞积模型的Hall-Pctch(H-P)关系式；而当单层膜厚小于100nm时，屈服强度与膜厚的关系偏离了H-P线性关系。基于程开甲等人位错稳定性理论首次对金属多层膜变形行为偏离Hall-Petch关系的现象作了定量解释。     

DEPENDENCE OF PREDICTION MODEL OF FORMING LIMIT STRAINS ON FORMING METHOD AND MECHANICAL PROPERTIES OF SHEET METALS

ＤＥＰＥＮＤＥＮＣＥＯＦＰＲＥＤＩＣＴＩＯＮＭＯＤＥＬＯＦＦＯＲＭＩＮＧＬＩＭＩＴＳＴＲＡＩＮＳＯＮＦＯＲＭＩＮＧＭＥＴＨＯＤＡＮＤＭＥＣＨＡＮＩＣＡＬＰＲＯＰＥＲＴＩＥＳＯＦＳＨＥＥＴＭＥＴＡＬＳ①ＺｈｏｕＷｅｉｘｉａｎＤｅｐａｒｔｍｅｎｔｏｆＡｅ...     

INFLUENCE OF RESIDUAL STRESS AND SURFACE MORPHOLOGY ON FATIGUE PROPERTIES OF STEEL 60Mn

Influence of residual stress and surface morphology induced by shot-peening on fatigue behav-ior of a medium temperature tempered spring steel 60 Mn has been studied.The compressiveresidual stress induced in the near-surface region may improve fatigue limit from 930 to 1010MPa,and the very high tensile residual stress in the interior may reduce it from 1010 to 940MPa,whereas the severe surface damage may cause a drop-off of it from 1010 down to 800MPa.Fatigue cracks initiated in such position where the equivalent Mises stress,includingresidual stress,exceeded the local strength of the material.The compressive residual stress,induced by shot-peening,may intensify the effect of crack closure,so as to decrease the crackgrowth rate.