共查询到18条相似文献,搜索用时 406 毫秒
1.
2.
3.
本文针对四边固定载流矩形薄板,利用Mathieu方程解的稳定性,研究其在电磁场与机械荷载共同作用下的磁弹性稳定性问题。首先在载流薄板的磁弹性非线性运动方程、物理方程、几何方程、洛仑兹力表达式及电动力学方程的基础上,导出了载流薄板在电磁场与机械荷载共同作用下的磁弹性动力稳定方程,然后应用Galer-kin方法将稳定方程整理为Mathieu方程的标准形式,并将薄板的动力稳定性问题归结为对Mathieu方程的求解。利用Mathieu方程的稳定解区域与非稳定解区域的分界,即方程系数λ和η的本征值关系,得出了磁弹性问题失稳临界状态的判别方程。通过具体算例,给出了四边固定载流矩形薄板的磁弹性动力失稳临界状态与相关参量之间的关系曲线,并对计算结果及其变化规律进行了分析讨论。 相似文献
4.
5.
6.
在建立载流薄板的非线性磁弹性运动方程、电动力学方程和Lorentz力表达式的基础上,通过变量代换,将描述薄板的磁弹性状态方程整理成含有10个基本函数的标准Cauchy型.采用差分法及准线性化方法,将标准Cauchy型非线性偏微分方程组,变换成为能够用离散正交法求解的准线性微分方程组.通过算例,得到了电磁场与机械载荷联合... 相似文献
7.
弹性梁式薄板在横向绕流中的大变形 总被引:2,自引:0,他引:2
采用相容拉格朗日-欧拉(ULE)法,给出了弹性薄板理想流体横向绕流条件下变形与应力的理论算法,其中:对固体采用拉格朗日法;对流体采用欧拉法;对相互接触面采用拉格朗日法和欧拉法.建立了不问断横向绕流条件下弹性梁式薄板的大弯曲变形的非线性微分方程.求解该方程时,将纵向位移分量和曲率的改变量用挠度表示.通过具体算例分析了各参数对悬臂梁式薄板挠度、纵向位移及应力大小的影响.理论解与数值解进行比较,验证了理论解的可靠性. 相似文献
8.
针对磁场环境中受机械载荷作用变厚度载流旋转壳体热磁弹性问题,基于薄壳的几何方程、物理方程、运动方程、电动力学方程,建立其热磁弹性基本方程.应用线性化方法,得到了关于热磁弹性问题的线性迭代方程,转化为包括8个基本未知量的标准型方程组.关于载流旋转壳体,给出Lorentz力表达式,导出了温度场及温度场积分特征值.分析了变厚度锥形旋转壳体应力、温度及变形随外加电磁参量的变化规律,并通过数值模拟对理论分析进行了验证.研究结果可为载流旋转壳体热磁弹性问题研究提供理论参考. 相似文献
9.
10.
研究四边简支载流纳米板在电磁场及机械载荷作用下的磁弹性稳定问题。结合非局部理论与板壳磁弹性理论,导出考虑尺度效应的纳米板的磁弹性动力学方程,得出载流纳米板在磁场及机械载荷作用下的磁弹性动力稳定方程;利用伽辽金原理将稳定性方程整理为特殊函数马丢方程的标准形式,根据其系数的本征值关系,判别磁弹性稳定问题的最低失稳临界状态;通过数值模拟得到纳米板失稳临界电流密度与相关参数之间的关系图及变化规律。结果表明:磁感应强度、板长与板厚、外加机械载荷及小尺度参数均会影响纳米板的稳定性;当小尺度参数取1nm时,板长在200nm~450nm、板厚在1nm~10nm的区间内,纳米板的稳定性随着磁感应强度、板长及板厚的变化而急剧变化。在这个灵敏区间内改变磁感应强度、板长及板厚的大小,可以有效地提高纳米板的稳定性。 相似文献
11.
The temperature and stress field in a thin plate with collinear cracks interrupting an electric current field are determined. This is accomplished by using a complex function method that allows a direct means of finding the distribution of the electric current, the temperature and stress field. Temperature dependency for the heat-transfer coefficient, coefficient of linear expansion and the elastic modulus are considered. As an example, temperature distribution is calculated for an alloy (No. GH2132) plate with two collinear cracks under high temperature. Relationships between the stress, temperature, electric density and crack length are obtained. Crack trajectories emanating from existing crack are predicted by application of the strain energy density criterion which can also be used for finding the load carrying capacity of the cracked plate. 相似文献
12.
Using the finite element method, thermo-electro-structural coupled analyses of the cracked conducting plate under high electric current have been solved. The crack contact condition and temperature-dependent material properties are considered in this analysis. The crack tip temperature, electric current density factor, stress intensity factor and strain energy density factor are obtained for discussions. Due to high electric current density and Joule heating at the crack tip, a circular melting area may exist around the tip. After cooling, a circular void or hole may occur at the crack tip and the crack arrest is achieved. The crack tip temperature decreases when the crack contact area increases. The proper tensile load is necessary for making the crack open enough and causing high current density at the crack tip and associated crack arrest. On the other hand, the crack tip temperature increases with time by the increasing external current and Joule heating. The values of mode-I stress intensity factor and strain energy density factor decrease with time due to the thermal deformation around the crack tip. Because of the temperature-dependent resistivity, the variation of the electric current density factor is complicated. In addition, it is not easy to create a crack-arrest condition when the crack length relative to the plate width is too small. 相似文献
13.
为了研究内爆炸薄圆板的失效与作用载荷特性,在双圆筒装置内开展了铝质、钢质薄圆板内爆炸实验,分析了圆板破坏模式及比冲量载荷特性,并基于相同变形下载荷相等原理,得到了钢质圆板极限变形下的有效比冲量及作用时间,提出了该工况下圆板变形的预估模型。结果表明:在内爆炸载荷作用下,薄圆板的夹持边界和几何中心是应力集中区,产生了塑性大变形、拉伸撕裂、剪切断裂3种破坏模式;圆板的比冲量载荷由初始的波浪式增长逐渐转化为线性增长,30~80 g某温压装药使1 mm厚钢质圆板产生极限变形的有效比冲量作用时间在2.26~2.93 ms之间,经验证,圆钢板变形预估模型得到的装药质量与实验装药质量偏差小于13.3%。
相似文献14.
Introduction Manystructuralelements(pole,plate,shell)withunevenandvariablethicknessarewidely usedinallkindsofengineeringfields.Engineerscansavematerialswhentheydesignbecause theseelementshavebetteroptimizedshapeofstructuralfeature,butthisaddsdifficultytotheanalysisoftheirmechanicalcapability.Manypreviouspapers[1-4]havesolvedtheproblemof symmetricalaxis,butnobodyhassolvedtheunsymmetricalnonlineardeformationproblemof circularthinplatewithvariablethicknessandunsymmetricalaxisuptonow,afewworkonly … 相似文献
15.
研究了磁场环境中受机械载荷作用的导电圆柱薄壳的热磁弹性问题.首先,根据电动力学方程和广义Ohm定律,得到了导电薄壳电流密度的分布,考虑到Joule热效应及热平衡方程,得到了导电薄壳的温度分布.其次,通过几何方程、物理方程、运动方程和电动力学方程导出了导电薄壳在机械场、电磁场以及温度场作用下的基本方程.最后,采用差分法及准线性化方法,得到了可以应用离散正交法求解的准线性微分方程组.对于导电圆柱薄壳,得到了Lorentz力表达式,并且推导了温度场积分特征值.讨论了导电圆柱薄壳应力、温度及变形随外加电磁参量的变化规律,并通过实例证实了可以通过改变电、磁、力场的参数来实现对薄壳的应力、应变、温度的控制. 相似文献
16.
对于含圆孔及孔边非均匀材料圆环的无限大薄板,假设非均匀材料的弹性模量沿径向按照指数函数变化,而泊松比为常数,分别导出了双轴拉伸和纯剪切作用时孔边及界面处的应力集中系数的解析解.通过数值算例详细分析了非均匀材料圆环的弹性模量的变化对无限大薄板的孔边及界面处的应力集中系数的影响.研究结果表明,合理选择孔边非均匀材料圆环的材料性能变化参数可有效地缓解薄板的孔边应力集中程度.本文的研究结果可为含圆孔的薄板的设计提供一定的参考. 相似文献
17.
V. D. Kurguzov A. G. Demeshkin 《Journal of Applied Mechanics and Technical Physics》2016,57(3):494-500
The paper describes the processes of elastic deformation of thin films under mechanical loading. The film is modeled longitudinally by a compressed plate arranged on an elastic foundation. A computer model of the buckling of the narrow thin plate with a delamination portion located on an elastic foundation is constructed. This paper also touches upon the supercritical behavior of the plate–substrate system. The experiments on the axial compression of a metal strip adhered to a rubber plate are performed, and 2 to 7 buckling modes are obtained therein. The critical loads and buckling modes obtained in the numerical calculations are compared with the experimental data. It is shown that there is the possibility of progressive delamination of the metal plate from the foundation if the critical load is exceeded. It is found that the use of the proposed approach, which, in contrast to other approaches, accounts for the elastic deformation of the substrate, causes the dependence between the critical bending stress and the stiffness of the foundation. 相似文献
18.
基于形状记忆合金Brinson一维热力学本构关系和von
K\'{a}rm\'{a}n几何非线性薄板理论,研究了径向嵌入SMA丝复合材料加热圆板在横向均布
机械载荷作用下的弯曲响应,
获得了周边不可移简支和夹紧圆板的中心最大挠度与升温之间的关系曲线. 结果表明,形状
记忆合金丝在从马氏体向奥氏体的逆相变过程中所产生的相变回复力对板的弯曲变形具有明
显的调整作用. 通过嵌入SMA纤维丝和施加升温载荷可以主动而有效地调节受机
械载荷作用圆板的弯曲变形. 相似文献