斜磁场中矩形铁磁薄板的几何非线性磁弹性行为分析

基于复杂磁场中铁磁介质磁弹性广义变分原理,给出了包含磁场、铁磁薄板几何非线性的一组基本方程,并对斜磁场中铁磁薄板的磁弹性弯曲问题进行了分析.根据铁磁板内磁场分布特点定性分析了铁磁薄板所受磁力的特征,建立了考虑铁磁板磁场端部效应以及耦合非线性、几何非线性的磁弹性有限元模型,数值模拟了铁磁薄板的磁弹性耦合弯曲特性并给出铁磁悬臂、简支薄板随磁场倾角变化的磁弹性弯曲变形特征等,数值结果与定性分析结果吻合良好.     

悬臂铁磁板磁弹性耦合作用的力学分析

对有限板宽的悬臂铁磁板在外磁场中的磁弹性相互耦合作用的力学行为，建立了描述板弯曲和稳定性的理论模型及有限元定量分析程序，研究了外磁场倾斜角对板磁弹性失稳的临界磁场值的影响。     

Reissner矩形的板的弯曲问题

本文根据Ｒｅｉｓｓｎｅｒ平板理论，提出矩形中厚板弯曲问题的解答，应用本文中的（５），（９）式，可求解通常界条件下，承受横向均力Ｑ以及承受横向均布力和板边法向弯矩等组合荷载共同作用下的矩形中厚板的弯曲问题，而且使这类问题的解答规律化。     

铁磁梁式板的磁弹塑性动力特征分析

针对典型的矩形磁脉冲,研究了横向磁脉冲作用下线性强化材料铁磁梁式板的磁弹塑性动力响应及其动力失稳特征,给出了线性强化铁磁梁式板的弹塑性动力失稳特征曲线;探讨了塑性应变强化系数对铁磁梁式板的动力响应特征曲线、最终平衡位置、残余构形等的影响.数值结果表明:在同等条件下,塑性应变强化系数越大,其相应铁磁梁式板的动力失稳磁场值越大,其相应的残余构形越小.     

ANALYSIS ON THE MAGNETO-ELASTIC-PLASTIC BUCKLING/SNAPPING OF CANTILEVER RECTANGULAR FERROMAGNETIC PLATES

An analysis of buckling/snapping and bending behaviors of magneto-elastic-plastic interaction and coupling for cantilever rectangular soft ferromagnetic plates is presented.Based on the expression of magnetic force from the variational principle of ferromagnetic plates,the buckling and bending theory of thin plates,the Mises yield criterion and the increment theory for plastic deformation,we establish a numerical code to quantitatively simulate the behaviors of the nonlinearly multi-fields coupling problems by the finite element method.Along with the phenom- ena of buckling/snapping and bending,or the characteristic curve of deflection versus magnitude of applied magnetic fields being numerically displayed,the critical loads of buckling/snapping, and the influences of plastic deformation and the width of plate on these critical loads,the plastic regions expanding with the magnitude of applied magnetic field,as well as the evolvement of deflection configuration of the plate are numerically obtained in a case study.     

均布荷载下悬臂矩形中厚板的弯曲

本文从Reissner平板理论出发,对广义简支边的概念作了补充和推广,应用叠加法获得了均布荷载下悬臂矩形板弯曲的精确解。由于考虑了横向剪切变形的影响,所得结果可用于中厚板。     

一边简支二角点支承的矩形板弯曲

在分析求解条件完备性的基础上将矩形板的弯曲划分为广义静定问题和广义超静定问题，分别采用直接求解和叠加法解决了一边简支一角点支承和一边简支二角点支承的矩形板在板面分布荷载、板边分布荷载、角点集中力作用下以及角点支承产生支座沉陷时的弯曲。计算表明这种解法收敛快，计算精度高，适用范围广     

矩形智能板弯曲形状的主动控制

研究具有离散分布压电控制器的矩形智能板,在外加电场作用下的弯曲形状与压电元件外加控制电压之间的关系,建立了对智能矩形板的弯曲形状进行主动控制的方法,得到各离散分布压电元件控制电压的解析解,并给出了算例     

角支及多点支承矩形板的弯曲

本文取两对边简支另两对边自由的板为初始解,用迭加法在两边简支板上迭代消去板边上的剪力。为了简化消去板边剪力的复杂迭代过程,作者提出了高精度的简化方法,将无限迭代简化为一次计算,将角支板的求解化为计算两个对边简支矩形板的简单问题。对于多点支承矩形板,则可取角点支承板为基本结构用力法求解。文中还提出了一些实用经验公式,列出了典型算例,验证了方法的适用性和高精度。     

悬臂矩形板的对称弯曲与稳定性

运用弹性理论的里兹法,选择多项式和三角函数混合形式作为挠曲函数,讨论是悬臂形板的对称弯曲和稳定性问题,通过算例分析与比较,表明本文结果与文献基本吻合,且计算过程简单。     

A free rectangular plate on elastic foundation

This article will discuss the bending problems of the rectangular plates with free boundaries on elastic foundations. We talk over the two cases, that is, the plate acted on its center by a concentrated force and the plate subjected to by a concentrated force equally at four corner points respectively. We select a fiexural function which satisfies not only all the geometric boundary conditions on free edges wholly but also the boundary conditions of the total internal forces. We apply the variational method meanwhile and then obtain better approximate solutions.     

一边固定一角点或二角点支承的矩形板弯曲统一求解方法

本文的统一法可以解决悬壁板或带有角点支承时在任意荷载作用下的弯曲。这种方法求解思路清晰、收敛速度快,计算精度高。     

BENDING SOLUTION OF A RECTANGULAR PLATE WITH ONE EDGE BUILT－IN AND ONE CORNER POINT SUPPORTED SUBJECTED TO UNIFORM LOAD

ＢＥＮＤＩＮＧ　ＳＯＬＵＴＩＯＮ　ＯＦ　Ａ　ＲＥＣＴＡＮＧＵＬＡＲ　ＰＬＡＴＥ　ＷＩＴＨ　ＯＮＥ　ＥＤＧＥ　ＢＵＩＬＴ－ＩＮ　ＡＮＤ　ＯＮＥ　ＣＯＲＮＥＲ　ＰＯＩＮＴ　ＳＵＰＰＯＲＴＥＤ　ＳＵＢＪＥＣＴＥＤ　ＴＯ　ＵＮＩＦＯＲＭ　ＬＯＡＤＸｕＱｉｌｏ...     

无网格法在点弹性支承矩形薄板横向振动中的应用

基于薄板理论和弹性动力学Hamilton原理的推广,采用无网格伽辽金法,建立了具有有限多个点弹性支承的弹性矩形薄板横向振动的无量纲量运动微分方程,给出了其特征方程。通过求解特征方程,得出了四边简支板的无量纲固有频率随点弹性支承的刚性系数和支承位置的变化曲线,分析了点弹性支承的刚性系数和支承位置对矩形薄板横向振动特性的影响。数值计算结果表明,无网格法求解点弹性支承板横向振动问题是切实可行的。     

四边自由各向异性矩形中厚板弯曲解析解

将基于阿穆巴诸米扬各向异性中厚板理论的控制方程、不同支撑下建立的板与支撑的协调方程以及板的自由边界条件,通过对称性分解成中心对称问题和中心反对称问题的叠加。利用傅立叶三角级数求解混合奇偶阶偏微分方程组,求得包括板的内力和支撑反力表达式的弯曲解析解。本文方法取消了直法线假设,克服了数学上的求解困难,去除了数值法的弊端,得出的结果更贴近实际。用该方法不但可以研究四边自由各向异性中厚板的弯曲特性和振动特性,而且还可分析不同边界约束下各向异性矩形中厚板的静动力特性。     

Magnetoelastic bending and stability of soft ferromagnetic rectangular plates

I.IntroductionSofar,twokindsofphenomenaofmagnetoelasticinteractiontoferromagneticplatesinappliedmagneticfieldshavebeenfound.Oneisthemagnetoelasticbuchlingorillstabllitytoacantileveredbeam-plateinatransversemagneticfieldt'],thatisthephen1Onlenollot'negiltivemagneticstiffness,whiletheotheristheincreaseofnaturalfrequencyoftheplatewhichisfreelyviratinginanin-planemagneticfieldl=],thatisthephenomenonofpositivemagneticstiffness.Inordertosimulatethesetwokindsofexperimentalphenomena,sometheoreticalmo…     

Series solutions for a transversely loaded and completely clamped thick rectangular plate based on the three-dimensional theory of elasticity

Summary The bending of a thick rectangular plate with all the edges completely clamped is analyzed by the three-dimensional theory of elasticity. A partially distributed uniform load over the top face is dealt within the analysis. The boundary conditions of the completely clamped edges are prescribed by three-dimensional, exact conditions that three displacement components vanish at the faces. The stress distributions at the edges are minutely examined by making the best use of advantages of the exact analysis. The stress distributions for the case of a fully distributed uniform load are compared with those obtained by Reissner's theory. The values of deflections and internal forces for various thickness-length ratios are also presented. Accepted for publication 5 June 1997     

The growth of the void in a hyperelastic rectangular plate under a uniaxial extension

In the present paper, the finite deformation and stress analysis for a hyperelastic rectangular plate with a center void under a uniaxial extension is studied. In order to consider the effect of the existence of the void on the deformation and stress of the plate, the problem is reduced to the deformation and stress analysis for a hyperelastic annular plate and its approximate solution is obtained from the minimum potential energy principle. The growth of the cavitation is also numerically computed and analysed.Project supported by the National Natural Science Foundation of China     

An approximate solution with high accuracy of transverse bending of thin rectangular plates under arbitrarily distributed loads

Ritz method is an effective way widely used to analyze the transverse bending ofthin rectangular plates.Its accuracy depends completely on the basis functions selected.This paper selects the superposition of sine series with polynomials as the basisfunctions of thin rectangular plates.The calculating formulae are not only simple andeasily programmed,but also have high accuracy.Finally,two numerical results aregiven and compared with those obtained by the classical method.