层状弹塑性板动力变形的数值研究(英文)

本文研究了搁置在任意形状轴承上的层状平板,加上脉冲载荷(如炸药爆炸),结果产生塑性流动,改变了板和轴承的接触和破坏了层状板之间的接合,使之发生滑移,最后板形成残余形变,强动载冲击板产生形变的实际过程可分为两个阶段:第一阶段为应力波的传播和在板内应力波的相互作用,主要是从自由面反射的应力波和从轴承面反射的应力波,波经重复几次反射后,造成板的屈曲状态,其间,板的中间层始终保持中线弹性状态。第二阶段为板内某些截面发生塑性形变,随厚度不同而不同地收缩,同时所有的板均拉伸而增加了板的弯曲,最后,塑性形变消耗掉能量后,板各单元变为弹性状态而产生某种模型的振动。     

固支圆板安定性的实验研究

本文利用机动法求解固支圆板在循环集中力作用下的安定问题,得到了安定载荷的理论解;利用激光全息的实验方法研究固支圆板的塑性累积现象,测得了安定载荷的上下限,并对实验结果进行了分析研究.     

基于高阶位移模式的压电层合板动力有限元模型

建立了含压电片层合板的有限元动力学模型。以位于压电层上下表面处的电场强度和层间电压为未知量,给出了三次函数的电势分布模式,采用Reddy的高阶剪切理论描述板的位移场,假设板厚度方向的正应力为零给出了减缩的本构方程,采用有限元方法,基于Hamilton原理导出结构的动力学方程,然后用静态缩聚的方法压缩掉电场自由度和次要的位移自由度。最后用四边形矩形单元求解了一对称铺层和非对称铺层悬臂板的固有频率,并与ANSYS结果对比验证了本文模型的精确性。     

样条边界元法分析圆形基础板非线性非光滑接触

本文用样条边界元法分析轴对称圆形基础板的非线性非光滑接触。除事先给出外力与地基表面位移的对应关系外,地基的模型、板的厚薄(Reissner/Kirchhoff型)和外荷载沿径向的分布均可是任意的。文中将地基反力看作板的外载,对变量沿径向采用不等距祥条插值,并用无地基效应的板基本解。算例表明本文方法只要用少量自由度,便可得到令人满意的结果。     

复合材料面层夹层板中转动一致有效理论

采用分层位移模式，引入夹层板层间和表面剪应力协调条件，导出位移场的修正形式。根据能量误差一致原则，应用最小位能原理建立了复合材料层夹层板的基本方程和边界条件。     

A METHOD OF DETERMINING BUCKLED STATES OF THIN PLATES AT A DOUBLE EIGENVALUE

A method of determining bifurcation directions at a double eigenvalue is presented by combining the finite element method with the perturbation method. By using the present method, the buckled states of rectangular plates at a double eigenvalue are numerically analyzed. The results show that this method is effective.     

软铁磁薄板磁弹性屈曲的理论模型

铁磁弹性薄板的磁弹性屈曲问题一直作为电磁——弹性力学相互作用的一个基本模型进行研究，而作用在其磁介质上的磁力计算则是定量理论预测准确与否的关键．到目前为止，文献上已有的理论模型对悬臂铁磁梁式悬臂板在横向磁场中磁弹性屈曲的理论预测值始终高于实验值，有的甚至相差１００％左右．本文基于电磁力计算的微观安培电流模型，严格给出了软铁磁薄板等效横向磁力的宏观计算表达式．在此基础上，建立了电磁——力学相互耦合作用的非线性理论模型．该模型能描述铁磁薄板结构在非均匀横向磁场环境中的磁弹性失稳（或屈曲）．其定量分析采用了有限元法和有限差分法相结合．数值结果显示：本模型给出的磁弹性屈曲的临界磁场值与实验值符合良好．与此同时，文中还对文献中认为较成功的Ｍｏｏｎ－Ｐａｏ模型的基本假设进行了分析．定量结果发现：Ｍｏｏｎ－Ｐａｏ理论模型的基本假设仅在梁式板的长厚比Ｌ／ｈ比较大时（约在２００左右），是可以接受的，而当Ｌ／ｈ较小时，该假设将导致理论值与实验值的较大误差．Ｌ／ｈ比值越小，理论值与实验值的误差越大     

Effects of boundary conditions and anisotropy on elastically bent silicon

In four-point bending, the rollers that are used for load application impose additional constraints on the specimen that affect the anticlastic specimen curvature and cause the specimen displacement and stress profiles to deviate from the pure beam bending case. In this study, x-ray microdiffraction is used to map both the principal and anticlastic curvatures of elastically bent, rectangular (100)-type Si strips possessing width:thickness ratios of 40:1. We quantify the amount of roller constraint and show that the region over which the anticlastic specimen curvature is affected away from the roller is approximately five times the roller diameter. Consequently, for bending tests used to determine Poisson's ratio, if a region on the sample that is free from roller effects is not chosen, measurement errors as high as 46% can occur. Furthermore, we show that, due to the anisotropy of single crystal Si, this roller-constraining effect depends on crystallographic orientation and is more pronounced when the principal bending axis lies along the <100> direction as compared with the <100> direction.     

粘弹层合板的稳态振动和层间应力

应用混合分层理论和Ressiner混合变分原理，在板厚方向取二次位移插值函数和三次、四次横向应力插值函数推导出粘弹层合板的动力学方程，得出简支粘弹层合板稳态振动的解。不仅得出与三层弹性板精确的自振频率吻合良好的解，而且对于粘弹层合板，所计算的自振频率和结构损耗因子也与三维结果吻合较好。计算了自由阻尼层合板对应的低阶法向位移响应幅值和层问横向应力的幅值。结果表明，较高的层间横向正应力是低频稳态振动中引起粘弹层合板分层破坏的主要因素，采用适当模量和厚度的粘弹性材料将有效地降低粘弹层合板的层间横向正应力的幅值。     

On the finite displacement analysis of quadrangular plates

In this paper, a numerical method for the linear and geometrically non-linear static analysis of thin plates is presented. The method begins with the elasticity equations pertaining to strain components, stresses, displacement components, strain energy and work due to externally applied loads. The plate geometry is defined by a quadrangular boundary with four straight edges and the natural coordinates in conjunction with the Cartesian coordinates are used to map the geometry. The matrix equation of equilibrium is derived using the work-energy principle with the displacement fields expressed by algebraic polynomials, the coefficients of which are then manipulated to satisfy the kinematic boundary conditions. To validate the results from the present method, square plates having all sides fully fixed and all sides simply supported without in-plane movement are analysed. Comparison is made for the uniformly loaded square plate with the results obtained by Levy who solved the non-linear plate bending problem using the Th.von Ka’rma’n’s equations. Rhombic plates are examined and numerical results corresponding to these cases are presented in this paper. Very good comparison of the results regarding deflection and bending stresses with other sources available in the literature is found.