弹性力学反平面剪切问题的半逆解法

半逆解法是求解弹性力学问题的重要解析方法,它通过假设部分或全部应力分量的函数形式,推导出满足相容方程的应力函数,再求出满足边界条件的应力分量,进而利用位移边界条件求出位移分量。弹性力学教学中一般只介绍半逆解法在弹性力学平面问题中的运用,文章通过实例介绍了弹性力学反平面剪切问题及其应力函数法,给出了半逆解法求解弹性力学反平面剪切问题的过程,发展了半逆解法在弹性力学问题中的应用。     

考虑剪切效应有限变形粘弹性板的动力稳定性

Based on Reddy‘s theory of plates with higher-order shear deformations and the Boltzmann superposition principles,the governing equations were established for dynamic stability of viscoelastic plates with finite deformations taking account of shear effects,The Galerkin method was applied to simplify the set of equations.The numerical methods in nonlinear dynamics were used to solve the simplified system.It could e seen that there are plenty of dynamic properties for this kind of viscoelastic plates under transverse harmonic loads.The influences of the transverse shear deformations and material parameter on the dynamic behavior of nonlinear viscoelatic plates were investigated.     

固支Mindlin 板弯曲问题的辛本征解

Hamiltonian system for the problem on clamped Mindlin plate bending was established by introducing the dual variables for the generalized displacements in this letter. By separation of variables, the transverse eigen-problem was derived based on the sympletic geometry method. With the solved sympletic eigen-values, the generalized sympletic eigen-solution was derived through eigenfunction expansion. An example of plate with all edges clamped was given. The sympletic solution system was worked out directly from the Hamiltonian system. It breaks the limitation of traditional analytic methods which need to select basis functions in advance. The results indicate that the sympletic solution method could find its more extensive applications.     

弹性圆环域的混合基本问题

本文讨论弹性圆环域的混合基本问题，借助级数方法得到了弹性体应力分布封闭形式的解，并在文末给出了算例。     

弹性力学平面问题的双调和方程的格林函数解法

讨论了弹性力学双调和方程Δ4U＝0的格林（Green)函数解法。     

磁电弹性圆环板屈曲问题的哈密顿体系方法

运用哈密顿体系方法给出了磁电弹性圆环板屈曲问题的解析解,并对磁电弹性圆环板的纯弯曲问题进行了分析.算例结果表明,采用哈密顿体系方法求解磁电弹性圆环板屈曲问题非常方便快捷.     

考虑孔隙损伤的黏弹性材料压力容器问题

应用线弹性微结构理论和黏弹性理论,讨论了带孔隙损伤的黏弹性材料压力容器问题.所得的解是准静态的.应力的解和线弹性的压力容器的应力解相同,位移场和损伤场与带孔隙损伤的线弹性材料压力容器问题的位移场和损伤场相似.     

考虑泊松效应的黏弹性轴向功能梯度Timoshenko微梁的尺寸依赖行为(英文)

建立了黏弹性功能梯度(FG) Timoshenko微梁的尺寸依赖连续模型,其材料参数沿轴向随幂律变化.为研究微梁的尺寸效应,利用修正偶应力理论和Kelvin-Voigt黏弹性模型将材料的黏性项纳入应力和偶应力张量的偏离分量中;结合Timoshenko梁理论导出了应变、曲率、应力和偶应力的分量;基于哈密顿原理,给出了任意截面形状的微梁在任意荷载作用下的控制微分方程和边界条件.然后,以点荷载作用下的简支微梁为例,研究了尺寸效应、功能梯度效应、泊松效应以及截面形状对黏弹性微梁力学行为的影响.结果表明:当微梁尺寸足够小时,其转角、正应力和偶应力的尺寸效应明显;当微梁尺寸足够大时,微梁的功能梯度效应较为明显;此外,泊松比对尺寸效应影响较大,梁截面形状也是影响微梁力学性能的重要因素.     

与霍尔效应有关的几个问题

在2000年高考理科综合能力测试卷(浙江、江苏、吉林卷)中，第29题是一道关于霍尔效应的考题，它综合考查了力学、电磁学知识在实际问题中的应用．题目的具体内容请参见本期第51面，笔者现就其解答以及几个与霍尔效应有关的问题作一讨论．     

微分求积法求解不可压二阶粘弹性流体和热迁移模型中的稳态流动

1IntroductionAlthoughthe computation of the fluid mechanics hasgreat development during the last decades,due to themodel in nonlinear fluid mechanics is very complicat-ed,the more efficient techniques for solvingthis prob-lemstill attract the interest of many researchers.Thedifferential quadrature method(DQM)introduced byBell man,et al.[1,2]is an efficient numerical methodfor solving partial differential equations.In recentyears,the DQMhas been widely used for solving theproblems of enginee…     

混合型微分求积法对求解联立的二维不可压Navier-Stokes方程和热方程的应用

1　Introduction　Variousnumericaltechniques,suchasthefinitedifferencemethodandfiniteelementsmethod ,havebeenusedinthepasttosolvetheincompressibleflowproblemnumerically .Usually ,thesemethodsrequirealargenumberofdiscretizedpointsinthecomputa tionaldomainforaccurateresults .Becausetheinfor mationonallgridpointsisusedtofitderivativesatgrid pointsinthedifferential quadrature (DQ )method ,itisenoughtouseonlyfewgridpointstoob tainhigh accuracynumericalsolutions .Therefore ,thenumberofgridpointscanb…     

结合非线性互补问题函数的滤子逐次二次规划算法

A mechanism for proving global convergence in filter-SQP(sequence of quadratic programming)method with the nonlinear complementarity problem(NCP)function is described for constrained nonlinear optimization problem.We introduce an NCP function into the filter and construct a new SQP-filter algorithm.Such methods are characterized by their use of the dominance concept of multi-objective optimization,instead of a penalty parameter whose adjustment can be problematic.We prove that the algorithm has global convergence and superlinear convergence rates under some mild conditions.     

三类一阶微分方程的求解公式

文献对三类一阶徽分方程的求解，采用先找积分因子，再利用积分因子转化为全微分方程，然后按全徽分方程的求解方法求解，其过程较繁复．本文借用变量替换法，化为变量可分离的方程，直接给出通解的积分形式，推广了方程的可积类型，并使求解过程大为简化．