在有限变形条件下损伤粘弹性梁的动力学行为

本文在有限变形条件下,根据损伤粘弹性材料的一种卷积型本构关系和温克列假设,建立了粘弹性基础上损伤粘弹性Timoshenko梁的控制方程.这是一组非线性积分--偏微分方程.为了便于分析,首先利用Galerkin方法对该方程组进行简化,得到一组非线性积分-常微分方程.然后应用非线性动力学中的数值方法,分析了粘弹性地基上损伤粘弹性Timoshenko梁的非线性动力学行为,得到了简化系统的相平面图、Poincare截面和分叉图等.考察了材料参数和载荷参数等对梁的动力学行为的影响.特另,考察了基础和损伤对粘弹性梁的动力学行为的影响.     

多孔Mooney-Rivlin材料矩形板的单向拉伸

本文利用不可压超弹性材料大变形的Mooney-Rivlin应变能函数研究了含有多个微孔的矩形板在单向拉伸作用下的有限变形和受力分析.首先利用不可压条件得到了文中所给的含有某种对称性分布的多个微孔的矩形板的变形模式函数,其中所含的一个参数可由远离微孔的无穷远处的变形状态确定,另一个参数可用最小势能原理导出变分近似解.文中详细分析了板中微孔(一个、三个和五个)随载荷作用的增长情况和微孔边缘应力的分布情况,并进行了比较.讨论了微孔的个数和排列方式、微孔的大小和孔间距离等因素对微孔增长和应力分布的影响.     

粘弹性介质中逆散射问题的求解方法

本文讨论了一维粘弹性介质中的逆散射问题,给出了两种反演粘弹性介质松弛模量的方法。这两种方法只利用了介质层一侧波的反射数据,其中一种方法只需已知一个走时来回时间内的反射数据就可以确定介质的松弛模量在任意时刻的值。文中最后给出了数值算例,可以看出,数值反演的结果与初始给定的松弛模量吻合得很好。     

Generalized variational principles of the viscoelastic body with voids and their applications

From the Boltzmann‘ s constitutive law of viscoelastic materials and the linear theory of elastic materials with voids, a constitutive model of generalized force fields for viscoelastic solids with voids was given. By using the variational integral method, the convolution-type functional was given and the corresponding generalized variational principles and potential energy principle of viscoelastic solids with voids were presented. It can be shown that the variational principles correspond to the differential equations and theinitial and boundary conditions of viscoelastic body with voids. As an application, a generalized variational principle of viscoelastic Timoshenko beams with damage was obtained which corresponds to the differential equations of generalized motion and the initial and boundary conditions of beams. The variational principles provide a way for solving problems of viscoelastic solids with voids.     

Differential quadrature method for bending of orthotropic plates with finite deformation and transverse shear effects

Based on the Reddy ‘s theory of plates with the effect of higher-order shear deformations, the governing equations for bending of orthotropic plates with finite deformations were established. The differential quadrature ( DQ ) method of nonlinear analysis to the problem was presented. New DQ approach, presented by Wang and Bert ( DQWB), is extended to handle the multiple boundary conditions of plates. The techniques were also further extended to simplify nonlinear computations. The numerical convergence and comparison of solutions were studied. The results show that the DQ method presented is very reliable and valid. Moreover, the influences of geometric and material parameters as well as the transverse shear deformations on nonlinear bending were investigated. Numerical results show the influence of the shear deformation on the static bending of orthotropic moderately thick plate is significant.     

BOUNDARY ELEMENT METHOD FOR SOLVING DYNAMICALRESPONSE OF VISCOELASTIC THIN PLATE(II)──-THEORETICAL ANALYSIS

I.IntroductionInpaper[l],thedynamicresponseoftheviscoelasticthinplate-onrectangledomainisdiscussedbytheusingofthetwokindsofapproximatefundamentalsolutionsandthecorrespondingboundaryelementmethod(BEM)inLaplacespace.Theanalysisofthenumericalexamplesshowsthatonlywhenthetruncatednumberkintheapproximatefundamentalsolutionandthemaximummeshsizehsatisfycertainrelation,itcouldbeguaranteedthattheapproximatesolutionhaveenoughaccuracy.Inpresentpaper,theerrorestimationfortheapproximateboundaryelemelltmet…     

考虑损伤时带微孔粘弹性体的应力分布

本文根据粘弹性理论和带空沿材料的线性理论,利用Laplace变换及其逆变换,给出了粘弹性损伤材料的一种本构模型。应用这种本构关系。讨论了带损伤的圆环形板或圆筒体在内外压力作用下的平面问题,得到了圆孔边缘附近的应力场和损伤增量场的分布情况,同时根据Laplace变换的终值定理,得到圆环或圆筒的终态应力和损伤增量的分布,并分析了工程中的一个典型的例子。得到了最终损伤的一种近似分布。可为工程设计提供一定的参考。