Mathematical Model for the Numerical Solution of Nonstationary Problems in Solid Mechanics by a Modified Godunov Method

A mathematical model of substance behavior under developed elastoplastic strains is worked out for solving onedimensional problems of solid mechanics. The model is based on the fundamental laws of conservation of mass, momentum, and total energy, Wilkins model, kinetic model of substance destruction, and modified Godunov method for the numerical solution of problems in mathematical physics. A hybrid difference scheme is constructed, which approximates acoustics equations with constant coefficients in smooth flows for the case of plane symmetry with the second order in time and space.     

底部两层框剪砖房层间侧移刚度比的合理取值

底部框剪结构多层砖房在城市建设中应用广泛。这种房屋的特点是由两种承重和抗侧力体系构成的。以典型房屋为基础。编制了剪切型结构弹塑性动力时程分析通用程序，通过减小剪力墙厚度。数量或材料标号的方法，基佗层的质量和刚度不变，采用多种层间侧移刚度比以及多种层数进行了弹塑性动力分析。讨论了这类房屋相邻层间侧移刚度比的合理取值问题，可供工程设计和编制有关的规范，规程参考。     

On two approaches to determining the axisymmetric elastoplastic stress-strain state of laminated shells made of isotropic and transversely isotropic bimodulus materials

The paper compares two approaches to determining the axisymmetric elastoplastic stress-strain state of laminated shells made of isotropic and transversely isotropic materials with different elastic moduli in tension and compression. The approaches use different nonlinear constitutive equations describing the elastic deformation of the transversally isotropic bimodulus materials. Both approaches employ the theory of deformation along paths of small curvature and the Kirchhoff-Love hypothesis for the whole laminate to describe the deformation of the isotropic materials. The problem is solved by the method of successive approximations. The solutions of specific problems obtained by the two approaches are analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 6, pp. 59–69, June 2008.     

应变硬化薄板夹持型滚弯成形过程分析

现存文献对薄板的连续滚弯成形过程的数学模拟多限于讨论三辊轮解锥型弯板过程,且基于较多的假定和板的小变形情况。而开发有更多的功能和更高的生产效率的四辊轮连续弯板机需研究夹持型滚弯成形过程。本文将「１」的工作,理想塑性材料平面应变薄板的夹持型连续滚弯成形过程的弹塑性大变形弯曲的力学分析,推广至一般应变硬化材料的情形。得出了控制微分方程的解析解。采用固支边界条件模拟刚度很大的平持系统对板的夹持。通过对线     

广义弹塑性梁理论及接触问题中的时偶变分不等式*

为研究摩擦接触问题,本文建立了一个具有二类独立交量的二维弹塑性梁模型。由此提出了一个新的非线性二次互补性问题。其中的外部互补性条件定义了自由边界;而内部互补性条件则控制了弹塑性分界面。文中证明了此二次互补性问题等价于一非线性变分不等式,并导出了其对偶变分不等式。本文结果显示对偶问题较原问题有更多的优越性。应用于塑性极限分析理论中,文中最后证明了一个简单的下限定理。     

THE CONSTITUTIVE EQUATION RESEMBLANCE OF ELASTIC-PLASTIC MULTIPHASE SOLID

Based on composite materials,the equivalent elastic-plastic constitutive equations ofmultiphase solid are researched.According to the suggested definition of.constitutiveequivalence it is demonstrated that the multiphase solid,composed of several kinds ofhomogeneous elastic-plastic media that conform to the generalized normality rule,has thesame type of constitutive equations as its constituents have that also conform to thegeneralized normality rule.     

砂井地基的一个简化计算模型

基于三维有限元方法,提出了一个预测和评价砂井地基的简化计算模型。该计算模型采用块体单元模拟砂井周围的土体,用砂井单元模拟砂井的竖向排水和水平排水过程,并且推导了反映土体单元和砂井单元之间排水过程的连续性方程。克服了以往有限元法计算砂井地基时,需要将砂井和周围土体作均质化等价的缺点,并可用弹塑性模型反映砂井周围土体的非线性变形和强度特性。计算了单个砂井地基固结排水过程。通过和理论解的比较表明,用本文简化计算模型得到的结果和理论解比较接近。同时,还计算了日本某高速公路路基用砂井 堆载预压法处理的过程,通过分析表明,该简化模型能反映砂井地基的固结排水过程,可以应用于实际工程。     

New finite strain elastoplastic equations for accurately and explicitly simulating pseudoelastic-to-plastic transition effects of shape memory alloys

A new finite strain elatoplastic J₂-flow model with coupling effects of both isotropic and anisotropic hardening is proposed with the co-rotational logarithmic rate. In terms of certain single-variable shape functions representing uniaxial loading and unloading curves, explicit multi-axial expressions for the three hardening quantities incorporated in the new model proposed are derived in unified forms for the purpose of automatically and accurately simulating complex pseudoelastic-to-plastic transition effects of shape memory alloys (SMAs) under multiple loading-unloading cycles. Numerical examples show that with only a single parameter of direct physical meaning for each cycle, accurate and explicit simulations may be achieved for extensive data from multiple cycle tests.     

Mohr-Coulomb准则主应力回映算法及在地基问题的应用

针对Mohr-Coulomb准则在应力空间中存在奇异点的问题,提出了主应力空间应力回映算法。分析了多屈服面下塑性流动法则,给出了应力更新过程中应力回映区域的判定方法,推导了不同映射区域下塑性因子的Newton-Raphson迭代求解式和应力更新方程,建立了对应的一致切线模量表达式。利用C++语言,编制了弹塑性有限元求解程序,并对岩土地基问题进行求解,计算结果的比对证明了所编程序的可行性和精确性。