Effects of local thickness defects on the buckling of micro-beam

A buckling model of Timoshenko micro-beam with local thickness defects is established based on a modified gradient elasticity. By introducing the local thickness defects function of the micro-beam, the variable coe-cient differential equations of the buckling problem are obtained with the variational principle. Combining the eigensolution series of the complete micro-beam with the Galerkin method, we obtain the critical load and buckling modes of the micro-beam with defects. The results show that the depth and location of the defect are the main factors affecting the critical load, and the combined effect of boundary conditions and defects can significantly change the buckling mode of the micro-beam. The effect of defect location on buckling is related to the axial gradient of the rotation angle, and defects should be avoided at the maximum axial gradient of the rotation angle. The model and method are also applicable to the static deformation and vibration of the micro-beam.     

The Saint-Venant problem of plane bar under an axial force

I.PrefaceAsweknow,theSaint-Venanttheoryisawell-knownanduniversallyacceptedtheory.Butasoneofthegeneraltheoriesofelasticmechanics,itisnotprovedperfectely,althoughitistestedbyexperiments.Infact,onlyforthesimplestproblemofelasticity,itisnoteasytofindanalytics…     

滑带土动力学性质试验研究

为了研究地震高烈度区老滑坡的复活变形原因,本文对滑坡滑带土的动力学特性进行了系列研究。本次试验采用扰动土样,制样基本物理指标按滑带土的现场测试指标确定,在不固结不排水条件下,运用MTS810Teststar程控液压伺服土动三轴仪对单个样品逐级放大动应力的分级试验方法进行。侧向压力 (围压 )分别采用 100kPa、20 0kPa、300kPa三级,通过施加轴向振动荷载 (力 )模拟地震作用,振动波形为正弦波,频率为 1Hz,振幅随试样性质确定。研究结果表明,滑带土在动荷载作用下的动力学性质与其静荷载作用下的力学性质有着较大的差异,主要表现在滑带土的动应力与动应变关系的非线性、滞后性及变形积累特点,动弹性模量与动强度的显著降低以及动阻尼比的显著增大特性。这揭示了动力作用下的滑坡复活原因之一,同时为滑坡稳定性评价和动力作用下的变形机制模拟分析提供了基础资料,也为分析滑带土动力本构模型提供了基本内容。     

BEM for simulation of a 2D elastic body with randomly distributed circular inclusions

Based on our 2D BEM software THBEM2 which can be applied to the simulation of an elastic body with randomly distributed identical circular holes, a scheme of BEM for the simulation of elastic bodies with randomly distributed circular inclusions is proposed. The numerical examples given show that the boundary element method is more accurate and more effective than the finite element method for such a problem. The scheme presented can also be successfully used to estimate the effective elastic properties of composite materials. Project supported by the National Natural Science Foundation of China (No. 19772025).     

Hitting probabilities and the Hausdorff dimension of the inverse images of a class of anisotropic random fields

Let X = {X(t):t ∈ R~N} be an anisotropic random field with values in R~d.Under certain conditions on X,we establish upper and lower bounds on the hitting probabilities of X in terms of respectively Hausdorff measure and Bessel-Riesz capacity.We also obtain the Hausdorff dimension of its inverse image,and the Hausdorff and packing dimensions of its level sets.These results are applicable to non-linear solutions of stochastic heat equations driven by a white in time and spatially homogeneous Gaussian noise and anisotropic Guassian random fields.     

解弹性力学第二类边界积分方程的求积法与分裂外推

利用Sidi奇异求积公式,提出了解曲边多角形域上线性弹性力学第二类边界积分方程的求积法,即离散矩阵的每个元素的生成只需赋值不需计算任何奇异积分.通过估计离散矩阵的特征值和利用Anselone聚紧收敛理论,证明了近似解的收敛性;同时得到了误差的多参数渐近展开式;通过并行地解粗网格上的离散方程,利用分裂外推获得了高精度近似解和后验误差.     

需求弹性在价格决策中的应用

将着眼点由总收益改变为总利润,对于需求弹性用于价格决策,利用微积分方法,分5种情况进行推导,得到的结论修正和补充了现行"经济数学"、"市场营销学"和"管理经济学"等教科书里讲的内容,并在此基础上进一步研究了最佳调价量问题.     

On stress-based piecewise elasticity for limited strain extensibility materials

A one-dimensional stress-based elasticity model with limited strain extensibility is developed in this paper, based on thermodynamics arguments. Such nonlinear elastic models can be used to model certain rubber-like and biological materials with limiting chain extensibility. The derived constitutive function is a non-smooth piecewise expression, which can be regularized for numerical or physical considerations. This non-smooth constitutive expression is derived from a Gibbs potential. A three-dimensional extension of this stress-based model is also proposed in the paper. Some simple structural examples are investigated for a bar composed of this non-smooth elastic body. A homogeneous bar composed of this new class of nonlinear elastic material that is loaded is studied for different tension states, namely for concentrated or distributed axial loading. It is shown that the displacement limit extensibility can be observed at the structural scale, with finite or infinite axial load parameters.     

Generating functions for volume-preserving transformations

A general implicit solution for determining volume-preserving transformations in the n-dimensional Euclidean space is obtained in terms of a set of 2n generating functions in mixed coordinates. For n=2, the proposed representation corresponds to the classical definition of a potential stream function in a canonical transformation. For n=3, the given solution defines a more general class of isochoric transformations, when compared to existing methods based on multiple potentials. Illustrative examples are discussed both in rectangular and in cylindrical coordinates for applications in mechanical problems of incompressible continua. Solving exactly the incompressibility constraint, the proposed representation method is suitable for determining three-dimensional isochoric perturbations to be used in bifurcation theory. Applications in non-linear elasticity are envisaged for determining the occurrence of complex instability patterns for soft elastic materials.     

GPU-accelerated molecular dynamics simulation for study of liquid crystalline flows

We have developed a GPU-based molecular dynamics simulation for the study of flows of fluids with anisotropic molecules such as liquid crystals. An application of the simulation to the study of macroscopic flow (backflow) generation by molecular reorientation in a nematic liquid crystal under the application of an electric field is presented. The computations of intermolecular force and torque are parallelized on the GPU using the cell-list method, and an efficient algorithm to update the cell lists was proposed. Some important issues in the implementation of computations that involve a large number of arithmetic operations and data on the GPU that has limited high-speed memory resources are addressed extensively. Despite the relatively low GPU occupancy in the calculation of intermolecular force and torque, the computation on a recent GPU is about 50 times faster than that on a single core of a recent CPU, thus simulations involving a large number of molecules using a personal computer are possible. The GPU-based simulation should allow an extensive investigation of the molecular-level mechanisms underlying various macroscopic flow phenomena in fluids with anisotropic molecules.