Several results in the dynamic theory of thermoelastic Cosserat shells with voids

In this paper we investigate the boundary-initial-value problem of the dynamic linear theory for thermoelastic Cosserat shells with voids. We prove a reciprocity relation and derive a uniqueness theorem. Then, we study the continuous dependence of the solution on external body loads and heat supply and on initial data. A variational characterization of the solution is also established.     

Variational principles for Cosserat body

Two variational principles are derived for the mixed boundary value problem of Cosserat solid. These principles are a generalization of the stationary principle of potential energy and the stationary principle of complementary energy from non-linear theory of elasticity.     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES(Ⅶ)—INCREMENTAL RATE TYPE

The purpose is to establish the rather complete equations of motion, boundary conditions and equation of energy rate of incremental rate type for micropolar continua. To this end the rather complete definitions for rates of deformation gradient and its inverse are made. The new relations between various stress and couple stress rate tensors are derived. Finally, the coupled equations of motion, boundary conditions and equation of energy rate of incremental rate type for continuum mechanics are obtained as a special case. Contributed by Dai Tian-min, Original Member of Editorial Committee, AMM Foundation items: the National Natural Science Foundation of China (10072024); the Research Foundation of Liaoning Education Committee (990111001) Biography: Dai Tian-min (1931≈)     

Entropy Structure Within a Cosserat Fluid Involving Chemical Reactions,Heat, and Mass Transfer

In this contribution, the entropy balance equation of a Cosserat-type fluid involving chemical reactions, heat and mass transfer is derived from Gibbs relation. To this aim, the balance equations of internal, kinetic, potential and total energies of a Cosserat-type fluid are derived. Some new terms appear in the aforementioned equations in comparison to the classical theory. In the case of kinetic energy, a new balance equation is derived from the conservation law of angular momentum. The obtained equations give a deep insight into the energy content and structure of entropy within such a continuum as well as the mechanisms of energy dissipation.     

Simulation of Flow Field for Pulsatile Blood Flow in a Femoral Artery Based on Cosserat Continua

This investigation describes unsteady, pulsatile, laminar, and locally fully developed blood flow velocity and rotation fields during cardiac cycle in the femoral artery using Cosserat continuum mechanics approach. After solving the continuity, linear momentum, and angular momentum equations for flow of blood through artery, the time and position dependent velocity and rotation fields have been calculated. It is shown that the maximum values of velocity occur at the inlet core, while the maximum values of rotation occur on the arterial boundary. It is also demonstrated that the flow of blood in artery is laminar and a good agreement with existing data is established. A time dependent Gaussian equation for non-Newtonian blood viscosity coefficient γ_v has also been found.     

基于Cosserat理论的四边简支自由振动微平板尺度效应研究

微观下材料内部结构将极大地影响材料的力学性能,对微纳米器件中典型的微平板结构尺度效应进行研究具有十分重要的意义.论文基于Cosserat理论推导出了微平板自由振动的微分方程,并根据四边简支边界条件假设振型函数,给出了固有频率的计算公式,对不同尺寸微平板固有频率的尺度效应进行了仿真分析.结果表明,考虑了尺度效应的微平板自由振动固有频率要高于经典理论中的固有频率.当特征长度与微平板厚度大小相当时,微平板固有频率表现出明显的尺度效应,并随着特征长度的增加而增大.同时,自由振动的尺度效应将随着微平板厚度的减小而逐渐增强,振动模态及长宽比不影响尺度效应.论文的研究将为微结构与系统的应用提供一定的理论基础.     

基于参数变分原理的Cosserat连续体弹塑性分析

基于参数变分原理,提出了Cosserat模型弹塑性计算的算法,给出了基于Cosserat理论的参数最小势能原理,基于所提出的变分方程,建立了Cosserat理论弹塑性分析的参数二次规划模型,进一步将算法应用于平面应变软化问题计算中,获得的结果具有良好的非网格依赖性.     

Pre-stressed and reinforced hollow cylindrical mixture of non-linearly elastic solid and ideal fluid subjected to combined deformations: A study within the context of the theory of interacting continua

The theoretical result dealing with the saturation boundary condition, first investigated by [On boundary conditions for a certain class of problems in mixture theory, Int. J. Eng. Sci. 24 (1986) 1453-1463], has been recently extended by [On the saturation boundary condition within the context of the theory of interacting continua containing a certain distribution of fibers, Int. J. Eng. Sci. 41 (2003) 2273-2280] to the case of fibers-reinforced solid-ideal fluid mixture. Taking advantage of this new result, the problem of a hollow cylindrical mixture subjected to combined deformations, previously treated by Gandhi et al. [Some non-linear diffusion problems within the context of interacting continua, Int. J. Eng. Sci. 25 (1987) 1441-1457], is revisited in this contribution and improved by introducing the presence of fibers and residual stress (or pre-stress) characterized by the opening angle of the sector-like cross-section.