NonLinearly Elastic Membrane Model For Heterogeneous Shells by Using a New Double Scale Variational Formulation: A Formal Asymptotic Approach

This paper is concerned with the asymptotic analysis of shells with periodically rapidly varying heterogeneities. The asymptotic analysis is performed when both the periods of changes of the material properties and the thickness of the shell are of the same orders of magnitude. We consider a shell made of Saint Venant–Kirchhoff type materials for which we justify a new two-scale variational formulation. We assume that both the data and the displacement field admit a formal asymptotic expansion with a negative order of the leading term. We prove that the lowest order term of the displacement field must be of order zero. When the space of nonlinear inextensional displacement is reduced to , this displacement field is a solution of a two-dimensional membrane model which is obtained by solving two coupled problems. The first, posed on the middle surface of the shell is two-dimensional and global and the second, posed on the periodicity cell, is three-dimensional and local.     

A Note on the Existence of Solutions to the Oseen System in Lipschitz Domains

We study the boundary-value problem associated with the Oseen system in the exterior of m Lipschitz domains of an euclidean point space We show, among other things, that there are two positive constants and α depending on the Lipschitz character of Ω such that: (i) if the boundary datum a belongs to L^q(∂Ω), with q ∈ [2,+∞), then there exists a solution (u, p), with and u ∈ L^∞(Ω) if a ∈ L^∞(∂Ω), expressed by a simple layer potential plus a linear combination of regular explicit functions; as a consequence, u tends nontangentially to a almost everywhere on ∂Ω; (ii) if a ∈ W^1-1/q,q(∂Ω), with then ∇u, p ∈ L^q(Ω) and if a ∈ C^0,μ(∂Ω), with μ ∈ [0, α), then also, natural estimates holds.     

A Generalized Fourier Approximation in Anti-plane Cosserat Elasticity

In the present paper we use the modification of Kupradze’s method of generalized Fourier series for the treatment of interior and exterior Dirichlet and Neumann boundary-value problems arising in a linear theory of anti-plane elasticity which includes the effects of material microstructure.     

On Compactness, Domain Dependence and Existence of Steady State Solutions to Compressible Isothermal Navier–Stokes Equations

The steady state system of isothermal Navier–Stokes equations is considered in two dimensional domain including an obstacle. The shape optimisation problem of minimisation of the drag with respect to the admissible shape of the obstacle is defined. The generalized solutions for the Navier–Stokes equations are introduced. The existence of an optimal shape is proved in the class of admissible domains. In general the solutions are not unique for the problem under considerations.     

P波作用下饱和土中深埋圆形复合式衬砌隧道动应力响应研究

采用波函数展开法,推导出了平面P波入射下饱和土中深埋圆形双层衬砌动应力集中问题的解析解,并将该解退化为弹性介质中双层衬砌对平面P波散射的稳态解,验证了计算结果的正确性。研究结果表明,饱和土中双层衬砌的内边界动应力集中系数值大于外边界;外侧衬砌及内侧衬砌弹性模量对衬砌的动应力集中系数影响较大,在保证外侧衬砌稳定性较好的条件下,内侧衬砌尽可能选择刚度较小的材料;增加外侧衬砌及内侧衬砌的厚度可明显地减小衬砌内的动应力集中系数。     

Stress resultants and moments around holes in unsymmetrical composite laminates subjected to remote uniform loading

Stress resultants and moments around the holes of infinite unsymmetrical composite laminates under remote uniform loading are analyzed using the complex potential approach developed by Chen and Shen [Mech. Res. Commun. 28 (4) (2001) 423; 28 (5) (2001) 513]. In the analysis, the authors’ previous work has been modified to determine the complex constants B_k appeared in the complex potential functions of Chen and Shen [Mech. Res. Commun. 28 (5) (2001) 513]. Herein B_k are the unknown quantities related to the remote loading conditions. The effect of bending extension coupling has been discussed for several laminates such as [0/90]_T, [45/−45]_T and [0/90/45/−45]_nT. Results indicates that the coupling between bending and extension significantly affects the stresses around the hole of an unsymmetrical laminate containing one sub-laminate only. Such the effect rapidly decreases as the number of the sub-laminates increases. The results confirm the validity of the developed complex potential approach.     

Instabilities in an open top horizontal porous layer subjected to pulsating thermal boundary conditions

   Received October 30, 2000 / Published online January 23, 2001     

Onset of failure in finitely strained layered composites subjected to combined normal and shear loading

A limiting factor in the design of fiber-reinforced composites is their failure under axial compression along the fiber direction. These critical axial stresses are significantly reduced in the presence of shear stresses. This investigation is motivated by the desire to study the onset of failure in fiber-reinforced composites under arbitrary multi-axial loading and in the absence of the experimentally inevitable imperfections and finite boundaries.By using a finite strain continuum mechanics formulation for the bifurcation (buckling) problem of a rate-independent, perfectly periodic (layered) solid of infinite extent, we are able to study the influence of load orientation, material properties and fiber volume fraction on the onset of instability in fiber-reinforced composites. Two applications of the general theory are presented in detail, one for a finitely strained elastic rubber composite and another for a graphite-epoxy composite, whose constitutive properties have been determined experimentally. For the latter case, extensive comparisons are made between the predictions of our general theory and the available experimental results as well as to the existing approximate structural theories. It is found that the load orientation, material properties and fiber volume fraction have substantial effects on the onset of failure stresses as well as on the type of the corresponding mode (local or global).     

A directional crack path criterion for crack growth in ductile materials subjected to shear and compressive loading under plane strain conditions

A directional crack growth criterion in a compressed elastic perfectly plastic material is considered. The conditions at the crack-tip are evaluated for a straight stationary crack with a small incipient kink. Remote load is a combined hydrostatic pressure and pure shear applied via a boundary layer. Crack surfaces in contact are assumed to develop homogenous Coulomb friction.The crack opening displacement of an extended kink is examined in a finite element analysis to judge the risk of opening mode failure. It has been found that the direction that maximizes the crack opening displacement of an extended kink tip coincides very well with a prediction of the crack growth direction obtained by using a criterion for continued crack growth direction discussed by the authors elsewhere [Int. J. Fract. 108 (2001) 351].Moreover, the by the model predicted incipient crack growth directions are qualitatively comparable with reported crack paths obtained in ductile materials in a limited number of experiments performed under a combined load of in-plane shear and compression.     

A variational analytical approach to time dependent flow of oldroyd B fluid in circular tube

In the present investigation the time dependent flow of an Oldroyd fluid B in a horizontal cylindrical pipe is stuided by the variational analytical approach developed by author. The time dependent problem is mathematically reduced to a partial differential equation of third order. Using the improved variational approach due to Kantorovich the partial differential equation can be reduced to a system of ordinary differential equations for different approximations. The ordinary differential equations are solved by the method of the Laplace transform which is led to an analytical form of the solutions. Project supported by TWAS and Chinese Academy of Sciences and the National Science Foundation of China