随动强化材料壳体的安定分析

在循环加载下壳体结构的安定分析,特别是对于具有应变强化的材料制成的壳体结构的安定分析具有很大的实际意义.文中对随动强化材料的安定定理有了进一步的认识并应用它去分析壳体结构的安定载荷.对于一个真实状态其残余应力与塑性应变之间是相关的.但我们在定理中所示的与时间无关的残余应力场(σ_ijr)和与时间无关的几何容许的塑性应变场(σ_ijp)可以是不相关的.明确指出这点对于工程应用带来很多方便,否则将是十分困难的.为此还给出了该定理的新的证明方法.我们还应用了上述定理对一个半球封头的圆柱壳体进行了安定分析.根据所求得的弹性解,各种可能的残余应力和塑性应变分布,结构的安定分析可归结为一个数学规划问题.计算结果表明应变强化材料的安定载荷要比理想塑性材料的安定载荷高出30～40%,这说明在安定分析中考虑材料强化是重要的,可使壳体结构的设计承载能力有相当大的提高,同时对改进目前壳体结构的设计提供了科学依据.     

有初始几何缺陷的一般壳体的非线性应变分量公式

本文从非线性三维连续介质的应变分量公式出发,导出具有初始几何缺陷一般薄壳的非线性应变分量公式,在推导过程中没有局限于任何一种特定的壳体,因此公式具有一般性.这组公式可以为研究有初始几何缺陷的壳体几何非线性问题提供应变几何学理论基础.     

厚壳理论及其在圆柱壳中的应用

本文从Hellinger-Reissner广义变分原理出发,以位移和应力的假设为基础,建立了厚壳理论.文中把壳体的位移展开为其厚度方向的幂级数,对平行和垂直于中面的位移分别保留其级数的前四项和前三项.并假定壳体的法向挤压和横向剪切应力沿壳厚为三次曲线,使其满足上下壳面上的应力条件,利用变分原理推导出分析厚壳所需的物理方程,平衡方程和边界条件.文中对圆柱壳的情况作了实例计算,并作了光弹性实验,结果表明理论和实验符合良好.     

薄扁球壳受冲击载荷作用时动力屈曲的数值计算

本文在轴对称变形的假设前题下,通过将扩展了的Marguerre’s方程化为差分方程,对其上作用荷载面积不同时的固支弹性薄扁球壳的屈曲问题作了一些探讨.由此发现,固支薄扁球壳在外界冲击荷载作用下,在λ(=2[3(1-v~2)]~(1/4)(H/h)~(1/2))的某一范围内发生了跳跃屈曲,并得到轴对称跳跃屈曲荷载随壳体上荷载作用面积的增大而提高的结论.     

多孔材料夹芯的分层复合双壁面圆柱壳体中波的传播

在经典的理论框架内,对分层的复合材料壳体——多孔材料夹芯的双壁面圆柱壳体,研究自由谐和波在其中的传播.借助于一个具有同样几何特性的展开平板,评估波通过多孔夹芯层传播时大部分有效的成分.通过有效波成分的考虑,将多孔层模拟为具有等效特性的流体.因此,模型简化为一个集满流体介质的双壁面圆柱壳体.最后,评估带宽频率中结构的传播损失,并对结果加以比较.     

ASYMPTOTIC ANALYSIS OF LINEARLY ELASTIC SHALLOWSHELLS WITH VARIABLE THICKNESS

g1. IntroductionIn this paper j we identify the two-dimensiona1 model of a shallow shell with variablethickness. More precisely we consider a family of linearly elastic shallow shells with variablethickness. We show that, if the aPplied forces are of specific order of magnitude, the covariaatcomponents of the scaled displacement field converge, as the thickness of the shell goesto zerQ, to a two dimensional problem that constitutes the model of a shallow shell withvariable thickness. The key …     

Exact Controllability and Asymptotic Analysis for Shallow Shells

The authors consider the exact controllability of the vibrations of a thin shallow shell, of thickness 2εwith controls imposed on the lateral surface and at the top and bottom of the shell. Apart from proving the existence of exact controls, it is shown that the solutions of the three dimensional exact controllability problems converge, as the thickness of the shell goes to zero, to the solution of an exact controllability problem in two dimensions.     

A REMARK ON FORMAL MODELS FOR NONLINEARLY ELASTIC MEMBRANE SHELLS

This paper gives all the two-dimensional membrane models obtained from formal asymptotic analysis of the three-dimensional geometrically exact nonlinear model of a thin elastic shell made with a Saint Venant-Kirchhoff material. Therefore, the other models can be quoted as flexural nonlinear ones. The author also gives the formal equations solved by the associated stress tensor and points out that only one of those models leads, by linearization, to the “classical“ linear limiting membrane model, whose justification has already been established by a convergence theorem.     

JUSTIFICATION OF A TWO-DIMENSIONAL NONLINEAR SHELL MODEL OF KOITER＇S TYPE

A two-dimensional nonlinear shell model “of Koiter‘s type“ has recently been proposed by the first author. It is shown here that, according to two mutually exclusive sets of assumptions bearing on the associated manifold of admissible inextensional displacements, the leading term of a formal asymptotic expansion of the solution of this two-dimensional model, with the thickness as the “small“ parameter, satisfies either the two-dimensional equations of a nonlinearly elastic “membrane“ shell or those of a nonlinearly elastic “flexural“ shell.These conclusions being identical to those recently drawn by B. Miara, then by V. Lods and B. Miara, for the leading term of a formal asymptotic expansion of the solution of the equations of three-dimensional nonlinear elasticity, again with the thickness as the “small“ parameter, the nonlinear shell model of Koiter‘s type considered here is thus justified, at least formally.     

ASYMPTOTIC ANALYSIS OF DYNAMIC PROBLEMS FOR LINEARLY ELASTIC SHELLS-JUSTIFICATION OF EQUATIONS FOR DYNAMIC FLEXURAL SHELLS

61. IntroductionIn this paper) or,P,a,T,' take their values in the set {1, 2}; i, i, k, l,' take their valuesin the set {1, 2, 3}.In [1] under appropriate conditions on the body force density and the middle surfaceof elastic shells, starting from the three-dimensional dynamic equations of elastic shells wehave given the justification of two-dimensional dynamic equations of membrane shells. Inthis paper, under different assumptions on the body force density and the middle surfaceof elastic…     

Dependence of Eigenvalues of Certain Closely Discrete Sturm-Liouville Problems

This paper is concerned with dependence of eigenvalues of certain closely discrete Sturm-Liouville problems. Topologies and geometric structures on various spaces of such problems are firstly introduced. Then, relationships between the analytic and geometric multiplicities of an eigenvalue are discussed. It is shown that all problems sufficiently close to a given problem have eigenvalues near each eigenvalue of the given problem. So, all the simple eigenvalues live in so-called continuous simple eigenvalue branches over the space of problems, and all the eigenvalues live in continuous eigenvalue branches over the space of self-adjoint problems. The analyticity, differentiability and monotonicity of continuous eigenvalue branches are further studied.     

An Arnoldi Method for Nonlinear Eigenvalue Problems

For the nonlinear eigenvalue problem T()x=0 we propose an iterative projection method for computing a few eigenvalues close to a given parameter. The current search space is expanded by a generalization of the shift-and-invert Arnoldi method. The resulting projected eigenproblems of small dimension are solved by inverse iteration. The method is applied to a rational eigenvalue problem governing damped vibrations of a structure.     

DERIVATIVES OF EIGENPAIRS OF SYMMETRIC QUADRATIC EIGENVALUE PROBLEM

Derivatives of eigenvalues and eigenvectors with respect to parameters in symmetric quadratic eigenvalue problem are studied. The first and second order derivatives of eigenpairs are given. The derivatives are calculated in terms of the eigenvalues and eigenvectors of the quadratic eigenvalue problem, and the use of state space representation is avoided, hence the cost of computation is greatly reduced. The efficiency of the presented method is demonstrated by considering a spring-mass-damper system.     

Approximation of sign-indefinite spectral problems

A variational sign-indefinite eigenvalue problem in an infinite-dimensional Hilbert space is approximated by a problem in a finite-dimensional subspace. We analyze the convergence and accuracy of approximate eigenvalues and eigenelements. The general results are illustrated by a sample scheme of the finite-element method with numerical integration for a one-dimensional sign-indefinite second-order differential eigenvalue problem.     

A New Implicit Iteration Process with Errors for the Family of Strongly Pseudocontractive Mappings

A method is presented for generating a sequence of lower and upper bounds for the eigenvalues of the problem (i) Tu-λSu = 0, where T and S belong to a class of unbounded and nonsymmetric operators in a separable Hilbert space. Sufficient conditions are derived for the convergence of the sequence of bounds to the eigenvalues of (i), and the applicability of the method is illustrated by approximating the smallest eigenvalue of a non-selfadjoint differential eigenvalue problem.     

On the eigenvalue problem of a class of linear partial difference equations

In this paper, the eigenvalue problem of a class of linear partial difference equations is studied. The results concern the existence of eigenvalues, their character (real, positive), as well as the behavior of its eigenfunctions (positivity, oscillation). Moreover a theorem is given concerning the existence of a unique solution of an associated non-homogeneous partial difference equation. The results generalize previously known results for ordinary linear difference equations. The method used is a functional-analytic one, which transforms the eigenvalue problem for the difference equation into the equivalent problem of the eigenvalues of an operator defined on an abstract separable Hilbert space.     

Universal inequalities for eigenvalues of a system of elliptic equations of the drifting Laplacian

Let \(\Omega \) be a bounded domain in a n-dimensional Euclidean space \(\mathbb {R}^{n}\). We study eigenvalues of an eigenvalue problem of a system of elliptic equations of the drifting Laplacian

$$\begin{aligned} \left\{ \begin{array}{ll} \mathbb {L_{\phi }}\mathbf{{u}} + \alpha (\nabla (\mathrm {div}{} \mathbf{{u}}) - \nabla \phi \mathrm {div}{} \mathbf{{u}})= -\bar{\sigma }\mathbf{{u}}, &{} \hbox {in} \,\Omega ; \\ \mathbf{{u}}|_{\,\partial \Omega }=0. \end{array} \right. \end{aligned}$$

Estimates for eigenvalues of the above eigenvalue problem are obtained. Furthermore, a universal inequality for lower order eigenvalues of the problem is also derived. Finally, we prove an universal inequality type Ashbaugh and Benguria for the drifting Laplacian on Riemannian manifold immersed in an unit sphere or a projective space.

     

The eigenvalue problem for solitary waves of a boussinesq equation,via a generalization of the rouché theorem

We consider the study of an eigenvalue problem obtained by linearizing about solitary wave solutions of a Boussinesq equation. Instead of using the technique of Evans functions as done by Pego and Weinstein in [R. Pego and M. Weinstein, Convective Linear Stability of Solitary Waves for Boussinesq equation. AMS, 99, 311–375] for this particular problem, we perform Fourier analysis to characterize solutions of the eigenvalue problem in terms of a multiplier operator and use the strong relationship between the eigenvalue problem for the linearized Boussinesq equation and the eigenvalue problem associated with the linearization about solitary wave solutions of a special form of the KdV equation. By using a generalization of the Rouché Theorem and the asymptotic behavior of the Fourier symbol corresponding to the eigenvalues problem for the Boussinesq equation and the Fourier symbol corresponding to the eigenvalues problem for the KdV equation, we show nonexistence of eigenvalues with respect to weighted space in a planar region containing the right-half plane.     

Spectrum of a Jacobi matrix with exponentially growing matrix elements

A Jacobi matrix with an exponential growth of its elements and the corresponding symmetric operator are considered. It is proved that the eigenvalue problem for some self-adjoint extension of this operator in some Hilbert space is equivalent to the eigenvalue problem of the Sturm-Liouville operator with a discrete self-similar weight. An asymptotic formula for the distribution of eigenvalues is obtained.     

The Problem of Eigenvalue on Noncompact Complete Riemannian Manifold

Let M be an n-dimensional noncompact complete Riemannian manifold, "Δ" is the Laplacian of M. It is a negative selfadjoint operator in L²(M). First, we give a criterion of non-existence of eigenvalue by the heat kernel. Applying the criterion yields that the Laplacian on noncompact constant curvature space form has no eigenvalue. Then, we give a geometric condition of M under which the Laplacian of M has eigenvalues. It implies that changing the metric on a compact domain of constant negative curvature space form may yield eigenvalues.