旋转壳及附属结构应力分析软件系统

本文概述了近年来旋转壳应力分析软件系统的一些最新发展。它主要是结合电力建设中超大、超高冷却塔设计和施工中提出的壳筒、离散支柱的整体静力分析及抗震研究，不均匀地基及其沉陷，大塔稳定性，离散支柱局部缺断后的壳体应力分布等力学问题，通过新单元的开发和新算法的数值实现两个方面的工作，在文［１］的基础上，开发了一个旋转壳及附属结构应力分析软件系统．近年来这个系统对一些工程的实际应用表明，它是有效可靠的．     

Stress analysis of functionally graded shells using a 7-parameter shell element

In this paper, finite element stress analysis of functionally graded structures using a high-order spectral/hp shell finite element is presented. The shell element is based on a seven-parameter first-order shear deformation theory in which the seventh parameter, in addition to the usual six degrees of freedom, is the thickness stretch. The continuum shell element is utilized for the numerical simulations of the fully geometrically nonlinear response of functionally graded elastic shell structures. Several nontrivial shell problems are considered to report deflections and stresses, the latter being the main focus of the current paper. It is found that the stresses computed in the current study agree only in some cases with those of ANSYS and/or ABAQUS and thus requires additional study to determine the cause of the disagreement.     

Stress function method in shakedown analysis of axisymmetric shells

A self-equilibrated stress obtained from the stress functions of thin shells is used for the static shakedown theorem as a residual stress. In combination with the finite element method, a linear programming formulation of the shakedown analysis of axisymmetric shells is derived. The physical meaning of the stress function method is clear and its computing amount is small. Some examples of the plates and shells show that the method is reasonable and efficient.The project was supported by the National Natural Science Foundation of China     

Stress analysis of hyperbolic shells of revolution with non-axisymmetrical geometric imperfections

In analyzing hyperbolic shells of revolution with non-axisymmeteric imperfections, an approximate method based on simulating the effect of imperfections by the application of fictitious normal pressure loading on the perfect shell is investigated. In the analysis of a shell of revolution with a bulge-type imperfection under non-axisymmetric loads, an efficient algorithm of applying the method is developed: the effect of individual curvature errors on stress resultants and couples are separately considered, while the interactions among various curvature errors are properly treated in the analysis by an iterative procedure. This algorithm avoids repeated analyses for non-axisymmetric loads and may be implemented with a purely axisymmetric analysis capability.A hyperbolic cooling tower shell with a bulge-type imperfection is analyzed under dead load and wind load conditions by the equivalent load method. A direct analysis of the imperfect shell is also made by a specialized finite element program. Through numerical studies, the accuracy and applicability of the equivalent load method are examined.     

Stress analysis of flexible noncircular cylindrical shells with hinged edges for different critical loads

An analytic nonlinear boundary-value solution is found and used in analysis of the precritical and postcritical stress states of a flexible long cylindrical shell with variable curvature and hinged longitudinal edges under nonuniform loading __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 43–50, February 2006.     

Stress analysis of nonthin elliptic cylindrical shells in refined and spatial formulations

A spatial model and a refined model based on the straight-line hypothesis are used to analyze the stress state of nonthin elliptic cylindrical shells with certain end conditions for different thicknesses and aspect ratios. The results obtained are compared, and the validity range of the refined model is established __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 8, pp. 44–57, August 2006.     

Stress concentration around a curvilinear hole in plates and shells

Azerbaidzhan Economic Institute, Baku. Translated from Prikladnaya Mekhanika, Vol. 27, No. 1, pp. 71–77, January, 1991.     

Asymptotic analysis of linearly elastic shells. I. Justification of membrane shell equations

We consider a family of linearly elastic shells with thickness 2?, clamped along their entire lateral face, all having the same middle surfaceS=φ(?ω) ?R ³, whereω ?R ² is a bounded and connected open set with a Lipschitz-continuous boundaryγ, andφ ∈l ³ ( $\overline \omega$ ;R ³). We make an essential geometrical assumption on the middle surfaceS, which is satisfied ifγ andφ are smooth enough andS is “uniformly elliptic”, in the sense that the two principal radii of curvature are either both>0 at all points ofS, or both<0 at all points ofS. We show that, if the applied body force density isO(1) with respect to?, the fieldtu(?)=(u _i(?)), whereu _i (?) denote the three covariant components of the displacement of the points of the shell given by the equations of three-dimensional elasticity, one “scaled” so as to be defined over the fixed domain Ω=ω×]?1, 1[, converges inH ¹(Ω)×H ¹(Ω)×L ²(Ω) as?→0 to a limitu, which is independent of the transverse variable. Furthermore, the averageξ=1/2ε _?1 ¹ u dx ₃, which belongs to the space $$V_M (\omega ) = H_0^1 (\omega ) \times H_0^1 (\omega ) \times L^2 (\omega ),$$ satisfies the (scaled) two-dimensional equations of a “membrane shell” viz., $$\mathop \smallint \limits_\omega a^{\alpha \beta \sigma \tau } \gamma _{\sigma \tau } (\zeta )\gamma _{\alpha \beta } (\eta ) \sqrt \alpha dy = \mathop \smallint \limits_\omega \left\{ {\mathop \smallint \limits_{ - 1}^1 f^i dx_3 } \right\}\eta _i \sqrt a dy$$ for allη=(η _i) εV _M(ω), where $a^{\alpha \beta \sigma \tau }$ are the components of the two-dimensional elasticity tensor of the surfaceS, $$\gamma _{\alpha \beta } (\eta ) = \frac{1}{2}\left( {\partial _{\alpha \eta \beta } + \partial _{\beta \eta \alpha } } \right) - \Gamma _{\alpha \beta }^\sigma \eta _\sigma - b_{\alpha \beta \eta 3} $$ are the components of the linearized change of metric tensor ofS, $\Gamma _{\alpha \beta }^\sigma$ are the Christoffel symbols ofS, $b_{\alpha \beta }$ are the components of the curvature tensor ofS, andf ⁱ are the scaled components of the applied body force. Under the above assumptions, the two-dimensional equations of a “membrane shell” are therefore justified.     

Stress concentration around holes in conical shells

Kiev University. Translated from Prikladnaya Mekhanika, Vol. 26, No. 7, pp. 38–43, July, 1990.     

Elastic stability of rectangular shells in membrane equilibrium

Summary This study furnishes an algorithm for determining, in accordance with Dirichelt's (energetic) principle, the critical load of rectangular membranes of any shape. The algorithm is formulated with reference to an extrinsic system of orthogonal Cartesian coordinates, that is the system used in statics for Pücher's method. This involved obtaining the expressions of the deformation characteristics and of the curvature variations of the shell up to the second order in the displacement components. These quantities yielded the final expression of the deformation energy and the second order work of internal stresses. In view of the applications, possible displacement terns are proposed characterizing the unstability secondary buckled lines, which are further detailed for the rectangular plan paraboloid. Finally, some numerical applications are given for the square plan shell.

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Sommario Col presente studio viene fornito un appropriato algoritmo per la determinazione, secondo il principio energetico del Dirichlet, dei moltiplicatori critici per le membrane di forma qualsiasi su pianta rettangolare. La formulazione è fatta con riferimento ad un sistema di coordinate cartesiane ortogonali estrinseco e cioè lo stesso adottato per il metodo di Pücher nella statica. Allo scopo è stato necessario ricavare le espressioni delle caratteristiche della deformazione e delle variazioni di curvatura della volta sino al secondo ordine nelle componenti dello spostamento. Tali quantità hanno permesso di dare in forma esplicita l'espressione dell'energia di deformazione ed il lavoro del secondo ordine degli sforzi interni. In vista delle applicazioni sono proposte delle possibili terne di spostamenti caratterizzanti le deformate secondarie instabilizzanti, particolarizzandole infine per il caso del paraboloide su pianta rettangolare.Si riportano infine alcune applicazioni numeriche relative alla volta su pianta quadrata.

     

Stress analysis of noncircular cylindrical shells with cross section in the form of connected convex half-corrugations

An approach is developed to solve the stress-strain problem for noncircular cylindrical shells with complex cross section in the form of connected convex half-corrugations. Numerical results are presented __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 4, pp. 73–82, April 2006.