一种复合材料的大挠度曲梁单元

本文研究了加劲壳的非线性有限元分析方法,提出了一种梁元素来模拟加筋。该元素具有曲轴线,任意形状的薄壁剖面和任意铺层方式,与三维退化曲壳元素完全协调,相对于壳中面可以有偏心,所分析的结构可以是层合复合材料加劲壳或各向同性材料单层加劲壳。     

Stress-Strain Analysis of Orthotropic Closed and Open Noncircular Cylindrical Shells

The paper proposes an approach to the stress-strain analysis of orthotropic open and closed cylindrical shells of variable thickness and noncircular cross section under various loading and boundary conditions. As an example, the circumferential distribution of deflection and tangential force in shells with elliptic cross section is analyzed for some cases of orthotropy __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 7, pp. 83–92, July 2005.     

On the stress-strain state of toroidal shells of elliptical cross section formed from nonlinear elastic orthotropic materials

Problems of the statics of toroidal shells with elliptical cross sections, which are formed from nonlinear elastic orthotropic materials, were examined. Investigations were carried out in accordance with a procedure based on the method of successive approximations, the variational-difference method, and the method of Lagrangian multipliers. Calculations were performed by varying the ellipticities of the cross section of the torus and the radii of the circular axis of the torus over a broad range. Numerical and analytical results are presented in tables and graphs. Attention was focused on the accuracy of the computational results obtained, and agreement between the internal and external forces in the cross section was adopted as an integral criterion. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 1, pp. 103–109. January, 2000.     

Accounting for axis curvature in calculating the strength of a circular cylindrical shell

Conclusions The mutual effect of strains of the contour of the cross section and bending of the axis of a shell is manifest in ovalization of the cross section and an increase in stresses in the structure. Ovalization of the cross section must be taken into account for long structural shells with the dimensions 0.6$$ " align="middle" border="0"> and _10max/E(R/)0.6.Saratov Higher Military Command School. Translated from Prikladnaya Mekhanika, Vol. 17, No. 5, pp. 83–88, May, 1981.     

Refined Analysis of the Influence of the Inhomogeneous Layers on the Stress State of Circular and Noncircular Cylindrical Shells

We study the stress state of laminated inhomogeneous closed cylindrical shells generally with an arbitrary cross section, taking transverse shear into account on the basis of the straight-line element hypothesis. As an example, results are presented for a two-layer cylindrical shell whose cross section is a combination of an oval and a circle.     

On the behavior of viscoelastic free jets with elliptical cross section

In [1,2] we develop a comprehensive theory of one space dimensional closure models (closed systems of 1-D equations for the unknown, or modal, variables) for free viscoelastic jets. These closure models are derived via asymptotics from the full 3-D boundary value problem under the conditions of a Von Kármán-like flow geometry, a Maxwell-Jeffreys constitutive model, elliptical free surface cross section, and a slender jet scaling. The focus of the present paper is to determine the consequences and predictions of the lowest order system of equations in this asymptotic analysis. For the special cases of elliptical inviscid and Newtonian free jets, subject to the effects of surface tension and gravity, our model predicts oscillation of the major axis of the free surface elliptical cross section between perpendicular directions with distance down the jet, and draw-down of the cross section, in agreement with observed behavior. In the absence of surface tension the transformation from a cross section with major axis in one direction to a cross section with major axis in the perpendicular direction occurs only once, in agreement with the observation of Taylor [4]. In viscoelastic regimes, our model predicts swell of the elliptical extrudate and distortion of the elliptical extrudate cross section from the dimensions of the die aperture.     

Stability of Axially Compressed Noncircular Cylindrical Shells Consisting of Panels of Constant Curvature

The stability problem is solved for an axially compressed cylindrical shell. Its cross section is formed by circular arcs of radius r with ends supported on a closed circle of radius R. The solution is based on the Flügge equations of the classic theory of deep cylindrical shells. It is shown that the critical axial load for shells of medium length and appropriately chosen cross-sectional profile can be increased by a factor of R/r approximately, compared with the circular shell. The shells length affects considerably the efficiency of noncircular shells of this type. This design model allows us to find out how the local properties of the shell and its stiffness are related     

Study of nonlinear deformation and stability of discretely reinforced elliptic cylindrical shells in transverse bending

A finite-element method for solving problems of nonlinear deformation and stability of nonuniformly discretely reinforced noncircular cylindrical shells is considered. An effective computer algorithm for the study of shells is developed. Stability of stringer cylindrical shells with an elliptical cross section in transverse bending is examined. The effect of ellipticity, nonlinearity of shell deformation at the subcritical stage, reinforcement discreteness, and heterogeneity on shell stability is determined.     

Stress Analysis of Orthotropic Noncircular Cylindrical Shells of Variable Thickness in a Refined Formulation

An approach is developed to solve stress–strain problems in a refined formulation for orthotropic cylindrical shells of variable thickness and noncircular cross section. It is shown, as an example, how the distributions of deflections and stresses depend on changes in the shell thickness at constant weight     

浅悬链线壳的轴对称问题

本文得到了中心无孔口和有孔口的浅悬链线壳的一般解答,并给出了有关算例.     

Study Into the Effect of Circumferential Variation in Thickness and Load on the Deformation of Cylindrical Shells of Elliptic Cross Section

By solving the boundary-value stress–strain problems for cylindrical shells with an elliptical cross section and a thickness varying along the directrix, the effect of variability in the thickness and load on their deformation is studied. Tables and plots present the deflection and the bending moment calculated under various boundary and loading conditions.     

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.     

Nonlinear deformation and stability of oval cylindrical shells under combined loading

A study is made of the stability of cylindrical shells of oval cross section loaded by a shear force combined with torsional and bending moments. The variational method of finite elements in displacements is used. The subcritical stress-strain state of the shells is considered momental and nonlinear. The effects of the nonlinearity of shell deformation and shell ovalization on the critical load and buckling mode are determined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 134–138, January–February, 2008.     

Postbuckling Behavior of Thin-Walled Open Cross-Section Compression Members

ABSTRACT

The postbuckling behavior of simply supported columns with thin-walled open cross section is investigated by means of the general nonlinear theory of elastic stability. Fourth-order terms in the series expansion of the total potential energy are disregarded.

It is shown that interaction between linearly independent simultaneous buckling modes is responsible for neutral equilibrium at bifurcation if the column cross section has two axes of symmetry, and unstable if it has only one. If the buckling modes are not simultaneous, the equilibrium is neutral in both cases. Finally, the equilibrium at bifurcation is usually unstable if the cross section has no axis of symmetry.     

The stress state of anisotropic conic shells with thickness varying in two directions

The problem on the stress state of thin layered conic shells consisting of rigidly joint layers is considered. The material of the layers has one plane of elastic symmetry. The thickness of each layer in the meridional direction varies linearly in such a manner that it is proportional to the distance from the axis of rotation to the coordinate surface and varies arbitrarily in the circumferential direction. The desired functions are represented by the product of a power function of the radial coordinate and the unknown function of the central angle in the cross section. This makes it possible to separate out the radial coordinate and to derive the resolving system of ordinary differential equations, which is solved numerically. An example of the solution of a specific problem is given. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 5, pp. 81–88, May, 2000.     

均布压力作用下悬链线波纹壳应力和位移的初参数积分方程分析

本文用初参数积分方程方法，对悬链线波纹壳在均布压力作用下的应力和位移进行了分析，并给出了一个算例。     

Refined analysis of the stress state of orthotropic elliptic cylindrical shells with variable geometrical parameters

An approach developed earlier to solve boundary-value problems is used to analyze the behavior of the stress-strain state of orthotropic elliptic cylindrical shells with variation in the geometric parameters of their cross section at constant volume (weight) Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 53–62, September 2008.     

Stability of bars with variable rigidity

A variable cross-section bar is considered. The bar is not uniform in length. The bar axis through the mass centers of all cross sections is a straight line. The bar is compressed by a longitudinal force applied to the mass center of the boundary cross section. The stability loss of the straight-line shape of the bar’s equilibrium is discussed when a curved shape is also possible. Approximate analytical formulas are obtained for the critical compressive force when four types of end fixing are used for a periodically nonuniform bar. The numerical results obtained by these formulas are compared with the known exact solutions to the stability equation for a bar whose cross section is stepwise variable and whose nonuniformity consists of only one period (the limiting case).     

The rigid inclusion with highest penetration

A cylindrical bounded rigid inclusion with cross section of bounded area and variable shape is embedded in an infinite elastic medium. Assuming that the cross section possesses an axis of symmetry and that it is pushed into the medium by a force acting in the direction of this axis, the question arises of finding the section's profile for which penetration is highest. A solution is found only for two particular classes of domains in plane elasticity.

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Sommario Un'inclusione clinidrica rigida con sezione trascersale di area limitata e forma variabile è immersa in un mezzo elastico infinito. Avendo supposto che la sezione possegga un asse di simmetria e che sia spinta nel mezzo da una forza agent secondo tale asse, si pone il problema di trovare il profilo della sezione per cui è massima la penetrazione. Una risposta si può dare solo per due classi particolari di domini in elasticità piana.

     

A Theoretical and Experimental Investigation of Torsional-Flexural Buckling in Thin-Walled Prismatic Members

In a previous paper [1]the authors presented a general solution to the problem of thin-walled prismatic members of doubly symmetric open cross section loaded by end forces only. Deep sections, in which the second moment of area about the major principal axis is much greater than that about the minor principal axis, were considered. Thus deflections due to major axis bending could be ignored. The end forces included an axial thrust and unequal major axis moment, both of which were considered constant. Force-deflection equations for the member were derived and the influence of the axial thrust and major axis moments upon these was considered.

In the present paper the general solution is applied to the problem of buck-ling in such members. Three sets o f end conditions-pinned, fixed. and mini-mum restraint-are considered. Formal and finite difference solutions are presented for each of these so that an independent check on all the theoretical results is obtained. A major portion of the paper is devoted to reporting an extensive series of tests cvried out on members of I and rectangular cross section. These are concerned with investigating all the major theoretical results o f this and the previous paper. Ageement is found to be good.