Numerical analysis method for studying local forms of stability loss of bearing layers of three-layered shells using mixed forms

Self Cite

The results of the investigation described in [2] show that upon realization of the mixed FSL of the load-carrying layers in three-layered structures in the precritical stress-strain state (SSS) of moment type, the SSS which is close to the three-dimensional perturbed one is formed in the core. The model of a transversally soft layer (see [3] and Refs. in [1]) cannot describe this state precisely enough. In [1], this model was developed, taking additional account of tangential stress components in the core [3]. The greatest error of the equations in [1] was caused, first of all, by the fact that the transverse tangential stresses in the core were approxlm~ted by constant functions. In the present study, we develop further the model constructed in [1] for a transversally stiff core. This development is based on an additional approximation of the transverse tangential stresses along the transverse coordinate by a linear function and elimination of the introduced unknown values of the sought functions using the generalized Reissner variational principle [4].

Section: Simplification Variants Of the System Of Stability Equationsmentioning

confidence: 99%

Section: Simplification Variants Of the System Of Stability Equationsmentioning

confidence: 99%

Refined stability theory for sandwich shells with transversally stiff core. 2. Linearized equations of neutral equilibrium

Паймушин¹,

Mushtari²

1997

Self Cite

“…It contains the synphasic and antiphasic forms, which have been thoroughly examined by many authors, the mixed form described and studied in [ 13,[16][17][18]20, 2 i ], as well as the form of shear-induced corrugation in the filler, which is similar to the above-mentioned shear form in load-carrying layers. This FSL also has not been studied in the scientific literature, although, judging by the experimental data, it can be realized in actual structural elements in combination with other forms mentioned.…”

Section: Shear Fsl In the Load-carrying Layers And Fillermentioning

confidence: 99%

“…It waS found in [14][15][16][17][18][19][20] that the equations used in [ 13] to examine the mixed FSL (based on the broken line-type model with account of the transverse compression) are maximally simplified. In this connection, for sandwich and multi-layered shells with transversely soft fillers, belonging to the thin shells, a refined theory ofprt~ritical deformation and a linearized stability theory were constructed, which admits, contrary to the data presented in [13], a great index of variability of the tangential stresses in the fillers for a much more precise description of the SSS compared with [ 13] due to the introduction of merely two additional unknown functions for each layer of the filler.…”

Section: Refined Statement Of Stability Problemsmentioning

confidence: 99%

A stability theory of sandwich structural elements 1. Analysis of the current state and a refined classification of buckling forms

Паймушин¹

1999

Self Cite

The main stages qf development of the stabili~, them T of sandwich structural elements are considered. The mechanism of their stability loss is revealed ushTg the r data and theoretical solutions obtahTed on the basis of refined statements of problems. A classification of all possible forms of stability loss is given within the limits of conthmum representation of load-bearing lavers and the core of these sDTtctio'es. Basic Stages of DevelopmentImproved efficiency of the constructions of modem technology and different structures is closely connected with the search for and realization of new engineering designs in creating their separate elements. One line of the quest is creation and ever-increasing implementation of sandwich structural elements in the form of plates and shells consisting of two external layers and a connecting midlayer of a filler made of a nonrigid light material. The scientific literature dedicated to the development ofthe theory and methods ofcalculation ofstructural elements is quite voluminous. Complete information on these studies, an analysis of the current status of the mechanics of sandwich structures, and some trends of further investigations were presented in the review [ I ].An advantage of sandwich structural elements is that, with their minimum weight, the critical loads can be significantly increased. In this connection, development of the stability theory is one of the principal trends of scientific investigations in the field of mechanics.The first fundamental results in the theory of sandwich structures were apparently obtained by E. Reissner [2] and some other authors mentioned in [ 1 ]. His model is the simplest of the refined models known in the scientific literature. It is based on the linear approximation of tangential displacements and the assumption of a constant deflection over the thickness of the filler, where the tangential stress components are regarded to be zero, and the external load-carrying layers are considered momentless. The use of this model for investigating the stability of sandwich plates and shells made it possible to study the effect of transverse displacements of the filler on the critical loads, which proved to be quite considerable for actual structural elements.Further development of the above model consisted in considering the work of moments in load-carrying layers within the framework of the classical KirchhoffmLove hypotheses for the same approximations of displacements in the filler as those described in [2]. Based on such a model, refined variants ofthe theory for shallow sandwich shells with and without account of tangential stress components in the filler were constructed by E. I. Grigolyuk [3,4]. All subsequent numerous investigations were, in one way or another, associated with generalizations of this model (named the broken line-type model) to nonshaUow shells, with different representation variants of the initial equations and their reduction to a smaller number of equations, as well as the solution of a larger number of particular pro...

“…To solve problem (2.9), the iteration method is used [15], which allows us to find ~'min and the corresponding vector {q* } by sequential solution of the equations…”

Section: )mentioning

confidence: 99%

Methods of finite element analysis of arbitrary buckling forms of sandwich plates and shells

Паймушин¹,

Golovanov²,

Bobrov³

2000

Self Cite

1o IntroductionBased on the results presented in [1][2][3][4][5][6][7], the following basic conclusions can be formulated: 1) the buckling forms (CBFs) realized in sandwich structural elements depend both on the type of the precritical stress-strain state (SSS) in load-carrying layers and filler and on the values of some defining parameters of the structure (the complex of defining parameters entering in the equations given in [8,9] for mixed flexural and flexural-shear BFs was defined, in particular, in [10]),.2) the tangential membrane forces in load-carrying layers and the transverse tangential stresses in the filler are the main parameters of the precritical SSS, which determine the critical loads and BFs, 3) the main defining parameters of a sandwich structure, which govern the BFs, are the transverse compression coefficient, the ratio of the filler thickness to the thickness of the load-carrying layer, and the ratio between the shear modulus of the load-carrying layer material and the normal elastic modulus in the plane tangential to the midsurface of the load-carrying layer, whose particular combinations lead to jumplike changes in the BF, 4) to ensure the necessary degree of accuracy in determining the critical parameters of external loading and particularly the BF, the problem of determination of the precritical SSS, as a rule, must be formulated based on equations having a degree of accuracy no smaller than that of the equations of neutral equilibrium, 5) within rather wide ranges of defming parameters describing the actual sandwich structures, the degree of accuracy of the equations given in [2,8,9] and constructed in terms of the model era transversely soft core, is quite sufficient for the statement and solution of problems on mixed flexural and flexural-shear BFs, 6) when investigating arbitrary BFs, where, of all parameters of the precritical SSS, prevailing are the membrane tangential internal forces in load-carrying layers made of composite materials with small shear moduii in the tangential plane, it is necessary to use equations with regard to all geometrically nonlinear summands in kinematic relations, and