Determination of the critical loads of nonideal shell models

Gavrilenko, G. D.; Pal'chevskii, A. S.; Yakubovskii, Yu. E.

doi:10.1007/bf01528734

Cited by 3 publications

(3 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The authors of [24] demonstrated that using experimentally measured initial deflections in the theoretical nonlinear analysis allows us to achieve good agreement between theoretical and experimental results. The authors of [17,18] analyzed the stability of ribbed shells with local dents by the mesh method but did not compare the results against experiment data.…”

Section: Experimental Technique and Test Shells With A Single Local Dmentioning

confidence: 77%

See 1 more Smart Citation

Stability and load-bearing capacity of smooth and ribbed shells with local dents

Gavrilenko

2004

Int Appl Mech

Self Cite

View full text Add to dashboard Cite

A method for analysis of the stability and load-bearing capacity of imperfect smooth and ribbed shells is developed. This method is based on the finite-difference method and is implemented as an algorithm for fast calculation of critical forces, as opposed to the finite-element method. The theoretical results discussed include both early and recent results. The emphasis is on shells with local dents. The numerical results are successively corrected and compared with available experimental data for shells with a single dent and with other data. The method enables us to discover new features in the behavior of thin-walled structures under loading: development of precritical state, change in the dent shape, and exhaustion of load-bearing capacity. The lower local critical loads and upper stresses are determined. They correspond to general buckling and agree well with available experimental data.Introduction. Methods combining numerical and classical analytical approaches are of special interest in the theory of shells. This is pointed out in [50, etc.].The present paper briefly describes a numerical approach to the analysis of the stability and load-bearing capacity of imperfect shells. If theoretical solutions are unavailable, we will use experimental data to justify the reliability of the method. Solutions that could improve results obtained within the framework of shell theory can be derived from the three-dimensional theory of deformable bodies and its applications [28][29][30]48].Well-known theoretical studies into the stability of shells with a local dent did not addressed the issue of load-bearing capacity of such shells. Such studies are discussed in Sections 1-3.Background Information and Problem Statement. The new approach and the theoretical results compared with experimental data are described in Sections 4-6. The strength loss process of real thin-walled shells includes, at least, three stages: subcritical, critical, and postcritical. These stages are shown graphically in [40].Consider the following approach to the buckling analysis of shells: (i) analyze the behavior of imperfect shells with a local dent (generally dents) growing in amplitude;(ii) determine the critical (lower) load under which the originally nonloaded dent transforms into a new (loaded) dent; (iii) study the behavior (whether stable or not) of the shell with new dent, which subsequently turns into the postcritical state, using nonlinear shell theory and the generalized mixed equations describing the entire process at all the three stages.The theoretical results are supported by experimental data [33] on stability of shells with dents. Smooth cylindrical shells with a single local dent were the subject of detailed theoretical and experimental research. The experiments involved steel specimens. All the shells were made by the same method and tested under identical conditions. The theoretical analysis was based on the mesh method and nonlinear shell theory. The experimental and theoretical critical forces were compared for shells

show abstract

Section: Experimental Technique and Test Shells With A Single Local Dmentioning

confidence: 77%

“…The deflections on the remaining surface of the shell were studied by the shadow moire method [24], which consists in the following (Fig. 16).…”

Section: Subcritical and Stability Analyses Of Imperfect Ribbed Truncmentioning

confidence: 99%

Stability and load-bearing capacity of smooth and ribbed shells with local dents

Gavrilenko

2004

Int Appl Mech

Self Cite

View full text Add to dashboard Cite

show abstract

“…This trick imposes restrictions on the freedom of motion of points of the surface and, hence a priori leads to the overestimated values of the critical loads. In [20], one can find a procedure of numerical analysis of imperfect smooth shells that does not require any restrictions on the form of the loss of stability. Moreover, it takes into account all parameters of the nonlinear stress-strain state of the shell.…”

mentioning

confidence: 99%

Stability of imperfect cylindrical shells

Gavrilenko

2008

Strength Mater

Self Cite

View full text Add to dashboard Cite

A procedure of approximate evaluation of the critical loads of shells proposed earlier on the basis of the nonlinear theory of shells is used to analyze the influence of initial imperfections of any shape on the parameters of the critical loads. The numerical results are compared with the available experimental and theoretical data corresponding to the complete loss of stability of shells and exhaustion of their load-carrying capacity.Keywords: nonlinear theory, models of shells, imperfections of the shape, critical loads. Introduction.A significant difference between the theoretical and experimentally established critical loads explains the necessity of development of new procedures of investigation of the process of loss of stability.The first procedures used for the numerical analysis of smooth cylindrical shells in the linear statement were based on an idealized computational scheme [1][2][3][4]. Thus, the shell was regarded as geometrically perfect and perfectly elastic and its initial state was assumed to be momentless.As indicated in [5], the application of the concepts of nonlinear theory can be traced back to S. P. Timoshenko and C. B. Biezeno who used these concepts in the problems of clicking the rods and spherical domes. Later, L. H. Donnell [6] and K. Marguerre [7] finally formulated the foundations of geometrically nonlinear theory for smooth shells. The following important feature of the behavior of compressed cylinders was established in [8,9]: The load decreases in the supercritical stage of deformation.In [10,11], an attempt was made to establish the improved experimental and theoretical values of the upper critical loads by using the linear momentless theory of shells. Despite the application of fairly accurately prepared models, the difference between the theoretical and experimental critical loads was quite large [10, Table 28]. Thus, in particular, the experimental values of critical loads for smooth shells differed from the theoretical values by a factor of 2-3 [10]. Ribbed shells were studied in [10] to get the required agreement between the theoretical and experimental results (see Tables 28 and 29 in [10]). As a result, the difference between the theoretical and experimental data for shells with four frames and increasing number of stringers (24, 32, 40, and 48) was greater than 70% (greater than 60% as compared with the mean experimental values). This means that the minimum theoretical critical loads were, as before, much higher than even the mean experimental values.The attempts to remove this difference were made in analyzing a batch of shells with stringers and frames with much larger cross-sectional areas than earlier [10, Table 29]. As a result, the minimum theoretical values of stresses for smooth and framed shells were 2-3 times higher than the experimental values. For shells with stringers, the experimental values were 1.9 (k =16 stringers) and 1.3 (k = 64) times lower than the theoretical values. For shells with stringers and frames, the theoretical values were twice higher tha...

show abstract

Stability of smooth and ribbed shells of revolution in a nonuniform stress-strain state (survey)

Gavrilenko¹

1995

Int Appl Mech

View full text Add to dashboard Cite

Determination of the critical loads of nonideal shell models

Cited by 3 publications

References 0 publications

Stability and load-bearing capacity of smooth and ribbed shells with local dents

Stability and load-bearing capacity of smooth and ribbed shells with local dents

Stability of imperfect cylindrical shells

Stability of smooth and ribbed shells of revolution in a nonuniform stress-strain state (survey)

Contact Info

Product

Resources

About