Numerical approaches to stability analysis of cylindrical composite shells based on load imperfections

Nikolay Asmolovskiy (Space Structures GmbH, Berlin, Germany.)
Anton Tkachuk (Center for Aerospace Structures, Colorado of University Boulder, Boulder, Colorado, United States.)
Manfred Bischoff (Institute for Structural Mechanics, Universität Stuttgart, Stuttgart, Germany.)

Engineering Computations

ISSN: 0264-4401

Publication date: 20 April 2015



Current procedures of buckling load estimation for thin-walled structures may provide very conservative estimates. Their refinement offers the potential to use structure and material properties more efficiently. Due to the large variety of design variables, for example laminate layup in composite structures, a prohibitively large number of tests would be required for experimental assessment, and thus reliable numerical techniques are of particular interest. The purpose of this paper is to analyze different methods of numerical buckling load estimation, formulate simulation procedures suitable for commercial software and give recommendations regarding their application. All investigations have been carried out for cylindrical composite shells; however similar approaches are feasible for other structures as well.


The authors develop a concept to apply artificial load imperfections with the aim to estimate as good as possible lower bounds for the buckling loads of shells for which the actual physical imperfections are not known. Single and triple perturbation load approach, global and local dynamic perturbation approach and path following techniques are applied to the analysis of a cylindrical composite shell with known buckling characteristics. Results of simulations are compared with published experimental data.


A single perturbation load approach is reproduced and modified. Buckling behavior for negative values of the perturbation load is examined and a pattern similar to a positive perturbation load is observed. Simulations with three perturbation forces show a decreased (i. e. more critical) value of the buckling load compared to the single perturbation load approach. Global and local dynamic perturbation approaches exhibit a behavior suitable for lower bound estimation for structures with arbitrary geometries.


Various load imperfection approaches to buckling load estimation are validated and compared. All investigated methods do not require knowledge of the real geometrical imperfections of the structure. Simulations were performed using a commercial finite element code. Investigations of sensitivity with respect to a single perturbation load are extended to the negative range of the perturbation load amplitude. A specific pattern for a global perturbation approach was developed, and based on it a novel simulation procedure is proposed.



The authors are thankful to Richard Degenhardt for fruitful discussions and drawing our attention to some important aspects of estimation of improved knock-down factors.


Asmolovskiy, N., Tkachuk, A. and Bischoff, M. (2015), "Numerical approaches to stability analysis of cylindrical composite shells based on load imperfections", Engineering Computations, Vol. 32 No. 2, pp. 498-518.

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