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1
Content available remote Buckling resistance assessment of steel I-section beam-columns not susceptible to LT-buckling
Giżejowski M. A., Szczerba R., Gajewski M. D., Stachura Z.
Archives of Civil and Mechanical Engineering
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2017
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Vol. 17, no. 2
205--221
EN
The authors focused on buckling resistance assessment of steel-I-section perfect beam-columns of the cross-section class 1 and 2, not susceptible to LT-buckling and subjected to compression and one directional bending about the section principal axes y–y or z–z. These assumptions lead to the case of elements considered as only sensitive to the flexural failure including second order in-plane bending and compression. The stability behaviour of elements subjected to different bending configurations and different static schemes was investigated through comprehensive numerical study with use of the finite element method. Geometrically and materially nonlinear analyses GMNA in case of perfect beam-columns and GMNIA fo the imperfect ones were carried out in reference to shell and beam element models. Static equilibrium paths accounting for pre- and post-limit behaviour were determined with use of the incremental-iterative algorithm taking into consideration displacement-control parameters. An analytical formulation for a quick verification of the perfect I-section beam-column resistance is proposed. Finally, the global effect of imperfections is also investigated using GMNIA. The verification method developed for perfect elements is extrapolated for imperfect beam-columns. The good agreement of the proposed analytical formulation is shown through an extensive comparison with more than 3500 results of finite element numerical simulations conducted with use of ABAQUS/Standard program.
2
Content available remote Thermoconvective magnetized ferrofluid with internal angular momentum: a nonlinear stability analysis
Sunil, Mahajan A.
International Journal of Applied Mechanics and Engineering
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2011
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Vol. 16, no 2
557-580
EN
The generalized energy method is developed to study the nonlinear stability analysis for a magnetized ferrofluid layer heated from below with intrinsic rotation of the particles, in the stress-free boundary case. The mathematical emphasis is on how to control the nonlinear terms caused by the magnetic body force, inertia forces and body couple on a fluid element. By introducing a suitable generalized energy functional, we perform a nonlinear energy stability (conditional) analysis. It is found that the nonlinear critical stability magnetic thermal Rayleigh number does not coincide with that of the linear instability analysis, and thus indicates that the subcritical instabilities are possible. However, it is noted that, in the case of non-ferrofluid, the global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of magnetic parameters, this coincidence is immediately lost. The effect of the magnetic parameter M3, coupling parameter N1, and spin diffusion parameter N3, on the subcritical instability region has also been analyzed. It is shown that with the increase of the magnetic parameter (M3) the subcritical instability region between the two theories decreases quickly while with the increase of N1 and N3, the subcritical instability region between the two theories increases. We also demonstrate coupling between the buoyancy and magnetic forces in the nonlinear energy stability analysis as well as in the linear instability analysis.
3
Content available remote Nonlinear stability of symmetrically laminated cylindrically orthotropic truncated shallow conical shells including trunsverse shear
Liu R. H., Wei S.
International Journal of Applied Mechanics and Engineering
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2009
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Vol. 14, no 3
769-790
EN
In the present paper, based on the modified iteration method, the nonlinear stability problem of a symmetrically laminated cylindrically orthotropic truncated shallow conical shell with a non-deformable rigid body at the center under uniform pressure including transverse shear is investigated. The analytical formula of the critical buckling load is obtained. Results of this paper can be applied directly to engineering design.
4
Content available remote Nonlinear stability of corrugated shallow spherical shell
Liu R. H., Wang F.
International Journal of Applied Mechanics and Engineering
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2005
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Vol. 10, no 2
295-309
EN
In this paper, a nonlinear bending theory for a corrugated shallow spherical shell is constructed. By means of this theory and the modified iteration method, the analytical solution of the critical buckling pressure for a corrugated shallow spherical shell with a rigidly clamped edge under the action of uniform pressure is obtained.
5
Content available remote Nonlinear stability analysis of electrified liquid jet under the influence of a uniform axial periodic electric field
Mahmoud Y. D.
Mechanics and Mechanical Engineering
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2000
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Vol. 4, nr 2
251--267
EN
The parametric excitation of surface waves on a liquid jet in the presence of an axial periodic electric field is investigated . The method of multiple scales is used to derive and analyze the necessary and sufficient conditions for stability. Owing to the periodicity, resonant cases appear .Two parametrically nonlinear Schrodinger equations are obtained for the resonance cases . The formula for the surface elevation is derived in each case . A classical nonlinear Schrődinger equation is deduced for the non -resonance case . Investigation of the stability criterion by nonlinear perturbation shows that the periodic electric field has a stabilizing effect.
6
On nonlinear stability of shallow conical sandwich shells
Liu R. H., Li J.
Applied Mechanics and Engineering
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2000
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Vol. 5, no 2
367-387
EN
In this paper, a theory for nonlinear bending of shallow conical sandwich shells is established by means of the method of calculus of variations. Using the modified iteration method which was suggested by Yeh et al. (1965a, 1965b), analytic solutions of nonlinear stability for the shells with four types of boundary conditions under uniform pressure are obtained. The numerical discussions based on the analytic solutions have been given in detail, which indicate that our method is efficient for the analysis of shallow shells.
7
Content available Post-buckling analysis of elastic-plastic plates basing on the Tsai-Wu Criterion
Grądzki R., Kowal-Michalska K.
Journal of Theoretical and Applied Mechanics
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1999
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nr 4
893-908
EN
This work deals with the analysis of post-buckling state in rectangular plates subject to uniaxial in-plane compression within the elastic and elasto-plastic range. The problems of initial out-of-flatness and different geometry of rectangular plate are considered. The analysis is carried out on the basis of non-linear theory of plates involving plasticity. It is assumed that the yield values in tension and compression tests of a plate material are different. Thus, the Tsai-Wu Criterion is applied. The solution is obtained in the analytical-numerical way using the Prandtl-Reuss equations. As result of numerical calculations the load-shortening curves for the considered plates are obtained.
PL
W pracy przeprowadzono analizę stanu zakrytycznego w obszarze sprężystym i sprężysto-plastycznym prostokątnych płyt poddanych ściskaniu. Rozważano płyty wstępnie wygięte, o różnej geometrii, wykonane z materiału o różnych wartościach granic plastyczności na ściskanie i rozciąganie. Badania prowadzono w oparciu o nieliniową teorię cienkich płyt z uwzględnieniem kryterium plastyczności Tsai-Wu. Rozwiązanie uzyskano na drodze analityczno-numerycznej stosując równania Prandtla-Reussa w postaci przyrostowej. Wyniki obliczeń numerycznych przedstawiono na wykresach.
8
First integrals of evolution systems and nonlinear stability of stationary solutions for the ideal atmospheric, oceanic, hydrodynamical and plasma models
Gordin V.
Journal of Technical Physics
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1998
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Vol. 39, no 2
213-219
EN
First integrals of the systems of nonlinear equations governing the behaviour of atmospheric, oceanic and MHD plasma models are determined. The Lyapunov stability conditions for the solutions under small initial disturbances are analyzed. \
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