V. Piscopo

Publications

4 Refined Buckling Analysis of Rectangular Plates Under Uniaxial and Biaxial Compression

Authors: V. Piscopo

Abstract:

In the traditional buckling analysis of rectangular plates the classical thin plate theory is generally applied, so neglecting the plating shear deformation. It seems quite clear that this method is not totally appropriate for the analysis of thick plates, so that in the following the two variable refined plate theory proposed by Shimpi (2006), that permits to take into account the transverse shear effects, is applied for the buckling analysis of simply supported isotropic rectangular plates, compressed in one and two orthogonal directions. The relevant results are compared with the classical ones and, for rectangular plates under uniaxial compression, a new direct expression, similar to the classical Bryan-s formula, is proposed for the Euler buckling stress. As the buckling analysis is a widely diffused topic for a variety of structures, such as ship ones, some applications for plates uniformly compressed in one and two orthogonal directions are presented and the relevant theoretical results are compared with those ones obtained by a FEM analysis, carried out by ANSYS, to show the feasibility of the presented method.

Keywords: Buckling Analysis, Thick plates, Biaxial stresses

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3 Buckling Analysis of Rectangular Plates under the Combined Action of Shear and Uniaxial Stresses

Authors: V. Piscopo

Abstract:

In the classical buckling analysis of rectangular plates subjected to the concurrent action of shear and uniaxial forces, the Euler shear buckling stress is generally evaluated separately, so that no influence on the shear buckling coefficient, due to the in-plane tensile or compressive forces, is taken into account. In this paper the buckling problem of simply supported rectangular plates, under the combined action of shear and uniaxial forces, is discussed from the beginning, in order to obtain new project formulas for the shear buckling coefficient that take into account the presence of uniaxial forces. Furthermore, as the classical expression of the shear buckling coefficient for simply supported rectangular plates is considered only a “rough" approximation, as the exact one is defined by a system of intersecting curves, the convergence and the goodness of the classical solution are analyzed, too. Finally, as the problem of the Euler shear buckling stress evaluation is a very important topic for a variety of structures, (e.g. ship ones), two numerical applications are carried out, in order to highlight the role of the uniaxial stresses on the plating scantling procedures and the goodness of the proposed formulas.

Keywords: Buckling Analysis, shear, Uniaxial Stresses

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2 On the Exact Solution of Non-Uniform Torsion for Beams with Axial Symmetric Cross-Section

Authors: V. Piscopo, A.Campanile, M. Mandarino, A. Pranzitelli

Abstract:

In the traditional theory of non-uniform torsion the axial displacement field is expressed as the product of the unit twist angle and the warping function. The first one, variable along the beam axis, is obtained by a global congruence condition; the second one, instead, defined over the cross-section, is determined by solving a Neumann problem associated to the Laplace equation, as well as for the uniform torsion problem. So, as in the classical theory the warping function doesn-t punctually satisfy the first indefinite equilibrium equation, the principal aim of this work is to develop a new theory for non-uniform torsion of beams with axial symmetric cross-section, fully restrained on both ends and loaded by a constant torque, that permits to punctually satisfy the previous equation, by means of a trigonometric expansion of the axial displacement and unit twist angle functions. Furthermore, as the classical theory is generally applied with good results to the global and local analysis of ship structures, two beams having the first one an open profile, the second one a closed section, have been analyzed, in order to compare the two theories.

Keywords: Fourier Series, Helmholtz equation, Non-uniform torsion, Axial symmetric cross-section, FE method

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1 On the Exact Solution of Non-Uniform Torsion for Beams with Asymmetric Cross-Section

Authors: V. Piscopo, A.Campanile, M. Mandarino

Abstract:

This paper deals with the problem of non-uniform torsion in thin-walled elastic beams with asymmetric cross-section, removing the basic concept of a fixed center of twist, necessary in the Vlasov-s and Benscoter-s theories to obtain a warping stress field equivalent to zero. In this new torsion/flexure theory, despite of the classical ones, the warping function will punctually satisfy the first indefinite equilibrium equation along the beam axis and it wont- be necessary to introduce the classical congruence condition, to take into account the effect of the beam restraints. The solution, based on the Fourier development of the displacement field, is obtained assuming that the applied external torque is constant along the beam axis and on both beam ends the unit twist angle and the warping axial displacement functions are totally restrained. Finally, in order to verify the feasibility of the proposed method and to compare it with the classical theories, two applications are carried out. The first one, relative to an open profile, is necessary to test the numerical method adopted to find the solution; the second one, instead, is relative to a simplified containership section, considered as full restrained in correspondence of two adjacent transverse bulkheads.

Keywords: Fourier Series, asymmetric cross-section, Helmholtz equation, Non-uniform torsion, FE method

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