A theoretical formulation for frequency analysis of thin shells laminated with LASMP

This paper presents a free vibration analysis of shell panels made of functionally graded material (FGM) in the form of the ordinary and sandwich FGM and laminated shells using the isogeometric B3-spline finite strip method (IG-SFSM). B3-spline and Lagrangian interpolation are employed along the longitudinal and transverse directions respectively in this type of finite strip. The introduced finite strip formulation is based on the degenerated shell method, which provides variable thickness, arbitrary geometries, and analysis of thin or thick shells. Validity of the obtained natural frequencies by IG-SFSM is checked by comparison with results extracted from references for similar cases in different examples. These examples incorporate several geometries, materials, boundary conditions, and continuous thickness variation. A comparison of these two kinds of results and their proximity showed that the introduced IG-SFSM is a reliable tool which can be used in analysis of shells with the aforementioned properties.

To account for plastic deformation in plate and shell structures an elasto‐viscoplastic solution algorithm is considered based on Perzyna's model for material behaviour. This algorithm can be employed to solve for time‐dependent elasto‐viscoplastic situations and by allowing steady‐state conditions to be reached, elasto‐plastic problems can also be considered.For the large displacement elasto‐viscoplastic analysis of thin shells, an incremental stiffness procedure is employed together with a Lagrangian description of the stress and strain vectors. The Semiloof plate and shell elements are used for finite element space discretization.The procedures developed are applied to the solution of several numerical examples and the solutions compared with results from other sources where available.

Large deflection elastoplastic analysis of thin shells

This review article is devoted to an analysis of the literature on the stress-strain state of shells with developable middle surfaces. Wide choices of design methods for the developable surfaces provide not only the necessary shapes and special properties; they also prove to be convenient to apply. Representative examples are given for the static analysis of thin elastic shells by both analytic and numerical methods. Generally, the curvilinear non-orthogonal conjugate coordinates of the developable middle surface are used. Lines of principal curvatures are used as coordinates only for the strength analysis of thin shells in the form of Monge’s ruled surfaces. It is shown that momentless and moment theories give similar results if certain conditions are met a priori. The parabolic (isometric) bending of thin developable shells is also analyzed. This review article contains 97 references.

The principal achievements of science and engineering in the sphere of static and dynamic analysis of thin-walled objects, structures, and shells in the shape of analytic surfaces are used for practical needs of people. Classes of surfaces that found the application in forms of architectural erections and machine building products are considered. This is confirmed by presented illustrations of real products and erections. Classes of surfaces which did not attract the attention of architects and designers working with curvilinear forms are pointed out too. The presented materials confirm conclusions of most scientists, structural engineers, and architects on increasing interest to design and building of objects of curvilinear forms. The analysis noted the end of the recession of interest in thin shell and parish structures in the 21st century. These shell structures are produced due to the presence of new structural materials and the expansion of the list of analytical, point, spline, and frame surfaces that can be used as middle surfaces of shells. These surfaces are used for the study of certain physical processes, for solving particular mathematical problems and for determining surfaces isometric to surfaces of revolution, thus allowing the creation of more precise methods of calculating the strength of shells. This review paper contains 47 references, and these are practically all original sources dealing with applications, classifications, definition of analytical surfaces, and analysis of shells with middle surfaces in the form of analytical surfaces on strength, stability, and dynamic. It gives to use the opportunity of parametrical architecture.

Experimental investigation on reliable and accurate prediction of buckling analysis of thin cylindrical shells with geometric imperfections

The analysis of thin cylindrical shells is essential for a wide range of engineering applications, making it critical to understand their static behavior under various loading conditions. In this study, the static analysis of axisymmetric thin cylindrical shells is performed using the Complementary Functions Method (CFM). The research focuses on examining the static behavior of cylindrical shells made of homogeneous, isotropic, and linear elastic materials under various loading conditions. The governing differential equations for the static response of these structural elements are derived based on thin shell theory, utilizing the principle of minimum total potential energy. These equations are solved using CFM, an efficient numerical solution method. In this context, the CFM is coded in Wolfram Mathematica. To validate the accuracy and reliability of the proposed solution method, the results are compared with existing studies in the literature, demonstrating a high degree of consistency and confirming the effectiveness of the method. It has been observed that the type of loading significantly impacts the behavior of the shell.

Linear and non-linear analysis of thin shallow shells by mixed finite elements

Symplectic wave-based method for free and steady state forced vibration analysis of thin orthotropic circular cylindrical shells with arbitrary boundary conditions

The modal analysis of parabolic shells of revolution is based on using the finite-element model of inhomogeneous shell. The shells can have complex-shaped midsurface, geometrical features throughout the thickness, or multilayer structure. To develop the finite-element shell model we approximate a thin shell by one spatial finite element throughout the thickness. The structural elements of an inhomogeneous shell require the finite element to be universal: it should be eccentrically arranged relative to the mid-surfaces of the casing, it should be possible to vary the thickness of the lateral edges of the finite element and ets. The universal finite element is based on an isoparametric spatial finite element with polylinear shape functions for coordinates and displacements. Additional variable parameters are introduced to enhance the capabilities of the modified finite element. Two hypotheses are used to describe the features of the stress–strain state of a thin inhomogeneous shell. The static hypothesis assumes that the compressive stresses in the fibers throughout the thickness are constant. The nonclassical kinematic hypothesis of deformed straight line is used: a straight segment along the thickness remains straight though stretched or shortened during deformation. This segment is not necessarily normal to the mid-surface of the shell.The stress–strain state of a shell and its structural elements is determined using the geometrically nonlinear equations of the three-dimensional theory of thermoelasticity. A linear elastic continuous medium with large displacements and small strains is used as a model whose properties correspond to the generalized Duhamel–Neumann law. To derive the governing finite-element equations for displacements the moment finite-element scheme is used. The moment finite-element scheme approximations of displacements and strains guarantee a correct description of the rigid-body displacements of finite elements, which enhances the convergence and accuracy of solutions on coarse meshes.The natural vibrations of parabolic shells with various heights have been investigated. The convergence of solutions has been studied and compared with the results obtained by other authors.During operation, realistic shell structures often undergo various changes in the temperature field. This can significantly affect their dynamic characteristics. Extension of this work to modal analysis of parabolic shells considering heating is currently being pursued.

Input model for paper "Isogeometric analysis of thin Reissner-Mindlin shells: locking phenomena and B-bar method"

A simple formula is proposed, by which the error in the natural frequencies introduced by using the static condensation method can be evaluated prior to the numerical computation, though its effective applicability is found in simple structures such as plates and shells. The effectiveness of the proposed formula is examined in the vibration analysis of thin cylindrical shells having freely supported ends by using various reduction patterns. Not only the accuracy of natural frequencies, but also that of modal displacements and the corresponding modal stresses are investigated by comparing with the results obtained without reduction and with the exact analytical solutions given by Arnold and Warburton.

A generalized displacement method has been previously presented for the analysis of thin plate‐shell structures with the use of bilinear 4‐node isoparametric shell elements. Following this approach, a procedure for the geometrically non‐linear analysis of thin plates and shells based on both updated and total Lagrangian formulations is developed. The results of some numerical examples are presented to show the versatility and effectiveness of the method.

By introducing the application of the differential quadrature method (DQM) to the dynamic analysis of thin circular cylindrical shells, the work of this paper makes a step forward in furthering the potential of the DQM in the area of structural mechanics. The problem is identified by an eighth-order system of coupled partial differential equations in terms of the three displacement components. The proposed differential quadrature solution is semi-analytical in that Flu¨gge’s representation of the displacement components by trigonometric sine and cosine functions of the circumferential coordinate is employed. The results of the differential quadrature solutions of the natural frequencies of various shell cases are compared and shown to be in excellent agreement with the published, and also some recalculated, results of exact solutions for freely supported, clamped-clamped, clamped-free, and free-free shells. Comparisons are also made with the published experimental data of clamped-clamped and clamped-free shells.

Vibration analysis of thin shallow shells using spectral element method