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Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

In this paper we derive a simple finite element formulation for geometrical nonlinear shell structures. The formulation bases on a direct introduction of the isoparametric finite element formulation into the shell equations. The element allows the occurrence of finite rotations which are described by two independent angles. A layerwise linear elastic material model for composites has been chosen. A consistent linearization of all equations has been derived for the application of a pure Newton method in the nonlinear solution process. Thus a quadratic convergence behaviour can be achieved in the vicinity of the solution point. Examples show the applicability and effectivity of the developed element.

This study aims to provide a reliable and effective algorithm that is suitable for addressing the problems of continuous orders of frequencies and modes under different boundary conditions, circumferential wave numbers and thickness-to-length ratios of moderately thick circular cylindrical shells. The theory of free vibration of rotating cylindrical shells is of utmost importance in fields such as structural engineering, rock engineering and aerospace engineering. The finite element method is commonly used to study the theory of free vibration of rotating cylindrical shells. The proposed adaptive finite element method can achieve a considerably more reliable high-precision solution than the conventional finite element method.

On a given finite element mesh, the solutions of the frequency mode of the moderately thick circular cylindrical shell were obtained using the conventional finite element method. Subsequently, the superconvergent patch recovery displacement method and high-order shape function interpolation techniques were introduced to obtain the superconvergent solution of the mode (displacement), while the superconvergent solution of the frequency was obtained using the Rayleigh quotient computation. Finally, the superconvergent solution of the mode was used to estimate the errors of the finite element solutions in the energy norm, and the mesh was subdivided to generate a new mesh in accordance with the errors.

In this study, a high-precision and reliable superconvergent patch recovery solution for the vibration modes of variable geometrical rotating cylindrical shells was developed. Compared with conventional finite element method, under the challenging varying geometrical circumferential wave numbers, and thickness–length ratios, the optimised finite element meshes and high-precision solutions satisfying the preset error limits were obtained successfully to solve the frequency and mode of continuous orders of rotating cylindrical shells with multiple boundary conditions such as simple and fixed supports, demonstrating good solution efficiency. The existing problem on the difficulty of adapting a set of meshes to the changes in vibration modes of different orders is finally overcome by applying the adaptive optimisation.

The approach developed in this study can accurately obtain the superconvergent patch recovery solution of the vibration mode of rotating cylindrical shells. It can potentially be extended to fine numerical models and high-precision computations of vibration modes (displacement field) and solid stress (displacement derivative field) for general structural special value problems, which can be extensively applied in the field of engineering computations in the future. Furthermore, the proposed method has the potential for adaptive analyses of shell structures and three-dimensional structures with crack damage. Compared with conventional finite element methods, significant advantages can be achieved by solving the eigenvalues of structures with high precision and stability.

A bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view is given. The bibliography at the end of the paper contains 1,726 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1996‐1999.

Presents a new B‐spline finite element for the dynamic analysis of unsymmetrical sandwich shells of revolution. The formulation takes account of the membrane and bending effects in isotropic or orthotropic elastic facings, and membrane, bending and transverse shearing effects in an isotropic or othotropic elastic core. Both geometry and local displacements are interpolated by a set of B‐spline functions. The main aspects added by the sandwich structure of the element are the transverse shearing and membrane‐bending coupling effects in the core. These are well represented by a set of new variables which are the mean end relative in‐plane displacements of the facing middle surfaces. Together with the transverse displacement, these variables constitute the degrees of freedom (dofs) of this new B‐spline sandwich element. The finite elements are grouped into super‐elements with C¹ continuity to obtain the whole finite element model. For each super‐element a total of five dofs per node is then obtained except for its end nodes where the derivatives of these dofs with respect to the meridional co‐ordinate are added. This choice reduces to a minimum the total number of dofs in comparison to existing sandwich elements. Evaluates the efficiency and accuracy of the proposed element through several benchmark examples. Compares the results with the analytical and numerical solutions found in the literature. A very satisfactory behaviour of the element was observed in all test cases.

A 4‐node flat shell quadrilateral finite element with 6 degrees of freedom per node, denoted QC5D‐SA, is presented. The element is an assembly of a modification of the drilling degree of freedom membrane presented by Ibrahimbegovic et al., and the assumed strain plate element presented by Bathe and Dvorkin. The part of the stiffness matrix associated with in—plane displacements and rotations is integrated over the element domain by a modified 5‐point reduced integration scheme, resulting in greater efficiency without the sacrifice of rank sufficiency. The scheme produces a soft higher order deformation mode which increases numerical accuracy. A large number of standard benchmark problems are analyzed. Some examples show that the effectiveness of a previously proposed “membrane locking correction” technique is significantly reduced when employing distorted elements. However, the element is shown to be generally accurate and in many cases superior to existing elements.

A stiffened shell element is presented for geometrically non‐linear analysis of eccentrically stiffened shell structures. Modelling with this element is more accurate than with the traditional equivalent orthotropic plate element or with lumping stiffeners. In addition, mesh generation is easier than with the conventional finite element approach where the shell and beam elements are combined explicitly to represent stiffened structures. In the present non‐linear finite element procedure, the tangent stiffness matrix is derived using the updated Lagrangian formulation and the element strains, stresses, and internal force vectors are updated employing a corotational approach. The non‐vectorial characteristic of large rotations is taken into account. This stiffened shell element formulation is ideally suited for implementation into existing linear finite element programs and its accuracy and effectiveness have been demonstrated in several numerical examples.

This paper aims to present a new numerical model for geometric nonlinear analysis of thin-shell structures based on a combined finite-discrete element method (FDEM).

The model uses rotation-free, three-node triangular finite elements with exact formulation for large rotations, large displacements in conjunction with small strains.

The presented numerical results related to behaviour of arbitrary shaped thin shell structures under large rotations and large displacement are in a good agreement with reference solutions.

This paper presents new computationally efficient numerical model for geometric nonlinear analysis and prediction of the behaviour of thin-shell structures based on combined FDEM. The model is implemented into the open source FDEM package “Yfdem”, and is tested on simple benchmark problems.

The purpose of this study is dedicated to use an efficient mixed strain finite element approach to develop a three-node triangular shell element. Moreover, large deformation analysis of the functionally graded material shells is the main contribution of this research. These target structures include thin or moderately thick panels.

Due to reach these goals, Green–Lagrange strain formulation with respect to small strains and large deformations with finite rotations is used. First, an efficient three-node triangular degenerated shell element is formulated using tensorial components of two-dimensional shell theory. Then, the variation of Young’s modulus through the thickness of shell is formulated by using power function. Note that the change of Poisson’s ratio is ignored. Finally, the governing linearized incremental relation was iteratively solved using a high potential nonlinear solution method entitled generalized displacement control.

Some well-known problems are solved to validate the proposed formulations. The suggested triangular shell element can obtain the exact responses of functionally graded (FG) shell structures, without any shear locking, instabilities and ill-conditioning, even by using fewer numbers of the elements. The obtained outcomes are compared with the other reference solutions. All findings demonstrate the accuracy and capability of authors’ element for analyzing FG shell structures.

A mixed strain finite element approach is used for nonlinear analysis of FG shells. These structures are curved thin and moderately thick shells. Small strains and large deformations with finite rotations are assumed.

FG shells are mostly made curved thin or moderately thick, and these structures have a lot of applications in the civil and mechanical engineering.

The social implication of this study is concerned with how technology impacts the world. In short, the presented scheme can improve structural analysis ways.

Developing an efficient three-node triangular element, for geometrically nonlinear analysis of FG doubly-curved thin and moderately thick shells, is the main contribution of the current research. Finite rotations are considered by using the Taylor’s expansion of the rotation matrix. Mixed interpolation of strain fields is used to alleviate the locking phenomena. Using fewer numbers of shell elements with fewer numbers of degrees of freedom can reduce the computational costs and errors significantly.

Offshore structures are generally constructed as frameworks of tubular members. The tubular joints should be designed to allow the full post yield or post buckled capacity of the members. However, design guidelines for ultimate strength capacity of these joints are based exclusively upon compilations of test data for simple configurations under simple loading conditions. A methodology based upon the finite element method is presented for analytically predicting the ultimate strength of arbitrary tubular joints. Eight node, isoparametric, curved shell elements were used for the majority of the tubular joint model. Twenty node, isoparametric, solid elements were used to capture the three‐dimensional stress state at the shell intersection while fifteen node, isoparametric, wedge elements modelled the weld profile. Solid‐shell transition elements provided the connection between the three‐dimensional solid elements and the surface based shell elements. Non‐linearities were included via an elastoplastic material model with isotropic strain hardening and the updated Lagrangian approach for finite deflections and rotations. Several experimental tubular joint analyses were reproduced to validate the analytical procedure. Non‐linear finite element analysis was shown to be a practical approach for the evaluation and extension of current design procedures for tubular joints.