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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.

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.

The present paper deals with the numerical calculation of the behaviour of vertical wind‐loaded cylindrical shells (large liquid storage tanks) with a very flexible bottom plate resting on an elastic foundation. The base of the tank, i.e. the lower boundary of the shell and the bottom plate, may partially uplift due to the shell deformations under the dead load, a hydrostatic pressure and due to wind forces. This behaviour represents non‐linear boundary conditions of the tank wall. Hence, the stability of the wind‐loaded tank is extremely influenced by the uplift conditions. This non‐linear problem (large deformations and variable contact) is solved by the FE method.

In this paper, the problem of the elasto‐viscoplastic dynamic and thermal behaviour of geometrically non‐linear plates and shells is studied under the assumption of small strains and large rotations. The first‐order shear deformation shell theory and the Chaboche constitutive viscoplastic model taking the temperature fields into account are used for computations. An effective procedure using the central difference method of solving the equations of motion is applied. The trapezoidal method is used to integrate the constitutive viscoplastic law. A nine node isoparametric shell element has been utilised for the finite element algorithm. Finally, some examples are presented and compared with the results obtained by moderate rotation theory.

The purpose of this article is to carry out the thermal buckling analysis of power and sigmoid functionally graded material Sandwich plate (P-FGM and S-FGM) under uniform, linear, nonlinear and sinusoidal temperature rise.

Thermal buckling of FGM Sandwich plates namely, FGM face with ceramic core (Type-A) and homogeneous face layers with FGM core (Type-B), incorporated with nonpolynomial shear deformation theories are considered for an analytical solution in this investigation. Effective material properties and thermal expansion coefficients of FGM Sandwich plates are evaluated based on Voigt's micromechanical model considering power and sigmoid law. The governing equilibrium and stability equations for the thermal buckling analysis are derived based on sinusoidal shear deformation theory (SSDT) and inverse trigonometric shear deformation theory (ITSDT) along with Von Karman nonlinearity. Analytical solutions for thermal buckling are carried out using the principle of minimum potential energy and Navier's solution technique.

Critical buckling temperature of P-FGM and S-FGM Sandwich plates Type-A and B under uniform, linear, non-linear, and sinusoidal temperature rise are obtained and analyzed based on SSDT and ITSDT. Influence of power law, sigmoid law, span to thickness ratio, aspect ratio, volume fraction index, different types of thermal loadings and Sandwich plate types over critical buckling temperature are investigated. An analytical method of solution for thermal buckling of power and sigmoid FGM Sandwich plates with efficient shear deformation theories has been successfully analyzed and validated.

The temperature distribution across FGM plate under a high thermal environment may be uniform, linear, nonlinear, etc. In practice, temperature variation is an unpredictable phenomenon; therefore, it is essential to have a temperature distribution model which can address a sinusoidal temperature variation too. In the present work, a new sinusoidal temperature rise is proposed to describe the effect of sinusoidal temperature variation over critical buckling temperature for P-FGM and S-FGM Sandwich plates. For the first time, the FGM Sandwich plate is modeled using the sigmoid function to investigate the thermal buckling behavior under the uniform, linear, nonlinear and sinusoidal temperature rise. Nonpolynomial shear deformation theories are utilized to obtain the equilibrium and stability equations for thermal buckling analysis of P-FGM and S-FGM Sandwich plates.

This bibliography contains references to papers, conference proceedings, theses and books dealing with finite strip, finite prism and finite layer analysis of structures, materially and/or geometrically linear or non‐linear.

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.

A simple beam element is developed for the solution of large deflection problems. The total Lagrangian formulation is based on the kinematic relations proposed by Reissner for finite rotations and stretching as well as shearing of plane beams. The motion is discretized by linear expansions of the global displacement components and the cross‐sectional rotation in two‐dimensional Euclidean space yielding a simple beam element with three degrees of freedom at the two nodes. The shear locking is reduced by selective integration in order to eliminate the spurious shear constraint similar to interdependent variable interpolation. The large rotation formulation is compared with two forms of moderate rotation theories which have been used in the past to develop the geometric stiffness properties for linear stability analysis of the so‐called Mindlin plate elements. The predictive value of different geometric stiffness approximations is assessed with several examples which range from the static and kinetic stability analysis of the classical Euler‐column to the large deflection problem of a clamped beam.

This paper aims to numerically study the effects of boundary conditions, pre-stress, material constants and thickness on the dynamic performance of a wrinkled thin membrane.

Based on the stability theory of plates and shells, the dynamic equations of a wrinkled thin membrane were developed, and they were solved with the Lanczos method

The effects of wrinkle-influencing factors on the dynamic performance of a wrinkled membrane are determined by the wrinkling stage. The effects are prominent when wrinkling deformation is evolving, but they are very small and can hardly be observed when wrinkling deformation is stable. Mode shapes of a wrinkled membrane are sensitive to boundary conditions, pre-stress and Poisson’s ratio, but its natural frequencies are sensitive to all these five factors.

The research work in this paper is expected to help understand the dynamic behavior of a wrinkled membrane and present access to ensuring its dynamic stability by controlling the wrinkle-influencing factors.

Very few documents investigated the dynamic properties of wrinkled membranes. No attention has yet been paid by the present literature to the global dynamic performance of a wrinkled membrane under the influences of the factors that play a pivotal role in the wrinkling deformation. In view of this, this paper numerically studied the global modes and corresponding frequencies of a wrinkled membrane and their variation with the wrinkle-influencing factors. The results indicate that the global dynamic properties of a wrinkled membrane are sensitive to these factors at the stage of wrinkling evolution.

This paper 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 bibliography at the end of the paper contains more than 1330 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 1999–2002.