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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 purpose of this paper is to derive knockdown factor functions in terms of a shell thickness ratio (i.e. the ratio of radius to thickness) for conventional orthogrid and hybrid-grid stiffened cylinders for the lightweight design of space launch vehicles.

The shell knockdown factors of grid-stiffened cylinders under axial compressive loads are derived numerically considering various shell thickness ratios. Two grid systems using stiffeners – conventional orthogrid and hybrid-grid systems – are used for the grid-stiffened cylinders. The hybrid-grid stiffened cylinder uses major and minor stiffeners having two different cross-sectional areas. For modeling grid-stiffened cylinders with various thickness ratios, the effective thickness (t_eff) of the cylinders is kept constant, and the radius of the cylinder is varied. Thickness ratios of 100, 192 and 300 are considered for the orthogrid stiffened cylinder, and 100, 160, 200 and 300 for the hybrid-grid stiffened cylinder. Postbuckling analyses of grid-stiffened cylinders are conducted using a commercial nonlinear finite element analysis code, ABAQUS, to derive the shell knockdown factor. The single perturbation load approach is applied to represent the geometrical initial imperfection of a cylinder. Knockdown factors are derived for both the conventional orthogrid and hybrid-grid stiffened cylinders for different shell thickness ratios. Knockdown factor functions in terms of shell thickness ratio are obtained by curve fitting with the derived shell knockdown factors for the two grid-stiffened cylinders.

For the two grid-stiffened cylinders, the derived shell knockdown factors are all higher than the previous NASA’s shell knockdown factors for various shell thickness ratios, ranging from 100 to 400. Therefore, the shell knockdown factors derived in this study may facilitate in the development of lightweight structures of space launch vehicles from the aspect of buckling design. For different shell thickness ratios of up to 500, the knockdown factor of the hybrid-grid stiffened cylinder is higher than that of the conventional orthogrid stiffened cylinder. Therefore, it is concluded that the hybrid-grid stiffened cylinder is more efficient than the conventional orthogrid-stiffened cylinder from the perspective of buckling design.

The obtained knockdown factor functions may provide the design criteria for lightweight cylindrical structures of space launch vehicles.

Derivation of shell knockdown factors of hybrid-grid stiffened cylinders considering various shell thickness ratios is attempted for the first time in this study.

This paper aims to present a new robustness-based design strategy for thin-walled composite structures under compressive loading, which combines strength requirements in terms of the limit and ultimate load with robustness requirements evaluated from the structural energy until collapse.

In order to assess the structural energy, the area under the load-shortening curve between several characteristic points such as local buckling, global buckling, onset of degradation and collapse load is calculated. In this context, a geometrically nonlinear finite element analysis is carried out, in which the ply properties are selectively degraded by progressive failure.

The advantage of the proposed methodology is observed by analyzing unstiffened composite plates under compressive loading, wherein the lightest plate that satisfies both strength and robustness requirements can be attained.

As a practical implication, this methodology gives a new argument to accept the collapse load close to the ultimate load once robustness is ensured.

The structural energy is employed to investigate the robustness of thin-walled composite structures in postbuckling, and new energy-based robustness measures are proposed. In the design of composite structures, this innovative strategy might lead to a more robust design when compared to an approach that only accounts for the ultimate load.

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.

Contact problems are among the most difficult ones in mechanics. Due to its practical importance, the problem has been receiving extensive research work over the years. The finite element method has been widely used to solve contact problems with various grades of complexity. Great progress has been made on both theoretical studies and engineering applications. This paper reviews some of the main developments in contact theories and finite element solution techniques for static contact problems. Classical and variational formulations of the problem are first given and then finite element solution techniques are reviewed. Available constraint methods, friction laws and contact searching algorithms are also briefly described. At the end of the paper, a bibliography is included, listing about seven hundred papers which are related to static contact problems and have been published in various journals and conference proceedings from 1976.

With the widespread use of the composites over other metallic materials in different fields of engineering, studies on damages of composite structures have assumed great importance. Among various kinds of damages, delamination is of very serious concern to composite applications. It may arise as a consequence of impact loading, stress concentration near a geometrical or material discontinuity or manufacturing defects. The presence of one or more delaminations in the composite laminate may lead to a premature collapse of the structure due to buckling at a lower level of compressive loading. So the effect of delamination on stability of composite structures needs attention and thus constitutes a problem of current interest. The purpose of this paper is to deal with both numerical and experimental investigations on buckling behaviour of single and multiple, delaminated, industry driven, woven roving glass/epoxy composite plates on clamped free clamped free (CFCF) rectangular plates.

For numerical analysis, a finite element model was developed with an eight noded two dimensional quadratic isoparametric element having five degrees of freedom per node. The elastic stiffness matrices were derived using linear first order shear deformation theory with a shear correction factor. Green's nonlinear strain equations are used to derive the geometric stiffness matrix. The computation of buckling load based on present formulation is compared with the experimental results for the effect of different parameters on critical load of the delaminated composite panels. In the experimental study, the influences of various parameters such as delamination area, fiber orientations, number of layers, aspect ratios on the buckling behaviour of single and multiple delaminated woven roving glass/epoxy composite plates were investigated. Buckling loads were measured by INSTRON 1195 machine for the delaminated composite plates.

Comparison of numerical results with experimental results showed a good agreement. Both the results revealed that the area of delaminations, fiber orientations, number of layers and aspect ratio have paramount influence on the buckling behaviour of delaminated plate.

The present study is part of Jayaram Mohanty's doctoral thesis, an original research work.

The purpose of this paper is to investigate an analytical modeling for the thermoelastic buckling behavior of functionally graded (FG) rectangular plates (FGM) under thermal loadings. The material properties of FGM are assumed to vary continuously through the thickness of the plate, according to the simple power-law distribution. Derivations of equations are based on novel refined theory using a new hyperbolic shear deformation theory. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. In addition, numerical results for a variety of FG plates with simply supported edge are presented and compared with those available in the literature. Moreover, the effects of geometrical parameters of dimension the length to width aspect ratio (a/b), the plate width to thickness ratio (b/h), and material properties index (k) on the FGM buckling temperature difference are determined and discussed.

In the current paper, the application of the refined theory proposed by Shimpi is based on the assumption that the in-plane and transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The most interesting feature of this theory is that it accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. It is extended to the analysis of buckling behavior of ceramic-metal FG plates subjected to the three types of thermal loadings, namely; uniform temperature rise, linear temperature change across the thickness, and nonlinear temperature change across the thickness. The material properties of the FG plates are assumed to vary continuously through the thickness of the plate, according to the simple power-law distribution. Numerical results for a variety of FG plates with simply supported edges are given and compared with the available results, wherever possible. Additionally, the effects of geometrical parameters and material properties on the buckling temperature difference of FGM plates are determined and discussed.

Unlike any other theory, the theory presented gives rise to only four governing equations. Number of unknown functions involved is only four, as against five in case of simple shear deformation theories of Mindlin and Reissner (first shear deformation theory). The plate properties are assumed to be varied through the thickness following a simple power-law distribution in terms of volume fraction of material constituents. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions.

To the best of the authors’ knowledge, there are no research works for thermal buckling analysis of FG rectangular plates based on new four-variable refined plate theory (RPT). The novelty of this paper is extended the use of the above-mentioned RPT with the addition of a new function proposed by Shimpi for thermal buckling analysis of plates made of FG materials. Unlike any other theory, the number of unknown functions involved is only four, as against five in the case of other shear deformation theories. The theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate, hence it is unnecessary to use shear correction factors. The plates subjected to the two types of thermal loadings, namely; uniform temperature rise and nonlinear temperature change across the thickness. Numerical results for a variety of FG plates with simply supported edges are given and compared with the available results.

The practical behaviour of problems exhibiting bifurcation with secondary branches cannot be studied in general by using standard path‐following methods such as arc‐length schemes. Special algorithms have to be employed for the detection of bifurcation and limit points and furthermore for branch‐switching. Simple methods for this purpose are given by inspection of the determinant of the tangent stiffness matrix or the calculation of the current stiffness parameter. Near stability points, the associated eigenvalue problem has to be solved in order to calculate the number of existing branches. The associated eigenvectors are used for a perturbation of the solution at bifurcation points. This perturbation is performed by adding the scaled eigenvector to the deformed configuration in an appropriate way. Several examples of beam and shell problems show the performance of the method.

Two efficient computational procedures are presented for generating the global approximation vectors used in conjunction with the reduction methods for the large‐deflection non‐linear analysis of symmetric structures with unsymmetric boundary conditions. Both procedures are based on restructuring the governing equations for each of the unsymmetric global approximation vectors to delineate the different contributions to the symmetric and antisymmetric components of this vector. In the first procedure the unsymmetric global approximation vectors are approximated by linear combinations of symmetric and antisymmetric modes, which are generated by using the finite element method. The amplitudes of these modes are computed by using the classical Rayleigh‐Ritz technique. The second procedure is based on using a preconditioned conjugate gradient (PCG) technique for generating the global approximation vectors, and selecting the preconditioning matrix to be the matrix associated with the symmetric response. In both procedures the size of the analysis model used in generating the global approximation vectors is identical to that of the corresponding structure with symmetric boundary conditions. The similarities between the two procedures are identified, and their effectiveness is demonstrated by means of two numerical examples of large‐deflection, non‐linear static problems of shells.