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A C° continuous finite element higher‐order displacement model is developed for the dynamic analysis of laminated composite plates. The displacement model accounts for non‐linear distribution of inplane displacement components through the plate thickness and the theory requires no shear correction coefficients. Explicit time marching schemes are adopted for integration of the dynamic equilibrium equation and a diagonal ‘lumped’ mass matrix is employed with a special procedure applicable to Lagrangian parabolic isoparametric elements. The parametric effects of the time step, finite element mesh, lamination scheme and orthotropy on the transient response are investigated. The effect of the coupling on the transient response is also investigated. Numerical results for deflections and stresses are presented for rectangular plates under various boundary conditions and loadings and compared with results from other sources.

This paper attempts to evaluate the transverse stresses that are generated within the interface between two layers of laminated composite and sandwich laminates by using Cℴ finite element formulation of higher‐order theories. These theories do not require the use of a fictitious shear correction coefficient which is usually associated with the first‐order Reissner‐Mindlin theory. The in‐plane stresses are evaluated by using constitutive relations. The transverse stresses are evaluated through the use of equilibrium equations. The integration of the equilibrium equations is attempted through forward and central direct finite difference techniques and a new approach, named as, an exact surface fitting method. Sixteen and nine‐noded quadrilateral Lagrangian elements are used. The numerical results obtained by the present approaches in general and the exact surface fitting method in particular, show excellent agreement with available elasticity solutions. New results for symmetric sandwich laminates are also presented for future comparisons.

A C° finite element formulation for flexure‐membrane coupling behaviour of an unsymmetrically laminated plate based on a higher‐order displacement model and three‐dimensional state of stress and strain is presented. This theory incorporates the more realistic non‐linear variation of displacements through the plate thickness, thus eliminating the use of a shear correction coefficient. The discrete element chosen is a nine‐noded quadrilateral with 12 degrees of freedom per node. The computer program developed incorporates the realistic prediction of interlaminar stresses from equilibrium equations. The present solution for deflection and stresses is compared with those obtained using three‐dimensional elasticity theory, another higher‐order shear deformation theory and Mindlin theory. In addition, numerical results for unsymmetric sandwich plates are presented for future reference.

A unified approach is presented for the pseudo‐transient (static) linear and geometrically non‐linear analyses of composite laminates. A finite element idealization with a four‐noded linear and a nine‐noded quadrilateral isoparametric elements, both belonging to the Lagrangian family are used in space discretization. An explicit time marching scheme is employed for time integration of the resulting discrete ordinary differential equations with the special forms of diagonal fictitious mass and/or damping matrices. The accuracy of the formulation is then established by comparing the presnt pseudo‐transient analysis results with the present static Newton‐Raphson method results and other available analytical closed‐form two dimensional and finite element solutions. The usefulness and effectiveness of this approach is established by comparing computational time required by this approach and Newton‐Raphson's approach.

Three‐dimensional transient analysis of a submerged cylindrical shell is presented. Three‐dimensional trilinear eight‐noded isoparametric fluid element with pressure variable as unknown is coupled to a nine‐noded degenerate shell element. Staggered solution scheme is shown to be very effective for this problem. This allows significant flexibility in selecting an explicit or implicit integrator to obtain the solution in an economical way. Three‐dimensional transient analysis of the coupled shell fluid problem demonstrates that inclusion of bending mode is very important for submerged tube design—a factor which has not received attention, since most of the reported results are based on simplified two‐dimensional plane strain analysis.

This paper focuses attention on a three field coupled problem consisting of two cylindrical shells submerged in an acoustic medium. Method of partitioning is used successfully to partition the three fields. It is shown that the two cylinders are coupled by three‐dimensional flow field and bending mode is important. The paper ends with concluding remarks for extending this method for safety analysis of submerged tubes to include non‐linear fluid/structure behaviour.

This paper demonstrates the capability of staggered solution procedure for coupled fluid‐structure interaction problems. Three possible computational paths for coupled problems are described. These are critically examined for a variety of coupled problems with different types of mesh partitioning schemes. The results are compared with the reported results by continuum mechanics priority approach—a method which has been very popular until recently. Optimum computational paths and mesh partitionings for two field problems are indicated. Staggered solution procedure is shown to be quite effective when optimum path and partitionings are selected.

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 simple shape-free high-order hybrid displacement function element method is presented for precise bending analyses of Mindlin–Reissner plates. Three distortion-resistant and locking-free eight-node plate elements are proposed by utilizing this method.

This method is based on the principle of minimum complementary energy, in which the trial functions for resultant fields are derived from two displacement functions, F and f, and satisfy all governing equations. Meanwhile, the element boundary displacements are determined by the locking-free arbitrary order Timoshenko’s beam functions. Then, three locking-free eight-node, 24-DOF quadrilateral plate-bending elements are formulated: HDF-P8-23β for general cases, HDF-P8-SS1 for edge effects along soft simply supported (SS1) boundary and HDF-P8-FREE for edge effects along free boundary.

The proposed elements can pass all patch tests, exhibit excellent convergence and possess superior precision when compared to all other existing eight-node models, and can still provide good and stable results even when extremely coarse and distorted meshes are used. They can also effectively solve the edge effect by accurately capturing the peak value and the dramatical variations of resultants near the SS1 and free boundaries. The proposed eight-node models possess potential in engineering applications and can be easily integrated into commercial software.

This work presents a new scheme, which can take the advantages of both analytical and discrete methods, to develop high-order mesh distortion-resistant Mindlin–Reissner plate-bending elements.

A new simple parametric shear deformation theory applicable to isotropic and functionally graded plates is developed. This new theory has five degrees of freedom, provides parabolic transverse shear strains across the thickness direction and hence, it does not need shear correction factor. Moreover, zero-traction boundary conditions on the top and bottom surfaces of the plate are satisfied rigorously. The paper aims to discuss these issues.

Material properties are temperature-dependent and vary continuously through the thickness according to a power law distribution. The plate is assumed to be initially stressed by a temperature rise through the thickness. The energy functional of the system is obtained using Hamilton’s principle. Free vibration frequencies are then calculated using a set of characteristic orthogonal polynomials and by applying Ritz method for different boundary conditions.

In the light of good performance of the present theory for all boundary conditions considered, it can be considered as an excellent alternative to some two-dimensional (2D) theories for approximating the tedious and time consuming three-dimensional plate problems.

To the best of the authors’ knowledge and according to literature survey, almost all published higher order shear deformation theories have been limited to simply supported boundary conditions and without taking into account the thermal stresses effects. The existing 2D shear deformation theories of Reddy, Karama and Touratier can be easily recovered. Furthermore, this feature can be highly appreciated in an iterative design process where a large number of derived plate models can be tested by selecting only two parameters in a simple polynomial function which is computationally efficient. Finally, new results are presented to show the effect of material variation, and temperature rise on natural frequencies of the FG plate for different boundary conditions.