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A linear and geometrically non‐linear computation of a laminated composite torispherical shell subjected to internal pressure was performed by using the layered finite element whose formulation is based on degeneration principle. Geometric non‐linearity in terms of large deformations with total Lagrangian formulation was taken into account. The effect of the lamination schemes on geometric non‐linear behaviour and stress resultant distributions was analysed. The fibre directions have not a great influence on the shape of the load‐displacement curves. In contrast to the hoop stress resultant distribution, the moment distribution is significantly influenced by the lamination schemes. The influence of the lamination schemes on bending moments is greater in non‐linear than in linear computations. Likewise, the effect of the fibre orientation is greater on the hoop than on the meridional moment distribution. In unsymmetric laminated shells the values of the hoop moments exceed those of the meridional moments which is a considerable difference from metallic isotropic shells.

This paper aims to present a new mathematical model for laminated rhombic conoids with reasonable thickness and depth. The presented model does not require the shear correction factor, as transverse strain variation through the thickness was assumed as a parabolic function. The zero transverse shear stress provision at the bottom and the top of rhombic conoids was enforced in the model. The presented model implemented a C⁰ finite element (FE) model, eliminating C¹ continuity requirement in the mathematical model. The proposed model was validated with analytical, experimental and other methods derived from the literature.

A novel mathematical model for laminated composite skew conoidal shells has been proposed. Parabolic transverse shear strain deformation across thickness is considered. FE coding of the proposed novel mathematical model was done. Slope continuity requirement associated with present FE coding has been suitably avoided. No shear correction factor is required in the present formulation.

This is the first attempt to study the bending response of laminated rhombic conoids with reasonable thickness and depth. After comparisons, the parametric study was performed by varying the skew angles, boundary conditions, thickness ratios and the minimum rise to maximum rise (hl/hh) ratio.

The novelty of the presented model is reflected by the simultaneous addition of twist curvature in the strain field as well as the curvature in the displacement field allowing the accurate analysis of reasonably thick and deep laminated composite rhombic conoids. The behavior of conoids differs from that of usual shells such as cylindrical and spherical due to the conoid’s inherent twist curvature with its complex geometry and different location of maximum deflection.

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.

Presents a robust and unconditionally stable return‐mapping algorithm based on the discrete counterpart of the principle of maximum plastic dissipation. Develops the explicit expression for the consistent elasto‐plastic tangent modulus. All expressions are derived via tensor formulation showing the advantage over the classical matrix notation. The integration algorithm is implemented in the formulation of the four‐node isoparametric assumed‐strain finite‐rotation shell element employing the Mindlin‐Reissner‐type shell model. By applying the layered model, plastic zones can be displayed through the shell thickness. Material non‐linearity described by the von Mises yield criterion and isotropic hardening is combined with a geometrically non‐linear response assuming finite rotations. Numerical examples illustrate the efficiency of the present formulation in conjunction with the standard Newton iteration approach, in which no line search procedures are required. Demonstrates the excellent performance of the algorithm for large time respective load steps.