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This paper deals with the well known degenerated shell element of Ahmad. The main concern focuses on the rank of the element stiffness matrix and the zero energy modes. Element formulation includes geometrical and material non‐linearities. The Lagrangian, heterosis and serendipity variants of displacement approximation are studied using full, selective or reduced in‐plane numerical integration. In the third direction the layered concept is adopted. The obtained results do not fully coincide with those published in References 2 and 3. The Figures presented in this paper, showing the displacement modes, clarify in a convenient form some of the element properties associated with particular element formulations. The work also shows the influence of the plastic and cracked material conditions on the stiffness matrix of the element.

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.

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.

Two isoparametric Lagrangian shallow shell elements are presented: a 4‐node element QUAD4 and a 9‐node element QUAD9. These elements are based on Mindlin/Reissner plate elements as described in a series of papers. These elements are sophisticated by adding conventional membrane stiffness and membrane‐bending coupling terms based on Maguerre's approximate shallow shell theory. This results in double curved shell elements which originally possess severe membrane locking behaviour. This defect is overcome in the same way as the shear locking problem is solved.

A generalized displacement method has been previously presented for the analysis of thin plate‐shell structures with the use of bilinear 4‐node isoparametric shell elements. Following this approach, a procedure for the geometrically non‐linear analysis of thin plates and shells based on both updated and total Lagrangian formulations is developed. The results of some numerical examples are presented to show the versatility and effectiveness of the method.

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.

The optimization of variable thickness plates and shells is studied. In particular, three types of shell are considered: hyperbolic paraboloid, conoid and cylindrical shell. The main objective is to investigate the optimal thickness distributions as the geometric form of the structure changes from a plate to a deep shell. The optimal thickness distribution is found by use of a structural optimization algorithm which integrates the Coons patch technique for thickness definition, structural analysis using 9‐node Huang‐Hinton shell elements, sensitivity evaluation using the global finite difference method and the sequential quadratic programming method. The composition of the strain energy is monitored during the optimization process to obtain insight into the energy distribution for the optimum structures. Several benchmark examples are considered illustrating optimal thickness variations under different loading, boundary and design variable linking conditions.

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.

A new four‐node (non‐flat) general quadrilateral shell element for geometric and material non‐linear analysis is presented. The element is formulated using three‐dimensional continuum mechanics theory and it is applicable to the analysis of thin and thick shells. The formulation of the element and the solutions to various test and demonstrative example problems are presented and discussed.

The purpose of this paper is to present an accurate and efficient element for analysis of spherical shell structures.

A scaled boundary finite element method is proposed, which offers more advantages than the finite element method and boundary element method. Only the boundary of the computational domain needs to be discretized, but no fundamental solution is required.

The method applies to thin as well as thick spherical shells, irrespective of the shell geometry, boundary conditions and applied loading. The numerical solution converges to highly accurate result with raising the order of high-order elements.

The modeling strictly follows three-dimensional theory of elasticity. Formulation of the surface finite elements using three translational degree of freedoms per node is required, which results in considerably simplifying the computation. In the thickness directions, it is solved analytically, no problem of high aspect ratio arises and transverse shear locking can be successfully avoided.