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This paper deals with structural shape and thickness optimization of axisymmetric shell structures loaded symmetrically. In the finite element stress analysis use is made of newly developed linear, quadratic, and cubic, variable thickness, C(0) elements based on axisymmetric Mindlin‐Reissner shell theory. An integrated approach is used to carry out the whole shape optimization process in a fully automatic manner. A robust, versatile and flexible mesh generator is incorporated with facilities for generating either uniform or graded meshes, with constant, linear, or cubic variation of thickness, pressure etc. The midsurface geometry and thickness variations of the axisymmetric shell structure are defined using cubic splines passing through certain key points. The design variables are chosen as the coordinates and/or the thickness at the key points. Variable linking procedures are also included. Sensitivity analysis is carried out using either a semi‐analytical method or a global finite difference method. The objective of the optimization is the weight minimization of the structure. Several examples are presented illustrating optimal shapes and thickness distributions for various shells. The changes in the bending, membrane and shear strain energies during the optimization process are also monitored.

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.

The purpose of this paper is to provide an axisymmetric model of tube hydroforming using a Fourier Series based finite element method.

Fourier series interpolation function, which considerably reduces the size of the global stiffness matrix and the number of variables, is employed to approximate displacements. The material of the tube is assumed to be elastic‐plastic and to satisfy the plasticity model that takes into account the rate independent work hardening and normal anisotropy. Numerical solution obtained from an updated Lagrangian formulation of the general shell theory is employed. The axial displacement stroke (a.k.a. axial feed) during tube hydroforming is incorporated using Lagrange multipliers. Contact constraints and boundary friction condition are introduced into the formulation based on the penalty function, which imposes the constraints directly into the tangent stiffness matrix. A forming limit curve based on shear instability and experimental measurements are used as fracture criteria.

The results obtained from this new formulation are compared against the nonlinear finite element code ABAQUS and experimental measurements for isotropic and transversely anisotropic tube materials. The hoop and axial strains predicted with AXHD code compared excellently with those from ABAQUS FEM code using plane stress axisymmetric (SAX1) and four‐node shell (S4R) elements. However, in the case of aluminum, the numerically predicted maximum hoop strain underestimated the actual hoop strain measured from the tube bulging experiment.

The axisymmetric hydroforming program (AXHD) developed in this work is very efficient in simulating the free‐forming stage of the tube hydroforming process under simultaneous action of internal pressurization and displacement stroke.

Although Fourier Series based finite element method has been used in metal forming, the extended application presented in this paper is novel in the finite element analysis of tube hydroforming.

A simple estimate of the accuracy of the widely‐used Geckeler approximation for the axisymmetric bending of non‐shallow spherical shells is presented. Based on the edge‐deformation coefficients associated with a pair of arbitrary edge loadings, this estimate is independent of the actual surface‐loading and edge conditions of a practical shell. In this respect, the note complements the findings of an earlier error study, which was based on specific surface loadings and boundary conditions. The complementary nature of the work lies in its use for providing (in the absence of more specialised results) a reasonable assessment of the accuracy of the Geckeler approximation for any loading and/or boundary 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.

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.

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography at the end contains 2,177 references to papers, conference proceedings and theses/dissertations dealing with the subjects that were published in 1990‐2000.

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.

The Semiloof shell element stiffness and mass matrices are analysed. Various integration rules for the stiffness matrix are used, and the influence of these rules on the existence of mechanisms and on the element spectra is studied. Some methods for lumping the mass matrix are attempted with special reference to a method imposing a given behaviour of the spectra of eigenvalues.

The purpose of this paper is to investigate the approximation performance of a family of piecewise rational polynomial shape functions, which are enriched by a set of monomials of order p to obtain high order approximations. To numerically demonstrate the features of the enriched approximation some examples on the mechanical elastic response and free‐vibration of axisymmetric plates and shells are carried out.

The global approximation is based on a particular family of weight function, which is defined on the parametric domain of the element, ξ∈[−1,1], resulting in shape functions with compact support, which have regularity C₀^k,k=0,2,4… in the global domain Σ. The PU shape functions are enriched by a set of monomials of order p to obtain high order approximation spaces.

Based on the numerical results of elastic axisymmetric plates and shells, it is demonstrated that the proposed methodology produces satisfactory results in terms of keeping the ill‐conditioning of the system of equations under accepted levels. Comparisons are established between linear and Hermitian shape functions showing similar results. The observed results for the free‐vibration problem of plates and shells show the potential of the proposed approximation space.

In this paper the formulation is limited to the modeling of axisymmetric plate and shell problems. However, it can be applied to model other problems where the high regularity of the approximation is required.

The paper presents an alternative approach to construct partition of unity shape functions based on a particular family of weight function.