Abstract

In this paper a finite element for the non-linear analysis of two dimensional beams and axisymmetric shells is presented. The element uses classical thin shell assumptions (no transverse shear strains). The main feature of the element is that it has no rotational degrees of freedom. Curvatures are computed using geometrical information from the patch of three elements formed by the main element and the two neighbour (adjacent) elements. Special attention is devoted to non-smooth geometries and branching shells. An elastic-plastic material law is considered. Large strains are treated using a logarithmic strain measure and a through-the-thickness numerical integration of the constitutive equations. Several examples are presented including linear problems to study convergence properties, and non-linear problems for both elastic and elastic-plastic materials and large strains.

Abstract

A two noded, straight element which includes shear deformation effects is presented and shown to be extremely efficient in the analysis of axisymmetric shells. A single point of numerical integration is essential for its success when applied to thin shells where the results compare favourably with those achieved with more complex curved elements.

Abstract

A unified approach for the vibration analysis of curved or straight prismatic plates and bridges and axisymmetric shells using a finite strip method based in Reissner—Mindlin shell theory is presented. Details of obtaining all relevant strip matrices and vectors are given. It is also shown how the use of the simple linear two node strip with reduced integration leads to direct explicit forms of all relevant matrices. Examples of application which show the accuracy of the linear strip for free vibration analysis of structures are presented.

Abstract

In this paper a finite strip formulation which allows to treat bridges, axisymmetric shells or plate structures of constant transverse cross section in an easily and unified manner is presented. The formulation is based on Mindlin's shell plate theory. One dimensional finite elements are used to discretize the transverse section and Fourier expansions are used to define the longitudinal/circumferential behavior of the structure. The element used is the simple two noded strip element with just one single integrating point. This allows to obtain all the element matrices in an explicit and economical form. Numerical examples for a variety of straight and curve bridges, axisymmetric shells and plate structures which show the efficiency of the formulation and accuracy of the linear strip element are given.