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Shells are among the most demanding structures to analyse, because of their complicated geometry and behaviour. Due to their importance in structural engineering, reliable and efficient methods are needed for their analysis and design, and there is a vast literature in this area. Analytical solutions are only available for simple geometries and loadings, and the solution of practical shell problems normally requires a numerical approach. The finite element method is by far the preferred method, due to its generality and ability to deal with complex geometries. The literature on finite elements for shells is also vast, and many shell elements have been developed.

The two basic load-carrying modes that need to be modelled in a shell are the in-plane (plane stress) mode and the transverse bending (plate bending) mode. Two fundamental approaches to the development of shell finite elements are possible. One option is to use curved finite elements to try to closely model the shell geometry. In this approach, the two load-carrying modes are also coupled in the formulation. However, the development of these elements is generally complex, and numerical integration is required to derive the element matrices. The other option is to use flat shell elements where the two load-carrying modes are treated separately, and the load-carrying coupling is achieved by approximating the curved geometry using flat elements that meet at different orientations.

Flat shell elements are generally simpler to formulate, because elements for plane stress and plate bending can be combined to form a shell element. However, these elements also need care in their development, due to such issues as element locking and spurious mechanisms, and many techniques have been used to alleviate these problems.

The current paper discusses some new low-order thick shell elements. The plate-bending elements are based on Mindlin's theory, which includes shear deformation, and their formulation avoids shear locking by design. These elements are combined with plane stress elements, which can include in-plane rotations as element variables, to produce various flat shell elements. The applications and advantages of the elements are presented and compared. Examples are given in the paper to demonstrate the accuracy that is achieved with the proposed elements.

shell analysis, thick shells, shear deformation, finite elements