Abstract
We have developed a curved finite element for a cylindrical thick shell based on the thick shell equations established in 1999 by Nzengwa and Tagne (N-T). The displacement field of the shell is interpolated from nodal displacements only and strains assumption. Numerical results on a cylindrical thin shell are compared with those of other well-known benchmarks with satisfaction. Convergence is rapidly obtained with very few elements. A scaling was processed on the cylindrical thin shell by increasing the ratioχ=h/2R(half the thickness over the smallest radius in absolute value) and comparing results with those obtained with the classical Kirchhoff-Love thin shell theory; it appears that results diverge at2χ=1/10=0.316because of the significant energy contribution of the change of the third fundamental form found in N-T model. This limit value of the thickness ratio which characterizes the limit between thin and thick cylindrical shells differs from the ratio 0.4 proposed by Leissa and 0.5 proposed by Narita and Leissa.
Highlights
In the field of structural mechanics the word shell refers to a spatial, curved structural member
We have developed a curved finite element for a cylindrical thick shell based on the thick shell equations established in 1999 by Nzengwa and Tagne (N-T)
After a brief presentation of Nzengwa and Tagne (NT) kinematic equations of elastic thick shells, we develop a curved cylindrical 3-node finite element based on both KL and N-T’s shell models using strain tensor interpolation assumption [23]
Summary
In the field of structural mechanics the word shell refers to a spatial, curved structural member. The very high structural and architectural potential of shell structures is used in various fields of civil, architectural, mechanical, aeronautical, and marine engineering. The strength of the double-curved structure is efficiently and economically used, for example, to cover large areas without supporting columns [1]. In addition to the mechanical advantages, the use of shell structures leads to aesthetic architectural appearance [2, 3]. Piping systems, curved panels, pressure vessels, bottles, buckets, and parts of cars are examples of shells used in mechanical engineering [4]. In aeronautical and marine engineering, shells are used in aircrafts, space crafts, missiles, ships, and submarines. Because of the spatial shape of the structure the behavior of shell structures is different from the behavior of beam and plate structures [4]
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