Approximation of linear elastic shells by curved triangular finite elements based on elastic thick shells theory

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 ratio χ = h / 2 R (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 at 2 χ = 1 / 10 = 0.316 because 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.