The linear analysis of thin shell problems using the numerical manifold method

Although the numerical manifold method (NMM) has successfully solved many solid and flow problems, it has scarcely touched upon the analysis of shell problems. A shell is a genuine visible manifold in the real world and in principle NMM is pretty suitable to solve shell problems. This study aims to fill in the gap by employing the Naghdi shell model to establish NMM for shell analysis. The mathematical cover is constructed using the lines of curvature on the shell middle surface so that the best interpolation precision can be ensured. Thereafter, the standard 4-noded isoparametric shape functions are taken as the weight functions subordinate to the mathematical cover. Taking advantage of the favorable features of NMM, especially the facility to perform the p-adaptive analysis without compromising the element conformity, a high-order NMM model is employed to suppress the membrane and shear locking phenomena. Several typical shell benchmarks have been analyzed to testify the performance of the formulation in the static analysis of thin shell problems, manifesting that the proposed method can yield desirable results for linear thin shell problems, thus richly deserving the word “manifold”.