A rotation‐free shell formulation using nodal integration for static and dynamic analyses of structures

Abstract

SUMMARYThis paper proposed a rotation-free thin shell formulation with nodal integration for elastic-static, free vibration, and explicit dynamic analyses of structures using three-node triangular cells and linear interpolation functions. The formulation is based on the classic Kirchhoff plate theory, in which only three translational displacements are treated as the filed variables. Based on each node, the integration domains are further formed, where the generalized gradient smoothing technique and Green divergence theorem that can relax the continuity requirement for trial function are used to construct the curvature filed. With the aid of strain smoothing operation and tensor transformation rule, the smoothed strains in the integration domain can be finally expressed by constants. The principle of virtual work is then used to establish the discretized system equations. The translational boundary conditions are imposed same as the practice of standard finite element method, while the rotational boundary conditions are constrained in the process of constructing the smoothed curvature filed. To test the performance of the present formulation, several numerical examples, including both benchmark problems and practical engineering cases, are studied. The results demonstrate that the present method possesses better accuracy and higher efficiency for both static and dynamic problems.

Stability Analysis of Circular Tunnels in Cohesive-Frictional Soil Using the Node-Based Smoothed Finite Element Method (NS-FEM)

“…Typical S-FEM models include the cell-based S-FEM model (CS-FEM) [26], node-based S-FEM model (NS-FEM) [27,28], and edge-based S-FEM model (ES-FEM) [29][30][31][32]. Several papers demonstrate that the NS-FEM performs well in heat transfer analysis [33,34], fracture analysis [35], acoustic problems [36,37], axisymmetric shell structures [38], static and dynamic analysis [39][40][41]. Recently, T. Vo-Minh and his co-workers [42][43][44][45] applied an upper bound limit analysis using NS-FEM and second-order cone programming (SOCP) to determine the twin circular and dual square tunnels' stability cohesive-frictional soils.…”

Stochastic analysis using the generalized perturbation stable node-based smoothed finite element method

“…The stable nodal integration method with strain gradient has been presented by Feng [36] and Wang [37][38][39]. Firstly, the operation of strain smoothing is carried out within every smoothing domain in the same manner of NS-FEM.…”