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A rotation‐free shell formulation using nodal integration for static and dynamic analyses of structures
Author(s) -
Wang G.,
Cui X. Y.,
Li G. Y.
Publication year - 2015
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4989
Subject(s) - smoothing , discretization , divergence theorem , mathematics , interpolation (computer graphics) , virtual work , finite element method , rotation (mathematics) , curvature , boundary (topology) , mathematical analysis , transformation (genetics) , node (physics) , mathematical optimization , geometry , classical mechanics , structural engineering , engineering , physics , motion (physics) , biochemistry , statistics , brouwer fixed point theorem , chemistry , fixed point theorem , gene
Summary This 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. Copyright © 2015 John Wiley & Sons, Ltd.