Abstract
This paper presents a computationally efficient numerical model for the analysis of thin shells based on rotation-free triangular finite elements. The geometry of the structure in the vicinity of the observed triangular element is approximated through a controlled domain consisting of nodes of the observed finite element and nodes of three adjacent finite elements between which a second-order spatial polynomial is defined. The model considers large displacements, large rotations, small strains, and material and geometrical nonlinearity. Material nonlinearity is implemented by considering the von Mises yield criterion and the Levi–Mises flow rule. The model uses an explicit time integration scheme to integrate motion equations but an implicit radial returning algorithm to compute the plastic strain at the end of each time step. The presented numerical model has been embedded in the program Y based on the finite–discrete element method and tested on simple examples. The advantage of the presented numerical model is displayed through a series of analyses where the obtained results are compared with other results presented in the literature.
Highlights
Shells, as structural elements, have been frequently applied in civil, automotive, naval, and aerospace engineering
This paper presents a computationally efficient numerical model for the analysis of thin shells based on rotation-free triangular finite elements
It cannot be concluded that the presented numerical model is better or worse than other numerical models of a similar type or that it can do something that could not be done with other numerical models
Summary
As structural elements, have been frequently applied in civil, automotive, naval, and aerospace engineering. The first numerical formulation, which belongs to the group of rotation-free numerical models, was proposed by Phaal and Calladine [14,15] This numerical model is based on the concept that the alteration of curvature at the examined finite element is related to the coordinates of three neighbouring FE nodes. Proposed numerical algorithms are based on the discretisation of plates and shells into three-noded triangles, the linear FE approximation of the displacement field within each triangle, and the finite-volume-type approach for computing the curvature and bending moment fields within the appropriate non-overlapping control domains using the mixed Hu–Washizu functional formulation. In the proposed numerical model, the hydrostatic and deviatoric stress tensors are presented in an incremental form given by: Td,t = Td,t−∆t + ∆Td Th,t = Th,t−∆t + ∆Th (11). Is implemented, where n, A, and B are three constitutive flow curve parameters
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