Three-node macro triangular shell element based on the assumed natural strains

Abstract

Finite element models with simple triangular geometry facilitate pre-processing for the finite element analysis. In the present study, a robust shear deformable triangular shell element formulation is presented for general plate and shell analysis, using three-node mesh discretization. The present formulation is developed on the basis of the assumed natural strain (ANS) formulation to attenuate the shear locking effect. Furthermore, this study proposes macro triangular element scheme by dividing a three-node triangular mesh into three parts to produce three individual ANS triangular elements and then merges these by condensing out the virtual center node. The performance of the macro ANS element is highly enhanced by reducing the number of sampling locations of three sub triangular element, but still utilizes three-node mesh discretization same as does the mesh used for three-node triangular elements. The macro ANS element has invariant stiffness, possesses no commutable zero energy mechanism. Numerical tests are presented to illustrate the high performance nature of the macro ANS element in general shell analysis. In particular, the numerical study demonstrates that the macro ANS element completely removes the shear locking effect that has been detrimental in shear deformable linear triangular elements so far.Keywords Finite element method (FEM), Three-node linear triangular element, Macro element, Shear locking effect, Assumed natural strain, Plate and shell analysis IntroductionThe finite element method is becoming a more powerful numerical tool, which is being conveniently utilized in the engineering community to simulate structure behavior. While the main computing process becomes very fast with the aid of growing computational power, the pre-processing of the complicated geometry of practical structures is still tedious and time-consuming. Specifically, mesh generation is one of great burdens for most engineers involved in the numerical simulation of practical structures. Automatic mesh generation techniques have been popularly utilized as a substitute for manual mesh generation. As far as mesh generation and its automatic processing are concerned, the simple triangular element with only three corner nodes has definite topological advantages over other element configurations.However, most simple triangular plate and shell elements suffer from low computational performance primarily due to the shear locking. Various approaches have been investigated to develop an efficient three-node triangular element formulation, which reduces the locking effect. Discrete Kirchhoff triangular (DKT) elements [Batoz (1980)] eradicate the shear locking effect by removing the shear deformation from element kinematics. However, the applicability of such elements is limited to thin structures, since transverse shear flexibility cannot be neglected in the analysis of thick or moderately thick shells. The discrete shear triangular plate element represents an improvement, whereby the shear deformation energy is included, and assume...

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