Corotational non‐linear analysis of thin plates and shells using a new shell element

Abstract

SUMMARYA new three-node triangular shell element is developed by combining the optimal membrane element and discrete Kirchhoff triangle (DKT) plate bending element, and is modified for laminated composite plates and shells so as to include the membrane-bending coupling effect. Using appropriate shape functions for the bending and membrane modes of the element, the 'inconsistent' stress stiffness matrix is formulated and the tangent stiffness matrix is determined. Non-linear analysis of thin-walled structures with geometric non-linearity is conducted using the corotational method. The new element is thoroughly tested by solving few popular benchmark problems. The results of the analysis are compared with those obtained using existing membrane elements.

A 3-Node Co-Rotational Triangular Elasto-Plastic Shell Element Using Vectorial Rotational Variables

“…A 3-node triangular shell element can be formulated by combining a membrane element and a bending element [9][10][11][12], or by relying on three-dimensional continuum mechanics with the Reissner-Mindlin kinematic hypothesis and the plane-stress assumption [8,13]. Existing 3-node triangular shell elements can be categorized into 4 types: Type 1 with only 3 displacement degrees-of-freedom (dofs) per node [14][15][16][17][18][19][20][21][22]; Type 2 with 3 displacement dofs and 2 rotational dofs per node [23][24][25]; Type 3 with 3 displacement dofs at the vertices and the rotational dofs at side nodes [26][27]; Type 4 with 3 displacement dofs and 3 rotational dofs per node [28][29][30][31][32][33].…”

“…A flat shell element with 5 degrees-of-freedom per corner node can be obtained by combining a conventional triangular membrane element with a standard 9-dof triangular bending element. On the other hand, if several elements of this type sharing the same node are coplanar, it is difficult to achieve inter-element compatibility between membrane and transverse displacements, and the assembled global stiffness matrix is singular in shell analysis due to the absence of in-plane rotation degrees-of-freedom [9][10][11][12]34]. In addition, flat shell elements with 5 degrees-of-freedom per node lack proper nodal degrees of freedom to model folded plate/shell structures, making the assembly of elements troublesome [35].…”

“…This type of elements cannot, however, be easily matched with other types of elements in modeling of complex structures. Alternatively, some researchers [9][10][11][12] added a sixth degree of freedom (the drilling rotation) at each node of flat triangular shell elements by combining a bending element and a membrane element with drilling rotational degrees-of-freedom. Such shell elements are very convenient for engineering applications since no special connection scheme is necessary at the shell edges and intersections, and no particular care needs to be taken when coupling shell and rod elements [36].…”

Sensitive couture for interactive garment modeling and editing

“…Before adopting IBM, we implemented a co-rotational treatment of the Discrete Kirchhoff Triangle [Batoz et al 1980;Khosravi et al 2007], but found that we needed a stronger guarantee of stability in the context of our interactive tool. We then adopted nonlinear hinges [Bridson et al 2003;Grinspun et al 2003], which lose some of the meshingindependence of DKT [Batoz et al 1980] but increase stability.…”

An Explicit Consistent Geometric Stiffness Matrix for the DKT Element

“…It is considered in several papers dealing with linear and nonlinear analysis of general shell structures (Bathe and Ho, 1981;Cook, 1993;Khosravi et al, 2007;Zhang et al, 2015). High-speed component impact analysis (Wu et al, 2005) demonstrates, for instance, that this element performs as good as the main element (Belytschko et al, 1984) used for crashworthiness analyses.…”