A new plate shell element of 16 nodes and 40 degrees of freedom by relative displacement method

Abstract

SUMMARYAn isoparametric plate shell element of 16 nodes and 40 degrees of freedom is developed in this paper directly from 3-D elastic theories. In order to overcome the difficulties caused by straightforward use of a 3-D formulation, the relative displacement method is introduced. For curved shell elements, the use of the orthogonal curvilinear co-ordinate system greatly reduces the computer effort. The new element can conveniently solve shell problems with variable thicknesses and also easily link with other finite elements using displacement d.0.f. such as 8-node to 21-node 3-D elements. Numerical examples demonstrate the efficiency of the element. . INTRODUCTIONDerived from the 3-D isoparametric element, the 8-node general shell element in the Cartesian co-ordinate system'" has quite good overall performance. As there exists the co-ordinate transformation, more computer time is needed to run a problem. To eliminate this time-costing co-ordinate transformation, Li4 introduced the orthogonal curvilinear co-ordinate system into the element, which largely saved computational time and resulted in a more excellent shell element. But these two curved shell elements have two rotational components, and their formulation is still a bit complex. The two non-displacement components also make them inconvenient to link with other 3-D elements using displacement d.0.f. Therefore, it seems natural trying to employ 3-D formulation to construct a plate shell element with simpler formulation. As is indicated in Reference 1 , it is indeed feasible to do so. The work in the present paper was such an attempt to establish a new element directly based on 3-D formulation, and it proved to be a success.However, the results offered by such an element with 48 d.0.f. would converge to a false solution, as is pointed out in Reference 1 . But if we use the two usual shell assumptions that the stresses and strains in the direction of plate shell normals are both assumed zero, then the correct convergence of the element can be guaranteed. The second hypothesis also makes the element possible to have only 40 degrees of freedom with the other eight eliminated. Figure 1 shows the 16-node platelshell element degenerated from a 20-node 3-D element. As is the usual practice, a relationship between the Cartesian co-ordinates of any point of the 0748-80251 9310 100 1 5-06%08.00 FORMULATION OF PLATE ELEMENT

An improved assumed strain solid–shell element formulation with physical stabilization for geometric non‐linear applications and elastic–plastic stability analysis

“…Xu and Cai [54] proposed a 16-node displacement-based isoparametric element with 40 degrees of freedom and plane-stress assumptions. Sze and Ghali [55] modified the 8-node hexahedral hybrid element first proposed by Pian and Tong [56] by introducing adjustable parameters in order to avoid excessively stiff behavior and to recover shell, plate, and beam solutions.…”

A new assumed strain solid-shell formulation “SHB6” for the six-node prismatic finite element

“…In this regard, considerable attention has been focused on the idea of modifying three-dimensional elements so that they are able to accurately reproduce the behavior of thin shell structures. The pioneering authors dealing with thin structure modeling by means of three-dimensional elements without rotational degrees of freedom include Graf et al [18], Xu and Cai [19], Sze and Ghali [20], Kim and Lee [21], and Buragohain and Ravichandran [22].…”

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“…Xu et al, (1993) proposed a 16-node displacement-based isoparametric element with 40 degrees of freedom and planestress assumptions. Sze et al, (1993) modified the 8-node hexahedral hybrid element, first proposed by (Pian et al, 1986), by introducing adjustable parameters in order to avoid too stiff behavior and to recover shell, plate and beam solutions.…”