An assumed strain triangular solid shell element with bubble function displacements for analysis of plates and shells

Abstract

SUMMARYBubble function displacements are used in conjunction with the assumed strain formulation to construct e cient triangular solid shell elements tailored for shell analysis. Two versions of 36-DOF triangular elements are presented with di erent bubble function displacements and the corresponding assumed strain ÿelds. In the ÿrst version the bubble function displacement is independent of the thickness while in the second version the bubble function varies linearly in the thickness direction. The assumed strain ÿelds are carefully selected to alleviate locking e ect. The ÿrst version models curved shells with at triangular elements. The second version is e ective in alleviating the membrane locking and thus allows more accurate modelling of curved shells. Various numerical examples demonstrate the validity and e ectiveness of the present assumed strain formulation elements with the bubble function displacements.

Curved quadratic triangular degenerated‐ and solid‐shell elements for geometric non‐linear analysis

“…Moreover, As, Bs and U for the present solid-shell element are di erent from that of the previous degenerated-shell element. To ensure the plane-stress condition or, equivalent, avoid the thickness locking, the in-plane and out-of-plane responses in the material compliance matrix are decoupled [18,27,29]. Thus, the virtual work statement in (23) can be generalized to include the additional strain components and becomes:…”

“…A considerable amount of research e ort has been channeled into the development of solidshell elements in the last decade [18][19][20][21][22][23][24][25][26][27][28][29]. The most distinctive feature of solid-shell elements as compared to degenerated-shell elements is that the former elements do not possess any rotational d.o.f.s.…”

“…Besides shear and membrane lockings, solidshell elements can also be plagued by trapezoidal and thickness lockings [20,21,24,26,28]. Similar to triangular degenerated-shell elements, there are only very few triangular solid-shell elements [22,[27][28][29] as compared to the large number of quadrilateral solid-shell elements [18][19][20][21][23][24][25][26]. The twelve-node element presented in Reference [22] is probably the only one that takes curved mid-surface geometry into consideration.…”

The use of 2D enriched elements with bubble functions for finite element analysis

“…Accordingly, the inter-element compatibility requirements for displacement are maintained for the element, and the bubble function parameters can be eliminated at the element level by static condensation [13] and can be recovered for subsequent calculations. Bubble functions have been introduced to construct plate element models [14][15][16][17]. For example, Pinsky and Jasti [14] developed fournode and nine-node plate bending elements which incorporated bubble function displacements.…”

The Use of Enriched Hexahedral Elements With Bubble Functions for Finite Element Analysis

“…Accordingly, the inter-element compatibility requirements for displacement are maintained for the element, and the bubble function parameters can be eliminated at the element level by static condensation and can be recovered for subsequent calculations [13]. Bubble functions have been introduced to construct plate element models [14,15,16,17]. For example, Pinsky and Jasti [14] developed four-node and nine-node plate bending elements that .incorporated bubble function displacements.…”